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Plenary Talks 14New Trends in Complex Networks: Temporal Networks, Vito Latora 16From Individuals to Collectivity: Multiscale Methods for Living
Complex Systems, Andrea Tosin . . . . . . . . . . . . . . . . . 17Variational models for dislocations, Adriana Garroni . . . . . . . . 19Breaking the Boltzmann complexity, Lorenzo Pareschi . . . . . . . 20Computational Concerns in Appearance Reproduction, Fabio Pel-
lacini . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Sampling and collocation methods for PDEs with random data,
Fabio Nobile . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Minisymposia 24Data Assimilation: an ill posed inverse problem. Numerical topics
and Applications, Luisa D’Amore . . . . . . . . . . . . . . . . 25Numerical methods for inverse problems and image processing, Marco
Donatelli and Marco Prato . . . . . . . . . . . . . . . . . . . 26NEW DEVELOPMENTS AND APPLICATIONS OF GROEB-
NER BASES, Rosanna Utano and Monica La Barbiera . . . . 27Complex Systems (SisCo-SIMAI Activity Group), Marina Dolfin
and Andrea Tosin . . . . . . . . . . . . . . . . . . . . . . . . . 28Mathematical Models and Computational Methods in Biomedicine,
Michele Piana . . . . . . . . . . . . . . . . . . . . . . . . . . . 29New perspectives on applicabilities in graph theory, Maurizio Imbesi
and Paola Lea Stagliano . . . . . . . . . . . . . . . . . . . . . 33Numerical methods for coupled problems, Marco Discacciati and
Christian Vergara . . . . . . . . . . . . . . . . . . . . . . . . . 35Computational models for natural hazards and extreme events sim-
ulation, Paola F. Antonietti, Ilario Mazzieri and Alfio Quar-teroni . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
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MINISYMPOSIUM “VARIATIONAL INEQUALITIES, IMMUNESYSTEMS AND LOCAL MINIMIZERS OF FUNCTION-ALS”., Maria Alessandra Ragusa and Annamaria Barbagallo 38
Modeling, simulation and optimization of complex systems usingPartial Differential Equations, Rosanna Manzo, Vincenzo Vespri,Maria Pia D’Arienzo and Cristian Tacelli . . . . . . . . . . . 40
GASVA minisymposium on Mathematical Modelling in Environ-mental and Life Sciences, Ezio Di Costanzo, Maria GraziaNotarangelo, Giuseppe Pontrelli, Alberto Bersani, Paolo Freguglia,Luigi Frunzo, Roberto Natalini and Luigi Preziosi . . . . . . . 42
Numerical methods and models for multiscale kinetic equations,Lorenzo Pareschi and Gabriella Puppo . . . . . . . . . . . . . 44
Proposal of minisymposium: The mathematics of learning fromdata, Lorenzo Rosasco and Silvia Villa . . . . . . . . . . . . . 46
Particle Laden Turbulent Shear Layers, Joern Sesterhenn . . . . . 47Discrete and continuous models for pedestrian movements,Marco
Di Francesco . . . . . . . . . . . . . . . . . . . . . . . . . . . 48“Mathematical Applications funded by the European Union”, Vale-
ria Artale, Cristina Milazzo and Angela Ricciardello . . . . . 51Models and applications of the theory of conservation laws, Stefano
Bianchini and Giuseppe Coclite . . . . . . . . . . . . . . . . . 53Mini-symposium Proposal: Coherent Structures and Nonlinear Waves,
Gaetana Gambino, Maria Carmela Lombardo and VincenzoSciacca . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Mini-symposium proposal: “Signal and image processing techniques,and applications”, Mariantonia Cotronei, Elisa Francomanoand Francesca Pitolli . . . . . . . . . . . . . . . . . . . . . . . 56
From computer aided geometric design to industrial CAD modelingand simulations, Carlotta Giannelli and Carla Manni . . . . . 57
High order schemes for nonlinear evolution Partial DifferentialEquations (Mini-symposium Proposals), Giovanni Naldi . . . 59
Title of minisimposium: Mathematical Problems from micro ansnano-electronics industry, Giovanni Mascali . . . . . . . . . . 60
Recent advances on the theory and applications of Semi-Lagrangianmethods, Maurizio Falcone and Roberto Ferretti . . . . . . . . 62
Contributed Talk 64Development of a family of cost-optimized prefactored high-order
compact schemes for low-speed aeroacoustics, Ivan Spisso, AldoRona and Sergio Pirozzoli . . . . . . . . . . . . . . . . . . . . 65
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A Supermodular Generalized Nash Equilibrium Problem for powerallocation in Cognitive Radio systems, Laura Prati . . . . . . 66
The interaction of a uniform vortex with a pointwise one, GiorgioRiccardi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Tensor Train Approximation of the First Moment Equation for theLognormal Darcy Problem, Francesca Bonizzoni and FabioNobile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Vortex merging in relativistic flows, Pierluigi Vellucci and GiorgioRiccardi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Active stress as a local regulator of global size in morphogenesis,Viola Pettinati, Davide Ambrosi and Pasquale Ciarletta . . . 70
Numerical Simulations of Self-Induced Thermodiffusion in PorousMedia, Melania Carfagna and Alfio Grillo . . . . . . . . . . . 71
Considerations On Thermodiffusion In Higher Order Binary Flu-ids, Alfio Grillo and Melania Carfagna . . . . . . . . . . . . . 72
Uncertainty quantification analysis in engineering design, ManoloVenturin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Compressed solving: a model reduction technique for PDEs basedon compressed sensing, Simone Brugiapaglia, Stefano Michelettiand Simona Perotto . . . . . . . . . . . . . . . . . . . . . . . 74
Long-term structure-preserving numerical methods for Hamiltonianproblems in Physics and Medicine, Raffaele D’Ambrosio . . . 75
Irregularization accelerates iterative regularization, Paola Brianzi,Fabio Di Benedetto, Andrea Di Stefano, Claudio Estatico andLuca Surace . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Data assimilation: an ill posed problem 78A Scalable Algorithm for Three Dimensional Variational Data As-
similation, Luisa D’Amore, Almerico Murli, Rossella Arcucciand Luisa Carracciuolo . . . . . . . . . . . . . . . . . . . . . . 79
Variational Data assimilation in Computational Hemodynamics:Applications to Parameter Estimation, Luca Bertagna, Huan-huan Yang and Alessandro Veneziani . . . . . . . . . . . . . . 81
Data Assimilation of Anthropogenic Land Subsidence for the Com-pressibility Calibration in Productive Hydrocarbon Reservoirs,Claudia Zoccarato, Domenico Bau, Massimiliano Ferronato,Giuseppe Gambolati, Carlo Janna and Pietro . . . . . . . . . 82
Conditioning of Incremental Variational Data Assimilation, AmosLawless, Nancy Nichols, Stephen Haben and Adam El-Said . 83
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Variational Ocean Data Assimilation for the Mediterranean Fore-casting System, Nadia Pinardi, Marina Tonani, Jenny Pistoia,Michelangelo Mariani, Alessandro Grandi, Srdjan Dobricic,Christopher K. Wikle, Ralph F. Milliff and Mark L. Berliner 85
Numerical methods for inverse problems and image processing 87Adaptive choice of the regularization parameter and matrix for the
Arnoldi-Tikhonov methods, Silvia Gazzola, Paolo Novati andMaria Rosaria Russo . . . . . . . . . . . . . . . . . . . . . . . 88
A method for constrained L1/TV image denoising, Germana Landi 90Inexact Bregman Regularization for astronomical images corrupted
by Poisson noise, Alessandro Benfenati and Valeria Ruggiero 91Levenberg-Marquardt and Adaptive Quadratic Regularized methods
for ill-posed nonlinear systems, Stefania Bellavia and BenedettaMorini . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
Unsupervised tissue segmentation and classification of three-dimensional3T prostate MRSI data by hierarchical non-negative matrixfactorization for automatic tumour detection and visualisa-tion, Teresa Laudadio, Anca Croitor Sava, Diana Sima, AlanWright, Arend Heerschap, Nicola Mastronardi and SabineVan Huffel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Conjugate Gradient method for p-norm minimization, Flavia Lenti,Claudio Estatico, Serge Gratton and David Titley-Peloquin . 97
On the application of spectral projected gradient methods in im-age segmentation,Laura Antonelli, Valentina De Simone andDaniela di Serafino . . . . . . . . . . . . . . . . . . . . . . . . 99
Optimization methods for large-scale deconvolution on HPC archi-tectures with applications in Microscopy, Gaetano Zanghirati,Riccardo Zanella, Federica Porta and Luca Zanni . . . . . . . 101
New developments and applications of Groebner bases 103Applications of Groebner bases to simple graphs, Monica La Bar-
biera and Maurizio Imbesi . . . . . . . . . . . . . . . . . . . . 104Graphs of paths and associated monomial algebras, Gaetana Restuc-
cia and Rosanna Utano . . . . . . . . . . . . . . . . . . . . . 106Which Principal Borel ideals are Gotzmann?, Vittoria Bonanzinga
and Shalom Eliahou . . . . . . . . . . . . . . . . . . . . . . . 107Algebraic and geometric models for business, Gioia Failla . . . . . 108On the Birkhoff model for ranking problems, Gaetana Restuccia . . 109Simplicial complexes, convex polytopes and art, Vincenzo Iorfida . 110
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Complex Systems (SisCo-SIMAI Activity Group) 111MODELING ALTRUISM AND SELFISHNESS IN WELFARE DY-
NAMICS, Marina Dolfin and Miroslaw Lachowicz . . . . . . . 112A kinetic approach to traffic flow on road networks, Luisa Fermo
and Andrea Tosin . . . . . . . . . . . . . . . . . . . . . . . . . 113Nonlocal interaction equations with two species, Simone Fagioli . . 114A Kinetic Model of Crowd Evacuation from Bounded Domains,
Juan Pablo Agnelli, Francesca Colasuonno and Damian Knopoff115An Easy-to-Use Approach for Simulating Traffic Flow on Net-
works, Gabriella Bretti, Maya Briani and Emiliano Cristiani . 116Some remarks on the risk driving index definition: mathematical
models, Paolo Freguglia . . . . . . . . . . . . . . . . . . . . . 118Kinetic description of optimal control problems and applications
to consensus modeling, Giacomo Albi, Michael Herty andLorenzo Pareschi . . . . . . . . . . . . . . . . . . . . . . . . . 119
On the Modeling Learning Dynamics of Large Living Systems, Sil-vana De Lillo . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
On a Model of Darwinian Dynamics and Competition between Tu-mor and Immune Cells, Elena De Angelis . . . . . . . . . . . 121
Transient states and congestion in simple dynamical models onroad networks, Armando Bazzani and Paolo Freguglia . . . . 122
A 2-population kinetic model for vehicular traffic, Matteo Semplice,Gabriella Puppo and Giuseppe Visconti . . . . . . . . . . . . 124
Mathematical Models and Computational Methods in Biomedicine125Compartmental Models for Nuclear Medicine Data: an Inverse
Problems Perspective, Michele Piana, Sara Garbarino, Fab-rice Delbary, Valentina Vivaldi and Giacomo Caviglia . . . . 126
A Small Angle X-ray Scattering Technique for Determining NanoscaleParticle Size Distributions, Federico Benvenuto and HoussemHaddar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
The Hough Transform and a Novel Prognostic Index for ChronicLeukemia, Anna Maria Massone, Cristina Campi, AnnalisaPerasso, Mauro Carlo Beltrametti and Michele Piana . . . . . 128
Sequential Monte Carlo Samplers for the determination of neuralactivity from neurophysiological data, Alberto Sorrentino, Gi-anvittorio Luria and Riccardo Aramini . . . . . . . . . . . . . 130
New Perspectives on Applicabilities in Graph Theory 131
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Graphs & Neuro-Fuzzy Approaches to Solve Inverse Problems inNon Destructing Testing and Evalutation, Mario Versaci . . . 132
Vertex covering optimization in Veronese bi-type graph ideals, Mau-rizio Imbesi and Monica La Barbiera . . . . . . . . . . . . . . 133
Graphs of paths and applications, Anna Maria Stanganelli . . . . . 135On Ideals Associated to Complete Bipartite Graphs, Maurizio Imbesi,
Monica La Barbiera and Paola Lea Stagliano . . . . . . . . . 136
Numerical methods for coupled problems 138Electromechanical modelling and in silico analysis of a rat cardiac
syncytium, Fabrizio Del Bianco, Piero Colli Franzone, SimoneScacchi and Lorenzo Fassina . . . . . . . . . . . . . . . . . . . 139
Interface Control Domain Decomposition (ICDD) Method for StokesDarcy coupling, Marco Discacciati, Paola Gervasio and AlfioQuarteroni . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
Finite elements for Immersed Boundary Method, Daniele Boffi,Nicola Cavallini and Lucia Gastaldi . . . . . . . . . . . . . . . 143
A hybrid level set/front tracking approach for fluid-structure in-teraction with large structural displacements, Steffen Basting,Annalisa Quaini, Suncica Canic and Roland Glowinski . . . . 144
An implicit high-order Discontinuous Galerkin solver for hybridRANS-LES simulations, Alessandro Colombo, Francesco Bassi,Lorenzo Botti, Nicoletta Franchina, Francesco Carlo Massa,Antonio Ghidoni and Stefano Rebay . . . . . . . . . . . . . . 146
Patient-specific model of the electrical activity in the heart: gener-ation of Purkinje networks driven by clinical measurements,Simone Palamara, Domenico Catanzariti, Maurizio Centonze,Elena Faggiano, Fabio Nobile, Alfio Quarteroni and ChristianVergara . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
Analysis and optimization of the generalized Schwarz method for el-liptic problems with application to fluid-structure interaction,Giacomo Gigante and Christian Vergara . . . . . . . . . . . . 150
Multiscale model of rift dynamics, Edie Miglio and Mattia Penati . 151Coupling Micro-Scale Dynamics to Collective Behaviors: The Case
of Living, hence Complex, Systems, Nicola Bellomo . . . . . . 152Optimized partitioned procedures for the Stokes-Darcy coupled prob-
lem, Luca Gerardo-Giorda and Marco Discacciati . . . . . . . 153
SIMAI 2014 7
Fluid-Structure-Interaction in Hemodynamics using Nonlinear, AnisotropicHyperelastic Wall Models, Daniel Balzani, Simone Deparis,Simon Fausten, Davide Forti, Alexander Heinlein, Axel Kla-wonn, Oliver Rheinbach, Alfio Quarteroni and Jorg Schroder 154
A novel implementation of the H-based formulation of the eddy cur-rent model, Ana Alonso, Enrico Bertolazzi, Riccardo Ghiloniand Alberto Valli . . . . . . . . . . . . . . . . . . . . . . . . . 156
Computational models for natural hazards and extreme eventssimulation 158A finite-difference ghost-point method for elliptic equations with
application to Cauchy-Navier equations, Giovanni Russo andArmando Coco . . . . . . . . . . . . . . . . . . . . . . . . . . 159
An accurate and efficient DG framework for adaptive numericalweather prediction, Giovanni Tumolo and Luca Bonaventura . 161
Numerical-based deterministic methods for earthquake risk analysisin large urban areas, Ilario Mazzieri, Paola F. Antonietti andAlfio Quarteroni . . . . . . . . . . . . . . . . . . . . . . . . . 163
Assessing volcanic hazard by using multiphase flow simulations,Augusto Neri, Tomaso Esposti Ongaro and Mattia De’MichieliVitturi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
Lessons learnt from recent earthquakes and the importance of 3Dphysical modeling in insurance and (re)insurance market, MarcoStupazzini . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
Variational inequalities, immune systems and local minimizersof functionals 166Multiscale modelling of living systems: a mathematical and com-
putational perspective, Francesco Pappalardo, Filippo Cas-tiglione, Carlo Bianca, Giulia Russo, Marzio Pennisi and SantoMotta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
Duality theory for dynamic vaccination games, Annamaria Barba-gallo, Antonino Maugeri and Maria Alessandra Ragusa . . . . 169
Approximate symmetries of Differential equations, Marianna Rug-gieri and Maria Paola Speciale . . . . . . . . . . . . . . . . . 170
General Financial Equilibrium Problem with Memory Term andAdaptive Constraints, Annamaria Barbagallo, Patrizia Daniele,Mariagrazia Lorino, Antonino Maugeri and Cristina Mirabella 171
A bilevel model of the continuous-time optimal pollution emissionprice problem, Laura Scrimali . . . . . . . . . . . . . . . . . . 173
SIMAI 2014 8
Inverse variational inequalities and applications to an economicequilibrium problem, Annamaria Barbagallo and Paolo Mauro 174
Modeling, simulation and optimization of complex systems us-ing Partial Differential Equations 175Flow Optimization in Vascular Networks, Radu C. Cascaval, Ciro
D’Apice, Maria Pia D’Arienzo and Rosanna Manzo . . . . . . 176Optimization of the input flow of a supply chain, Ciro D’Apice,
Carmine De Nicola and Rosanna Manzo . . . . . . . . . . . . 178A problem of train scheduling on the rail line Verona-Monaco of
Bavaria, Martina Mazzanti, Viola Pungetti and Vincenzo Vespri180Kernel estimates for Schrdinger type operators with unbounded dif-
fusion and potential terms, Anna Canale, Abdelaziz Rhandiand Cristian Tacelli . . . . . . . . . . . . . . . . . . . . . . . 182
GASVA on Mathematical Modelling in Environmental and LifeSciences 184Quasi Steady-State Approximations (QSSAs) in the CME-based
stochastic framework, Alberto Maria Bersani, Alessandro Borri,Francesco Carravetta, Gabriella Mavelli and Pasquale Palumbo185
A semi-analytical study in transdermal drug delivery systems, GiuseppePontrelli . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
A hybrid mathematical model for self-organizing cells in the ze-brafish lateral line primordium, Ezio Di Costanzo, RobertoNatalini and Luigi Preziosi . . . . . . . . . . . . . . . . . . . 187
Ago-Antagonist Theory in Darwinian Evolution, Paolo Fregugliaand Armando Bazzani . . . . . . . . . . . . . . . . . . . . . . 189
Wind-Blown Sand: An Erosion-Transport-Sedimentation-SlidingModel, Luca Bruno, Davide Fransos and Luigi Preziosi . . . . 190
Numerical modelling of initial formation in multispecies biofilms,Berardino D’Acunto, Luigi Frunzo and Maria Rosaria Mattei 191
A Multidomain Mathematical Model about the Intracellular Trans-port of Naked DNA Plasmids, Maria Grazia Notarangelo andRoberto Natalini . . . . . . . . . . . . . . . . . . . . . . . . . 192
Time Scale Separation, Normal Modes and Quasi-Steady State Ap-proximations in Enzyme Kinetics, Pierluigi Vellucci and Al-berto Maria Bersani . . . . . . . . . . . . . . . . . . . . . . . 193
Numerical Methods and Models for Multiscale Kinetic Equa-tions 194
SIMAI 2014 9
High Order Semi-Lagrangian Schemes for the BGK Model, GiuseppeStracquadanio, Maria Groppi and Giovanni Russo . . . . . . 195
Kinetic relaxation models for reacting gas mixtures, Maria Groppiand Giampiero Spiga . . . . . . . . . . . . . . . . . . . . . . . 197
Derivation of BGK models for gas mixtures, Stephane Brull . . . . 198Oxygen transport properties estimation by DSMC-CT simulations,
Gianpietro Ghiroldi, Domenico Bruno and Aldo Frezzotti . . 199A kinetic BGK model for a multi-component mixture, Marlies Pirner,
Christian Klingenberg and Gabriella Puppo . . . . . . . . . . 201Binary interaction algorithms for the simulation of self-organized
systems, Giacomo Albi and Lorenzo Pareschi . . . . . . . . . 202
The mathematics of learning from data 203Learning a set by kernel methods, Francesca Odone, Lorenzo Rosasco,
Alessandro Rudi, Alessandro Toigo and Ernesto De Vito . . . 204A Unifying Framework for Multi-task Learning, Carlo Ciliberto,
Youssef Mroueh, Tomaso Poggio and Lorenzo Rosasco . . . . 205A stochastic iteration process with applications to splitting and
learning, Patrick Louis Combettes and Jean-Christophe Pesquet206Dictionary Identification, Karin Schnass . . . . . . . . . . . . . . . 207Spectral k-Support Norm Regularization, Massimiliano Pontil . . . 208Stochastic proximal methods, Lorenzo Rosasco, Silvia Villa and
Bang Cong Vu . . . . . . . . . . . . . . . . . . . . . . . . . . 209
Mathematical Applications funded by the European Union 210Kore Hexacopter, Artale Valeria, Cristina Milazzo, Angela Riccia-
rdello and Andrea Alaimo . . . . . . . . . . . . . . . . . . . . 211A Mathematical Dynamic Numerical Model for Energy Recovery in
Water Distribution Network, Using Pump as Turbine, GabrieleFreni and Mauro De Marchis . . . . . . . . . . . . . . . . . . 212
upGraded REnewable ENergy system project, Andrea Alaimo, An-tonio Esposito and Giovanni Pipitone . . . . . . . . . . . . . 214
IPSE Project: Real Time Multi-View Video Tracking of People inIndustrial Environments, Giorgio M. Grasso and Alessio Plebe 215
Coherent Structures and Nonlinear Waves 216Systems with moving boundaries, Giuseppe Coclite . . . . . . . . . 217Coherent structures and large-scale instabilities in fingering con-
vection, Francesco Paparella . . . . . . . . . . . . . . . . . . . 218
SIMAI 2014 10
Oscillating Turing patterns and spiral wave behavior in a mathe-matical model for alloy electrodeposition, Benedetto Bozzini,Deborah Lacitignola and Ivonne Sgura . . . . . . . . . . . . . 219
Second-grade nematic fluids and nematoacoustics, Giovanni De Mat-teis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
Heat Transfer problems in Extended Thermodynamics, Elvira Bar-bera and Francesca Brini . . . . . . . . . . . . . . . . . . . . 223
Signal and image processing techniques, and applications 225Linear and nonlinear models for electrical conduction in biological
tissues, Micol Amar, Daniele Andreucci and Roberto Gianni . 226Image Contrast Enhancement by means of Fuzzy Techniques, Mario
Versaci . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228Topology preservation of radial basis functions for image registra-
tion, Roberto Cavoretto, Alessandra De Rossi, Hanli Qiaoand Bernhard Quatember . . . . . . . . . . . . . . . . . . . . 230
A Semi-Analytic Bayesian Approach for Multiple Static DipolesEstimation from a Time Series of MEG Data, Sara Som-mariva and Alberto Sorrentino . . . . . . . . . . . . . . . . . 232
Beyond the BEM Solution of the M/EEG Forward Problem: aMeshfree Approach, Guido Ala, Gregory Fasshauer, Elisa Fran-comano, Salvatore Ganci and Michael McCourt . . . . . . . . 233
Backlund Charts: commutative versus non-commutative EquationHierarchie, Sandra Carillo, Mauro Lo Schiavo and CorneliaSchiebold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
An anisotropic multiple multiresolution analysis for image dataprocessing, Mariantonia Cotronei, Milvia Rossini and TomasSauer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
A BeamFormer for source localization in ElectroCOrticoGraphy,Annalisa Pascarella . . . . . . . . . . . . . . . . . . . . . . . . 238
On the problem of recovering non regular surfaces from griddeddata, Milvia Rossini . . . . . . . . . . . . . . . . . . . . . . . 239
Magnetic Tomography by Random Spatial Sampling, Francesca Pitolli240Design of a portable (CW) fNIRS embedded system, Diego Agro,
Gabriele Adamo, Maurizio Pinto, Riccardo Canicattı, Alessan-dro Tomasino, Antonino Parisi, Salvatore Stivala, AntonioGiordano, Costantino Giaconia and Alessandro Busacca . . . 241
Wavelet packet as diagnostic tool: an EEG study, Alessandro Cala-muneri, Simona De Salvo, Angelo Quartarone, Placido Bra-manti and Lilla Bonanno . . . . . . . . . . . . . . . . . . . . . 243
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Baecklund Charts: commutative versus non-commutative EquationHierarchies, Sandra Carillo, Mauro Lo Schiavo and CorneliaSchiebold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
Applications of sampling Kantorovich operators to Image Process-ing, Danilo Costarelli and Gianluca Vinti . . . . . . . . . . . 246
Recent advances on the theory and applications of Semi-Lagrangianmethods 247A Semi-Lagrangian scheme for a degenerate second order Mean
Field Game system, Elisabetta Carlini and Francisco Silva . . 248Semi-Lagrangian methods for parabolic problems in divergence form,
Luca Bonaventura and Roberto Ferretti . . . . . . . . . . . . 249Semi-Lagrangian approximation schemes for non-Lambertian Shape-
from-Shading models, Silvia Tozza . . . . . . . . . . . . . . . 250Fast Semi-Lagrangian Schemes for Hamilton-Jacobi-Bellman Equa-
tions, Simone Cacace, Emiliano Cristiani and Maurizio Falcone252Experiments on adaptive semi-Lagrangian advection in a DG frame-
work, Giovanni Tumolo and Luca Bonaventura . . . . . . . . 254
High order schemes for nonlinear evolutionary Partial Differ-ential Equations 256High order semi-implicit schemes for evolutionary non linear par-
tial differential equations and applications, Sebastiano Boscarino257Time integration schemes for semidiscrete approximation of mul-
tiscale hyperbolic systems, Giovanni Naldi and Fausto Cavalli 258Implicit-Explicit Runge-Kutta schemes for optimal control prob-
lems and applications to hyperbolic system with relaxation,Giacomo Albi . . . . . . . . . . . . . . . . . . . . . . . . . . . 260
High order exponential schemes for nonlinear Fokker-Planck equa-tions, Lorenzo Pareschi . . . . . . . . . . . . . . . . . . . . . . 261
Mathematical Problems from micro and nano-electronics in-dustry 262Analytical and numerical characterization of the spin-wave proper-
ties emitted in a spintronic nano-waveguide, Giancarlo Consolo263
Particle Laden Turbulent Shear Layers 265On the importance of modeling the fluid acceleration term in a
particle laden, compressible turbulent boundary layer, ArneHeinrich, Flavia Cavalcanti Miranda and Jorn Sesterhenn . . 266
SIMAI 2014 12
Exact regularized point particle method for particle-laden flows inthe two-way coupling regime: application to turbulent freeshear flows, Paolo Gualtieri, Francesco Battista, FrancescoPicano and Carlo Massimo Casciola . . . . . . . . . . . . . . 268
Particle statistics in turbulent channel flows with wall-roughness.,Barbara Milici, Mauro De Marchis, Gaetano Sardina and En-rico Napoli . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
High-performance computing for Volcanic ash plumes: turbulence,heat transfer and particle dynamics., Matteo Cerminara, TomasoEsposti Ongaro and Luigi Berselli . . . . . . . . . . . . . . . . 275
Bubble dynamics and related acoustics, Enrico De Bernardis andGiorgio Riccardi . . . . . . . . . . . . . . . . . . . . . . . . . 277
Discrete and continuous models for pedestrian movements 278Crowd Dynamics and Conservation Laws with Non–local Point
Constraints and Capacity Drop. Theory and Numerical Simu-lations., Boris Andreianov, Carlotta Donadello, Ulrich Razafi-son and Massimiliano Rosini . . . . . . . . . . . . . . . . . . . 279
Macroscopic modelling and simulations of crowd dynamics, MonikaTwarogowska . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
On the Hughes model for pedestrian flows: including local effects,Jose Carrillo, Stephan Martin and Marie-Therese Wolfram . . 283
On the CR model and its applications at the bottlenecks, Massim-iliano D. Rosini . . . . . . . . . . . . . . . . . . . . . . . . . . 284
Mean field games with nonlinear mobilities in pedestrian dynamics,Martin Burger, Marco Di Francesco, Peter A. Markowich andMarie-Therese Wolfram . . . . . . . . . . . . . . . . . . . . . 286
Existence of weak solutions for Hughes’ model of pedestrian flows,Debora Amadori, Paola Goatin and Massimiliano Rosini . . . 287
Modeling Crowd Dynamics within the Framework of FPT7 Projects,Nicola Bellomo . . . . . . . . . . . . . . . . . . . . . . . . . . 288
Modeling rationality to control self-organization of crowds, Emil-iano Cristiani, Fabio Simone Priuli and Andrea Tosin . . . . 289
Models and applications of conservation laws 291Initial-boundary value problems for transport equations with rough
coefficients, Gianluca Crippa, Carlotta Donadello and LauraSpinolo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
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Rigorous derivation of the Lighthill-Whitham-Richards model fromthe follow-the-leader model as many particle limit, Marco DiFrancesco and Massimiliano D. Rosini . . . . . . . . . . . . . 294
NAVIER-STOKES EQUATIONS WITH INCOMPATIBLE DATAIN THE ZERO VISCOSITY LIMIT, Maria Carmela Lom-bardo and Marco Sammartino . . . . . . . . . . . . . . . . . . 295
From computer aided geometric design to industrial CAD mod-eling and simulations 296Compatible discretizations based on hierarchical splines, John Evans,
Michael Scott, Derek Thomas and Rafael Vazquez . . . . . . 2973D interaction and sketch-based surface modeling, Serena Morigi . 298Algebraic-Geometric Structures for Rational Camera Motions, Maria
Lucia Sampoli . . . . . . . . . . . . . . . . . . . . . . . . . . . 299Geometric Modeling for Turbine Engine Design, David Grossmann 300
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Plenary Talks
15
Plenary Talks
New Trends in Complex Networks:Temporal Networks
Vito LatoraSchool of Mathematical Sciences
University of LondonMile End Road, London E1 4NS, UK
Interacting agents moving over geographic space, functional relationshipsbetween the cortical areas of a brain during the performance of a task, mes-sages and contacts over online social systems, are all examples of networksin which the links are frequently changing over time. All such systems haveto be described in terms of temporal networks, i.e. time-ordered sequencesof graphs defined over a fixed set of nodes. Concepts, metrics and modelsfor static networks do not straightforwardly apply to temporal networks. Inthis talk we will discuss new metrics and models which allow to capturecrucial information on the time ordering and possible concurrency of linksin temporal complex networks from the real world. We will also investigatehow the additional dimension of time influences collective processes.
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Plenary Talks
From Individuals to Collectivity:Multiscale Methods for Living Complex Systems
Andrea TosinIstituto per le Applicazioni del Calcolo “M. Picone”
Consiglio Nazionale delle RicercheVia dei Taurini 19, 00185 Roma, Italy
Dynamics of living complex systems, such as e.g., human crowds, cell aggre-gates, vehicular traffic, social systems, are mainly ruled by microscopic mu-tual interactions among the individuals, who continuously assess and revisetheir strategies of local movement. This originates self-organized collectivetrends, clearly visible by looking at the macroscopic group as a whole. Agreat challenge for mathematical modeling is to explain the spontaneousemergence of self-organized behaviors at large scale out of individual in-teractions at smaller scales. Various modeling approaches to the problemare currently studied in the literature, for instance: dynamical systems atthe microscopic scale, macroscopic fluid dynamical models, (generalized)Boltzmann/Vlasov-type kinetic models, mean field games, cellular automatamodels. In addition, strategies to link models at different scales in a multi-scale perspective are under intense investigation.
In this talk I will give an account of recent research on multiscale modelsfor self-organizing living systems of the kind mentioned above, trying torelate the proposed mathematical methods to basic complexity features thatsuch methods are supposed to catch. The contents of the talk are mostlytaken from the works cited hereunder.
1. G. Ajmone Marsan, N. Bellomo, A. Tosin. Complex Systems andSociety - Modeling and Simulation, SpringerBriefs in Mathematics,Springer New York, 2013.
2. N. Bellomo, M. A. Herrero, A. Tosin. On the dynamics of socialconflicts: Looking for the Black Swan, Kinet. Relat. Models, 6(3):459-479, 2013.
3. A. Colombi, M. Scianna, A. Tosin. Differentiated cell behavior: a mul-tiscale approach using measure theory. Submitted (arXiv:1108.1212),2014.
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4. E. Cristiani, B. Piccoli, A. Tosin. Multiscale Modeling of PedestrianDynamics, Modeling, Simulation and Applications, Springer, 2014.
5. E. Cristiani, B. Piccoli, A. Tosin. Multiscale modeling of granularflows with application to crowd dynamics, Multiscale Model. Simul.,9(1):155-182, 2011.
6. L. Fermo, A. Tosin. Fundamental diagrams for kinetic equations oftraffic flow, Discrete Contin. Dyn. Syst. Ser. S, 7(3):449-462, 2014.
7. L. Fermo, A. Tosin. A fully-discrete-state kinetic theory approachto modeling vehicular traffic, SIAM J. Appl. Math., 73(4):1533-1556,2013.
SIMAI 2014 18
Plenary Talks
Variational models for dislocations
Adriana GarroniDipartimento di Matematica “G. Castelnuovo”
Universita di Roma “La Sapienza”Piazzale A. Moro 2, 00185 Roma, Italy
In the understanding of plastic behaviour of metals a fundamental role isplayed by dislocations. These are line defects in the crystalline structurethat favor the slip along slip planes, know to be the main mechanism forplastic deformation. These defects interact, move and organize in complexstructures producing other important effects, such as hardening. Disloca-tions have been introduced theoretically at the beginning of the 20th cen-tury, in order to explain such effects, and then observed at the microscopemany years later. In the last decades there have been considerable effortsto rigorously derive models for plasticity which could take into account ef-fectively the presence and the interaction of such defects. The main goal isto describe the collective behaviour of systems of dislocations by means ofa multi-scale analysis that starting from a microscopic, discrete, descriptioncontaining all the relevant details of the crystalline structure, could give riseto a continuum model at the macroscopic scale. In its generality this task isvery far from being completed, but many important steps have been madein special, but relevant, cases.
I will give an overview of some of the variational models for dislocationsat different length scales and I will illustrate some recent results concerningthe multi-scale analysis for dislocations via Gamma-convergence.
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Plenary Talks
Breaking the Boltzmann complexity
Lorenzo PareschiMathematics and Computer Science Department
University of FerraraVia Machiavelli 35, 44121 Ferrara, Italy
The construction of approximate methods of solution for the Boltzmannequation has a long history tracing back to D. Hilbert, S. Chapmann andD. Enskog at the beginning of the last century but only in recent years,the problem has been tackled numerically with particular care to accuracyand computational cost. Even nowadays, however, the deterministic numer-ical solution of the Boltzmann equation represents a challenge for scientificcomputing.
Most of the difficulties are due to the multidimensional nature of theproblem (usually a 7 dimensional problem, 6 space dimensions plus time)and to the structure of the collision integral which leads to the so-calledcurse of dimensionality. In addition the numerical integration requires greatcare since the collision term is at the basis of the macroscopic properties ofthe equation.
Therefore traditional grid-based methods are ineffective and the methodof choice has been the Monte Carlo method. However, Monte Carlo methodsuffers from two difficulties. One is the slow convergence rate. The otheris the numerical noise in the solutions. For this reason, it is still highlydesirable to develop effective grid-based methods that solve directly thepartial differential equations. In this talk we survey some recent progress inthe development of efficient solvers based on spectral methods which permitsto overcome the computational complexity of the Boltzmann equation.
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Bibliography
[1] G. Dimarco and L. Pareschi, Numerical methods for kinetic equations,Acta Numerica, 25, 369–383, (2014).
[2] F. Filbet, L. Pareschi and T. Rey, Steady state preserving spectralmethods for Boltzmann equations, preprint (2014).
21
Plenary Talks
Computational Concerns in AppearanceReproduction
Fabio PellaciniUniversita di Roma
Via Salaria 113, 00198 Roma, Italy
The introduction of 3D printing could change the dynamic of manufacturingforever by allowing everybody to print their own objects. This in turnchanges the manner in which objects’ are designed, going from a specialty fortechnically savvy users to a mass movement. For this reasons, the ComputerGraphics community as a whole is investigating new design paradigms toallow end-user to print novel objects with ease. My work focuses on usingprinters to reproduce the appearance of materials different than the onesused to print with. I will show that this is in fact possible with currenthardware by solving carefully-constructed optimization problems.
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Plenary Talks
Sampling and collocation methods for PDEs withrandom data
Fabio NobileCSQI-MATHICSE, Ecole polytechnique Fdrale de Lausanne
Station 8, CH 1015, Lausanne, Switzerland
In this talk we review sampling based techniques for the approximation ofoutput quantities related to the solution of a partial differential equationwith random input data. Such techniques evaluate the PDE and the corre-sponding output quantity only for specific (random or deterministic) valuesof the input data and therefore can use a PDE solver as a black-box.
We first consider global polynomial approximations of the input/out-put map and present sparse grid interpolation schemes on tensorized Gausspoints that can handle a large number of input data. Some recent theoret-ical and numerical results will be presented for elliptic PDEs with randomcoefficients.
In the case of rough spatially distributed random data, polynomial ap-proximations might become ineffective. We then turn to Monte Carlo ap-proximations based on random sampling and their corresponding multilevelvariants and show how coarse polynomial approximations can still be usedeffectively to accelerate the convergence of Multi-Level Monte Carlo estima-tors.
1. Nobile, F. and Babuska, I. and Tempone, R. 2010 A Stochastic Collo-cation Method for Elliptic Partial Differential Equations with RandomInput Data, Siam Review, 52, 317355.
2. Nobile, F. and Tamellini, L. and Tempone, R. 2014 Convergence ofquasi-optimal sparse grid approximation of Hilbert-valued functions:application to random elliptic PDEs, MATHICSE Report 12.2014.
3. Haji-Ali, A.-L. and Nobile, F. and von Schwerin, E. and Tempone,R. 2014 Optimization of mesh hierarchies in multilevel Monte Carlosamplers, MATHICSE Report 16-2014.
4. Haji-Ali, A.-L. and Nobile, F. and Tempone, R. 2014 Multi indexMonte Carlo: when sparsity meets sampling, MATHICSE Report 26-2014, 2014.
SIMAI 2014 23
Minisymposia
24
Minisymposia
Data Assimilation: an ill posed inverse problem.Numerical topics and Applications
Luisa D’AmoreUniversita degli Studi di Napoli, Federico II
Via Cintia, Napoli, Italy
Reliability of numerical methods is becoming a crucial issue as scientificcomputing has an increasing role in different fields of engineering and science(CSE: computational science and engineering). Models are far from perfect:due to the uncertainty in the initial conditions and computational limita-tions, models cannot provide accurate simulations. Observations measuredby instruments provide direct information of the solution. Such observationsare heterogeneous, inhomogeneous in space, irregular in time, and subjectto differing accuracies.
Data Assimilation (DA) is the mathematical methodology for combiningdata acquired experimentally (in vivo, i.e. the reality or observational data)to those obtained numerically (in vitro, i.e. the background knowledge) inorder to improve the understanding of complex systems or to improve theestimate of the system state (the forecast). To assimilate from the Latinjust means to make similar.
In the past years DA, used in principle only in atmospheric models, hasbecome a main component in the development and validation of mathemat-ical models (often these models are referred to with the term predictive tounderline that these are dynamical systems). The issue of assimilating datainto models arises in all scientific areas that enjoy a fusion of data.
The DA is an inverse and ill posed problem: retrieve the system statefrom sparse and noisy observations. Historically, the communities of inverseproblems and data assimilation have evolved independently, with particu-lar notation and approaches which are similar in content, but have beenexpressed in different type of notation or terminology. Understanding im-portant state-of-the-art algorithms within a uniform framework is a key steptoday to further develop the computation tools which are known to have thehighest impact on society, breaking down barriers to research and innovation(Horizon 2020). The Workshop on Data Assimilation addresses key conceptsarising from both numerical algorithmic developments (regularization, pre-conditioning, efficiency, scalability,) as well as from important applications(in oceanography, medical imaging, geosciences, ..).
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Minisymposia
Numerical methods for inverse problemsand image processing
Marco DonatelliUniversita degli Studi dell’Insubria
via Valleggio, 11 22100 - Como Italy
Marco PratoUniversita degli Studi di Modena e Reggio Emilia
via Campi, 213/b 41125 - Modena Italy
Many important image processing applications in medicine and astronomy,such as the deblurring of astronomical or medical images acquired throughoptical devices (telescopes, microscopes) and the noninvasive acquisitionof relevant biochemical information from magnetic resonance spectroscopyimaging, are extremely relevant problems in the scientific area with a mean-ingful social effect. The development of efficient methods and algorithmsfor their solution is an actual research topic because the algorithms imple-mented on the commercial systems are often too slow or too sensible tonoise on the data. Moreover, they do not determine numerical solutionspreserving specific image properties such as, for example, the edges of thebone tissue images or the bright of star cluster images.The aim of this symposium is to collect several experiences of real applica-tions in image processing addressed by means of effective numerical linearalgebra and optimization approaches. Since several difficulties in imagingproblems are related to the corruptive effect of the noise affecting the data,the symposium is open to recent general results on inverse problems andregularization approaches.Particular attention will be devoted to the description of the numerical com-plexity which characterizes the particular applications and the applicabilityto large-scale problems, possibly with the support of parallel architectures.Contributions to Krylov or Arnoldi-Tikhonov methods, first and second or-der optimization methods, dual or primal-dual approaches and non-negativefactorizations will be considered.
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Minisymposia
New developments and applications of Groebnerbases
Grobner bases are a universal tool for any kind of problems that can bemodeled by polynomial equations and one of the most powerful methods incommutative algebra and algebraic geometry, but the range of theoreticalissues and applications related to Grobner bases is enormous. It includestheoretical physics, applied science and engineering since many problems inmathematics, applied science and engineering can be represented by poly-nomials (ideals, modules, matrices, . . .). Grobner bases have been used byresearchers in optimization, statistics, coding, signal and image processing,computer vision science and in the field of security, to encrypt messages or totransmit confidential information. The Grobner bases technique has beenimplemented in mathematical software systems like Mathematica, Maple,CoCoA, Macaulay. Classes of ideals in polynomial rings can be investigatedvia Grobner bases in order to introduce algebraic objects useful in someapplications and to provide efficient algorithms. The study of the data ob-tained from the implementation and their processing can be a useful supportfor the development of the research. The goal is to show how algebraic andgeometric models built through Grobner bases theory are useful for settingsuitable solutions of several real problems concerning different areas. Theproposal covers recent developments within this context, in order to trans-late or evaluate theoretic results into concrete examples.
Organizers:
Monica La BarbieraDipartimento di Matematica e Informatica, Universita di Messina
Rosanna UtanoDipartimento di Matematica e Informatica, Universita di Messina
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Minisymposia
Complex Systems (SisCo-SIMAI Activity Group)
Marina DolfinUniversita degli Studi di Messina
Contrada Di Dio (S. Agata), 98166 Messina, Italy
Andrea TosinConsiglio Nazionale delle Ricerche
Via dei Taurini 19, 00185 Roma, Italy
This is the minisymposium of the SIMAI Activity Group on ComplexSystems (SisCo-SIMAI), which gathers scholars interested in the study ofcomplex systems through methods of mathematical modeling. The grouppromotes the development of modeling methods soundly based on mathe-matical structures able to deal with the typical features of complex systems:nonlinear interactions among the constituents, spontaneous emergence ofcollective behaviors and self-organization, multiscale issues, stochasticity,and many others.
In this spirit, the minisymposium proposes a few contributions, mostlyfrom the members of the Activity Group, which cover a quite wide spec-trum of applications in the field of complex systems: vehicular traffic onroad networks and related safety issues, crowd dynamics with control andoptimization of evacuation strategies, cooperation vs. competition and se-lection dynamics in biological and social systems. Attention is paid also tofoundational aspects, particularly the study of suitable theories which canserve as general frameworks for addressing complex systems from a rigorousmathematical point of view.
All of the applications mentioned above have a great social and industrialimpact on modern societies, for instance as far as the design of the so-called“smart cities” is concerned. They are therefore expected to be relevant forthe scope of SIMAI.
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Minisymposia
Mathematical Models and ComputationalMethods in Biomedicine
Michele PianaDipartimento di Matematica
Universita di GenovaVia Dodecaneso 35, 16146, Genova, Italy
This symposium aims at illustrating four problems in which the availabil-ity of an accurate mathematical model and the application of a sophis-ticated computational method allow the comprehension of crucial and tomany extents open physiological and biological issues. Three of such prob-lems have immediate or prospective clinical applications and are concernedwith, respectively: the determination of a novel prognostic parameter forthe assessment of chronic leukemia; the description of cancer metabolismin a comorbidity context, using nuclear medicine data; the identificationof dynamical patterns evoked in the brain by somato-sensory stimulation.The fourth problem involves the determination of the size of proteins (and,in general, nano-structures) by using small angle X-ray scattering. Froma mathematical perspective, the workshop will offer the description of awide set of up-to-date computational methods, ranging from statistical in-version algorithms all through inverse scattering methods, Sequential MonteCarlo samplers, Bayesian filters, pattern recognition approaches and com-putational geometry arguments. Finally, all four talks will present analysisof experimental data (some of them collected in clinical contexts) and dis-cuss the results in frameworks provided by interdisciplinary collaborationsinvolving oncologists, radiologists, neuroscientists, bioengineers and nano-scientists.
Talk 1 (biological structures)
TitleA Small Angle X-ray Scattering Technique for Determining Nano-scale Par-ticle Size Distributions
SpeakerFederico Benvenuto, Centre de Mathematiques Appliquees, Ecole Polytech-
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nique CNRS
AbstractThe determination of a protein’s scale size is a difficult problem that istypically addressed by means of crystallography. Small angle X-ray scatter-ing (SAXS) may offer an alternative approach, which does not require theavailability of a crystalline sample. Further, SAXS allows dynamic measure-ments and provides access to information not limited to the surface of thesample, being able to measure inside the material without sophisticated sam-ple preparation. A SAXS experiment typically produces a one-dimensionalscattering intensity obtained by circular averaging the 2D scattering pat-tern observed in the experiment. In order to determine the size informationfrom this intensity, one needs to solve an ill-posed inverse scattering prob-lem. This talk briefly introduces the SAXS modeling under the assumptionthat all nanoparticles in the system of interest are equally sized and shaped,and presents a statistical method to determine the size of the nanoparticles.SAXS data are obtained by an azimuthal re-groupment of scattered photonsacquired by a charged coupled device and therefore are Poisson distributed.The talk will show the effectiveness of Expectation Maximization, when cou-pled with an appropriate stopping rule, to retrieve positive parameters fromSAXS data.
Talk 2 (neural sources)
TitleSequential Monte Carlo Samplers for the determination of neural activityfrom neurophysiological data
SpeakerAlberto Sorrentino, Dipartimento di Matematica, Universita di Genova
AbstractMagnetoencephalography (MEG) records non-invasively the magnetic fieldsproduced by the brain. In the dipolar approximation, the neural current ismodeled as an unknown number of point sources, termed current dipoles.We consider the problem of estimating the number of dipoles, their locationand strength, from a single spatial distribution of magnetic field. We usea Bayesian approach, with uninformative priors for all parameters but thenumber of sources, which is assigned a Poisson prior with low mean. Weset up a sequential Monte Carlo sampler that samples from a tempering se-
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quence (a one-parameter family) of distributions, which closely reminds theregularization path. From the so-obtained posterior distribution we computepoint estimates of the source parameters. Simulated data show very goodlocalization properties, and experimental data evoked by somato-sensorystimulation confirm that the method can localize sources in real scenarios.
Talk 3 (systems physiology)
TitleCompartmental Models for Nuclear Medicine Data: an Inverse ProblemsPerspective
SpeakerMichele Piana, Dipartimento di Matematica, Universita di Genova
AbstractCompartmental analysis is a computational tool for the modeling of nu-clear medicine data that, in its most recent applications, exploits spatio-temporal information provided by Positron Emission Tomography (PET).This talk introduces two novel compartmental models describing the pro-cessing of 18Fluorodeoxyglucose (FDG) in the renal and hepatic systems.The first model accounts for variations in FDG concentration due to waterre-absorption in renal tubules and for increase of bladder’s volume duringthe excretion process. The second model accounts for the dual blood supplyproper of the liver circulatory system and uses tracer concentration in thegut to describe the flow in the portal vein at the liver entrance. The com-putational reduction of both models is performed by using inverse problemstechniques: in the first case we used a non-stationary steepest descent ap-proach that explicitly accounts for the Poisson nature of nuclear medicinedata; in the second case, we applied a regularized multi-dimensional Newtonalgorithm with an ad hoc rule for the optimal selection of the regulariza-tion parameter. The applications considered illustrate new insights aboutthe role of metformin in cancer metabolism and utilizes data recorded by aPET system for small animal models.
Talk 4 (clinical application)
TitleThe Hough Transform and a Novel Prognostic Index for Chronic Leukemia
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SpeakerAnna Maria Massone, CNR - SPIN, Genova
AbstractIt has been recently proved that a computational analysis of Positron Emis-sion Tomography / Computerized Tomography (PET/CT) images allowsthe assessment of alteration of bone structure and bone marrow metabolismin adult patients with advanced chronic lymphocytic leukemia and that thiskind of analysis may even offer prognostic potentials. The crucial require-ment for the reliability of this study is the application of a pattern recog-nition method able to accurately segment the intrabone space in clinicalCT images of the human skeleton. The talk shows how this task can beaccomplished by a procedure based on the definition of Hough transform forspecial classes of algebraic curves. The idea is the one to introduce a cata-logue of curves that satisfy some specific algebraic geometry conditions, tocompute their Hough transform and apply a standard recognition approachbased on the optimization of an accumulator function. The effectivenessof this method will be proved against low-resolution clinical CT data andlead to the recognition of complex profiles in many different districts of thehuman skeleton.
SIMAI 2014 32
Minisymposia
New perspectives on applicabilities in graphtheory
Maurizio ImbesiUniversity of Messina
Paola Lea StaglianoUniversity of Palermo
Abstract/Short descriptionGraph theory is becoming increasingly significant as it is directed to otherareas of mathematics, science and technology. It is being actively consideredin fields as varied as biochemistry, physics, statistics, engineering, computerscience, and so on. More in detail, graphs can be used to model manytypes of relations and processes in scientific systems: all transport networkscan be sketched by graphs in one way or the other; a telecommunicationsystem (mobile telephone networks or internet) can also be described as anetwork; coding theory is actively developed by planning configurations ofgraphs; servers can be reproduced as nodes within a graph while the physi-cal infrastructure between them, namely fiber optic cables, can act as links;even for assembly lines in the industry one can refer to graphs; not least, incomputer science, graphs are introduced to represent networks of communi-cation, data organization, optimization problems, the flow of computation,research algorithms for the web. Graph theory is also considered for study-ing molecules in chemistry, genomics and statistical physics: in chemistry, agraph makes a natural model for a molecule, where vertices represent atomsand edges bonds, and this approach is especially used in computer processingof molecular structures, ranging from chemical editors to database search-ing; in genomics, significant structures that give a real description of DNAsequencing methods may be illustrated by means of graphs; in statisticalphysics, graphs can represent local connections between interacting partsof a system, as well as the dynamics of a physical process on such system.The powerful combinatorial methods found in graph theory have also beenemployed to prove fundamental results in other fields of pure mathematics.Classes of graphs can be studied using computational and algebraic pro-cedures in order to introduce patterns in several practical problems. More
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precisely, algebraic objects associated to a graph are special classes of mono-mial ideals such as edge ideals, vertex covers ideals, paths ideals. Monomialideals are one of the keys intersections between commutative algebra andcombinatorics. In particular, in the square-free case, their connection withalgebraic graph theory and simplicial complexes is a crucial point for theapplications in different fields of commutative algebra and algebraic geom-etry.
Motivation/Relevance to SIMAIThe present minisymposium explains how commutative algebra, linear al-gebra, graph theory and combinatorics could help applied science and givesolutions for real problems concerning different technological areas. The aimof it is to inform about some recent surprising developments supported bygraphs, to show nice applications in the vast field of action for graph theory,to bring together experts which constitute different branches of research andto stimulate the exchange of ideas.
Confirmed/Proposed speakers
1. Maurizio IMBESI, Univ. MESSINA, [email protected]
2. Paola Lea STAGLIANO, Univ. PALERMO, [email protected]
3. Mario VERSACI, Univ. REGGIO CALABRIA, [email protected]
4. Anna Maria STANGANELLI, Univ.PALERMO, [email protected]
5. Mariafortuna PARATORE, Univ. MESSINA, [email protected]
SIMAI 2014 34
Minisymposia
Numerical methods for coupled problems
Marco DiscacciatiDepartament de Matematica Aplicada III
Universitat Politecnica de CatalunyaCampus Nord, C/Jordi Girona 1-3, C2 208, E-08034 Barcelona, Spain.
Christian VergaraDipartimento di Ingegneria
Universita di BergamoViale Marconi 5, 24044, Dalmine (BG), Italy
Modeling many physical phenomena requires to study problems of multi-physics and/or multi-scale nature. For example, this is the case in highlystructured flows in fluid dynamics, in structural mechanics, in viscous-inviscid fluid interactions, in heterogeneous materials, in electromagnetismor in geophysical and biomedical applications. The complexity of the un-derlying processes often poses a challenge at both the analytical and thenumerical level. In particular, special care has to be paid at the choice ofthe coupling conditions between the different models and to their mathemat-ical treatment in order to ensure the well-posedness of the global system ofequations. Moreover, effective and reliable algorithms involving robust pre-conditioning techniques must be considered. These numerical schemes canbe based on either segregated or monolithic methods. In this minisympo-sium we would like to bring together experts in coupled problems to discussthe model derivation, their theoretical mathematical properties, as well asthe set-up and analysis of efficient numerical tools.
Motivation/Relevance to SIMAIWe believe that the discussion of the numerical solution of varoius coupledproblems should be of interest for SIMAI since many practical and industrialproblems rely on the coupling among different phenomena.
Confirmed speakers
1. Paola Gervasio, Dipartimento di Ingegneria Civile, Architettura, Ter-ritorio, Ambiente e di Matematica, Universita di Brescia
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2. Ana Alonso, Dipartimento di Matematica, Universita degli Studi diTrento
3. Lucia Gastaldi, Dipartimento di Ingegneria Civile, Architettura, Ter-ritorio, Ambiente e di Matematica, Universita di Brescia
4. Edie Miglio, MOX, Dipartimento di Matematica, Politecnico di Milano
5. Annalisa Quaini, Department of Mathematics, University of Houston
6. Nicola Bellomo, Department of Mathematical Sciences, Politecnico diTorino
7. Simone Palamara, MOX, Dipartimento di Matematica, Politecnico diMilano
8. Alessandro Colombo, Dipartimento di Ingegneria, Universita di Berg-amo
9. Fabrizio Del Bianco, Dipartimento di Ingegneria Industriale e dell’Informazione,Universita di Pavia
10. Luca Gerardo-Giorda, Basque Center for Applied Mathematics
11. O. Rheinbach, Technische Universitat Bergakademie Freiberg, Fakultatfur Mathematik und Informatik
Other proposed speakersNicola Parolini, MOX, Dipartimento di Matematica, Politecnico di Milano
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Minisymposia
Computational models for natural hazards andextreme events simulation
Paola F. AntoniettiMOX, Politecnico di Milano
Ilario MazzieriMOX, Politecnico di Milano
Alfio QuarteroniEPFL Lausanne & MOX, Politecnico di Milano
Natural disasters, such as atmospheric, hydrologic, oceanographic, volcanologicand seismic events, have a catastrophic impact on the modern society interms of human, economic and environmental loss. For enhancing the mit-igation of hazards and decreasing the risk, advanced computational tech-niques are recognized to represent an effective tool for data analysis, earlywarning and planning purposes. In this minisymposium we aim to discussrecent developments on all aspects of natural hazards and extreme eventssimulation, from the forecasting of catastrophic events to the risk manage-ment. Particular attention will be devoted to recent advances on numericalmethods for the simulations of extreme events, challenging in code develop-ment and implementation of the models on modern supercomputers.
Tentative List of Speakers
1. Marino Marrocu, CRS4 (to be confirmed)
2. Ilario Mazzieri, MOX, Politecnico di Milano (confirmed)
3. Giovanni Russo, Universit di Catania (confirmed)
4. Augusto Neri, INGV Pisa (confirmed)
5. Giovanni Tumolo, ICTP, Trieste (confirmed)
6. Marco Stupazzini, MunichRe (to be confirmed)
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Minisymposia
Variational Inequalities, Immune Systems andLocal Minimizers of Functionals
Annamaria BarbagalloDepartment of Mathematics and Applications “R. Caccioppoli”
University of Naples “Federico II”Via Cintia - 80126 Naples, Italy
Maria Alessandra RagusaUniversity of Catania
Viale Andrea Doria, 6 95125 Catania, Italy
Main goals of Minisymposium are Variational Inequalities, Immune Sys-tems and Partial Regularity of Local Minimizers. The first one is consideredin the context of equilibrium problems and network design, the second andthird arguments are treated in a more theoretical sense.
Variational Inequalities proved to be a very useful and powerful tool forinvestigation of solutions of many equilibrium problems in Economics, En-gineering, Operations Research and Mathematical Physics. They provide,as a matter of fact, a unifying framework for the study of diverse problemsas boundary value problems, price equilibrium, traffic network equilibriumproblems, vaccination problem, oligopolistic market equilibrium problemand financial problem. In particular, when considering the above prob-lems in their evolution in time they are modeled by evolutionary variationalinequalities. Several classical and new theories, such as those of ProjectedDynamical Systems and Infinite Dimensional Duality, as well as researchin discretized computational methods, have received a decisive impulse inorder to offer effective solutions to hitherto unsolved problems. For this rea-son, particular emphasis will be given to the development of the VariationalInequalities.
Other argument concerned with analytical investigations on the com-petition between cancer cells and immune system cells. The mathematicalmodels is a Kolmogorov-type systems of three evolution equations where thegrowth rate of the cells is described by logistic law and the response of can-cer cells and immune cells is modeled according to Holling type-II function.The stability analysis of equilibrium points is performed and the persistenceof the model is proved.
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Moreover, the Minisymposium treated everywhere Holder regularity inthe interior for a minimizer of the p(x) energy functional.
Therefore, the Minisymposium aims to offer a review of research themes,methods and open problems together with outlines of the new researchtrends in all the above topics.
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Minisymposia
Modeling, simulation and optimization of complexsystems using Partial Differential Equations
The aim of this mini-symposium is the presentation of recent resultson model, simulation and optimization studies based on Partial Differen-tial Equations with applications to flows on vascular networks, flow of anincompressible, quantum behavior of a particle in a electric filed, supplychains and traffic train. In particular the modeling and the analysis of wavepropagation phenomena along spatial networks (such as vascular networks),inspired from (and with applications to) modeling blood flow in the cardio-vascular network is considered. For a spatial network such as the vascularnetwork, the dynamics is typically described first at the level of individualedges, then at junctions, then at parts of the network and finally, if fea-sible, at the level of the entire system. The aim is to study the effect oftruncation to the flow in the root edge in the case of a self-similar tree ornetwork, the effect of adding or subtracting an edge to a given network.The study of pulse propagation can help the understanding of the pulsewaveforms measured in-vivo and the effects of anastomoses in some arterialnetworks. As regards the model of a particle in a electric filed it is given bythe Schrodinger equation. Of relevant importance is the ground state of theparticle and it can be related to the heat kernel of the differential operator.For this reason can be useful to study the kernel of the semigroup gener-ated by a Schroedinger type operator with unbounded coefficient. Aboutthe supply chain the problem to adjust the inflow to a supply chain in orderto achieve a desired outflow, reducing the costs of inventory or the goodstiming in warehouses is studied. The supply chain is modeled by a conserva-tion law for the density of processed parts coupled to an ODE for the queuebuffer occupancy. The control problem is stated as the minimization of acost functional measuring the queue size and the quadratic difference be-tween the outflow and the expected one. The controls are the discontinuitypoints of the input flow chosen as a piecewise constant function. The sametechniques can be applied in some optimization problems. For instance incollaboration with Trenitalia and Bertolotti, it was considered a model tooptimize the train traffic between Germany and Italy.
Speakers
• Maria Pia D’Arienzo,Dipartimento di Ingegneria dell’Informazione, Ingegneria Elettrica e
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Matematica Applicata,University degli studi di Salerno,e-mail [email protected]
• Rosanna Manzo,Dipartimento di Ingegneria dell’Informazione, Ingegneria Elettrica eMatematica Applicata,University degli studi di Salerno,e-mail: [email protected]
• Cristian Tacelli,Dipartimento di Ingegneria dell’Informazione, Ingegneria Elettrica eMatematica Applicata,University degli studi di Salerno,e-mail: [email protected]
• Vincenzo Vespri,Dipartimento di Matematica e Informatica “Ulisse Dini”,University degli studi di Firenze,e-mail: [email protected]
OrganizerRosanna Manzo,Dipartimento di Ingegneria dell’Informazione, Ingegneria Elettrica e Matem-atica Applicata,University degli studi di Salerno,e-mail: [email protected]
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Minisymposia
GASVA minisymposium on MathematicalModelling in Environmental and Life Sciences
Ezio Di CostanzoUniversita di Roma La Sapienza
Maria Grazia NotarangeloUniversita di Roma La Sapienza
Giuseppe PontrelliIAC - CNR
Alberto BersaniUniversita di Roma La Sapienza
Paolo FregugliaUniversita dell’Aquila
Luigi FrunzoUniversita di Napoli
Roberto NataliniIAC - CNR
Luigi PreziosiPolitecnico di Torino
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The minisymposium aims at presenting the scientific results achieved bythe members of the SIMAI activity group on Environmental and Life Sci-ences. Several mathematical models will be described with application tocancer modelling, chemotherapy, morphogenesis, cell motion, tissue remod-elling and regeneration, protein networks, systems medicine, genetics, stemcell behaviour, biofilms, and environmental remediation strategies. Eightresearchers have already confirmed their participation. Others may join.It might be foreseen that the participant will fill three mini-symposia, onemore specifically oriented to environmental applications and the other two onbio-medical applications, possibly more biologically oriented and one moremedically oriented. For this reason more specific abstracts will be availablewhen the final list of speakers will be known.
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Minisymposia
Numerical methods and models for multiscalekinetic equations
Lorenzo PareschiUniversity of Ferrara
Gabriella PuppoUniversita dell’Insubria
We propose to organize a minisimposium within the Simai meeting on thetopic “Numerical methods and models for multiscale kinetic equations”
Kinetic equations are a tool to model phenomena on a macroscopic scalewhich are influenced by the behavior of the microscopic particles composingthe system. These models are particularly effective on multiscale problemswhen part of the system may have reached equilibrium (and thus the mi-croscopic scale can be underresolved) while in other regions the system canbe far off equilibrium and here the microscopic scale must be resolved evenif one is interested only in the macroscopic effects.
These models arised initially in gas dynamics, and have since been appliedto many other fields in physics, applied sciences, and even biological andsocial sciences. The potential for applications in so many fields makes thesemodels particularly suited for SIMAI, because their success in applied math-ematics and physical modeling is well established, while their exploitationin industrial applications is still in its infancy.
This minisimposium is designed to gather recent contributions to the field.In particular, we will concentrate on the modeling of mixtures of differentpopulations of particles, which can exchange momentum and energy (asin plasmas) or even mass (as in chemical reactions). Moreover, the min-isimposium will address also researchers interested in the numerical treat-ment of these equations, with particular emphasis on Asymptotic Preserv-ing schemes, which are designed to bridge the gap between microscopic andmacroscopic scales, with no need to resolve the fast scales of transient phe-nomena.
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Speakers who have already agreed to deliver a talk at the minisimposium are:
Giacomo Albi (University of Ferrara, PhD student): Flocking, Con-sensus formation, AP schemes and control
Gian Pietro Ghiroldi (Politecnico of Milano) Relaxation of vibrational-rotational modes in polytropic gases
Maria Groppi (University of Parma, Associate Professor) Modeling ofkinetic mixtures, chemical reactions
Christian Klingenberg (University of Wuerzburg) Plasma modelingand numerics for MHD equations
Giuseppe Stracquadanio (University of Parma) Lagrangian AP schemesfor the BGK equation
Potential speakers who will receive an invitation if the minisimposium isaccepted are:
Stephane Brull (University of Bordeaux)
Nicolas Crouseilles (Inria Rennes)
Luc Mieussens (University of Bordeaux)
Vittorio Rispoli (University of Toulouse)
Giovanni Russo (University of Catania)
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Minisymposia
Proposal of minisymposium: The mathematics oflearning from data
Lorenzo RosascoDIBRIS, Universita di Genova
Via Dodecaneso, 35 16146 Genova - Italy
Silvia VillaLaboratory for Computational and Statistical Learning, IIT & MIT
Bldg. 46-5155, 43 Vassar Street, Cambridge, MA
The last few years have seen an unprecedented growth in the scale, struc-ture and complexity of data in science and engineering. Machine learninghas become key to analyze these data, and nowadays enables systems suchas Siri, Kinect or Google self driving car, to name a few examples. At thesame time machine learning methods help deciphering the information inour DNA and make sense of the flood of information gathered on the web.It is widely recognized that a main reason for this success has been the devel-opment of a solid mathematical foundation of machine learning algorithms.Learning theory is nowadays becoming a mature field in the mainstreamof mathematics. The goal of this mini-symposium is to gather experts toprovide an overview of the state of the art and challenges in the field, andhighlight the connections of Learning Theory with other fields such as opti-mization, high dimensional probability and inverse problems among others.
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Minisymposia
Particle Laden Turbulent Shear Layers
Jorn SesterhennTU Berlin
Particle laden turbulent shear layers have recently received a very much in-creased attention due to the possibility to simulate those flows accurately athigh Reynolds numbers. This mini-symposium concentrates on shear layersfor example jets and boundary layers. Contributions from highly resolvednumerical simulation in the compressible and incompressible flow regimeare solicited. Applications for for industrial and geophysical applicationslike volcanic jets or pyroclastic density currents are welcome.
confirmed papers:
- Riccardo Scatamacchia, Federico Toschi and Luca Biferale
- Carlo Massimo Casciola
- Matteo Cerminara, Tomaso Ongaro Esposti
- Arne Heinrich, Flavia Cavalcanti, Jorn Sesterhenn
possible speakers:
- Markus Uhlmann
- Paolo Gualtieri
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Minisymposia
Discrete and continuous models for pedestrianmovements
Marco Di FrancescoDepartment of Mathematical Sciences
University of Bath & University of L’Aquila4W, 1.14, University of Bath, Claverton Down, Bath (UK), BA2 7AY.
The mathematical modelling of the motion of pedestrians is increasinglyattracting the interest of applied mathematicians. This is both due to theinterest in the applications (see next section “Motivation”), and due to thechallenging mathematical structure of the model arising.
Several models for the movement of crowds have been proposed in the litera-ture. One can distinguish between two general approaches: microscopic andmacroscopic models. In the microscopic framework, people are treated asindividual entities (particles). The evolution of the particles in time is deter-mined by physical and social laws which describe the interaction among theparticles as well as their interactions with the physical surrounding. Exam-ples for microscopic methods are social-force models (cf. Helbing 2002 andthe references therein), cellular automata, e.g Fukui 1999 and Muramatsu2000.
In contrast to microscopic models, macroscopic models treat the wholecrowd as an entity without considering the movement of single individuals.Classical approaches use well known concepts from fluid and gas dynam-ics, see Henderson 1971. More recent models are based on optimal trans-portation methods, cf. Santambrogio 2009, mean field games (see Burger-DiFrancesco-Markowich-Wolfram 2013) or non-linear conservation laws, cf.Colombo2005. In Piccoli2009, an approach based on time-evolving mea-sures is presented. In 2012, Burger-Markowich-Pietschmann-Wolfram pro-posed a cellular automata approach leading to a continuum limit resemblinga chemotaxis model. Starting from the paper by DiFrancesco-Markowich-Pietschmann-Wolfram in 2011, a great attention has been given to the socalled Hughes model, a conservation law based model with a non local dis-continuity which makes the existence theory a hard task, see Amadori-DiFrancesco 2012 and Amadori-Goatin-Rosini 2013.
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The proposed mini symposium will review the latest advances in this field,in both the theoretical analytical context and the numerical one. Contribu-tions will focus in particular on nonlinear transport type models, possiblywith constraints, with possible connections to control problems. The inter-play between microscopic ODE based models and macroscopic mean fieldequations will be also addressed. Particular attention will be devoted tothe Hughes model, with the leading experts in the field among the proposedspeakers (Debora Amadori and Massimiliano Rosini). Monika Twarogowskawill report of her numerical work with Paola Goatin et al. on a similar classof models. Marco Di Francesco will present a review on transport models forthe movement of pedestrians. If the participation of Marie Therese Wolframis confirmed, she will present recently developed models based on the meanfield games theory, with several collaborators (M. Burger among others).Carlotta Donadello (if confirmed) will present a recent paper on a transportmodel for pedestrians with constraints. Fabio Priuli will present a resultin collaboration with Tosin and Cristiani on controlling self-organization ofpedestrians by modelling the rationality of the individuals.
We would be delighted to have the participation of Nicola Bellomo, who isa world leading expert on the field. Jon Dawes (Bath) is another possibility(he is currently checking possible clashes with other events, he developedsimulations on a simple ODE based model trying to detect Maurys turningcondition). We are also considering the possibility of inviting Boris An-dreianov as a back-up plan. NOTE: the organizer would cancel his ownname from the list of speakers if the total number of speakers gets strictlylarger than 8.
Motivation/Relevance to SIMAI:The mathematical modelling of large human crowds has gained a lot of sci-entific interest in the last decades. This is due to various reasons. First ofall, a very serious issue in this context is to shed a light on the dynamics incritical circumstances. Moreover, the analytical and numerical study of thequalitative behaviour of human individuals in a crowd with high densitiescan improve traditional socio-biological investigation methods. The dynam-ics of a human crowd has also applications in structural engineering andarchitecture: the London Millennium Footbridge which had to be closed onthe day of its opening due to unexpected anomalous synchronization, is avery evocative example in this sense. Other applications of pedestrian flowmodelling arise in transport systems, spectator occasions, political demon-strations, panic situations such as earthquakes and fire escapes. More light-
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hearted examples are the simulation of pedestrian movement in computergames and animated movies. Another important application is related withthe development of smart building / smart cities, in which the descriptivepower of mathematical models for the motion of pedestrians can be of greathelp in optimal architectural design and urban planning.
Confirmed speakers:
1. Debora Amadori (University of LAquila)
2. Marco Di Francesco (University of Bath & University of LAquila)
3. Fabio Priuli (IAC-CNR Rome)
4. Massimiliano Rosini (University of Warsaw)
5. Monika Twarogowska (IAC-CNR Rome)
Other proposed speakers:Speakers who have been contacted and for whom I am awaiting for a confir-mation:
1. Marie-Therese Wolfram (University of Vienna)
2. Carlotta Donadello (Universite de Franche-Comte, Besanon)
Other possible speakers:
1. Nicola Bellomo (Politecnico di Torino)
2. Jonathan Dawes (University of Bath)
3. Boris Andreianov (Universite de Franche-Comte, Besanon)
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Minisymposia
“Mathematical Applications funded by theEuropean Union”
Valeria ArtaleFaculty of Engineering and Archietecture of the University of Enna Kore
Cristina MilazzoFaculty of Engineering and Archietecture of the University of Enna Kore
Angela RicciardelloFaculty of Engineering and Archietecture of the University of Enna Kore
The European Union provides funding and grants for a broad range ofprojects and programs, managed by different bodies. If the funds are man-aged by one of the member countries, they are known as structural fundsand usually finance regional policy, social and training programs, as well asagriculture (including support for farmers). There exist two kinds of fund-ing: the first one are grants for specific projects, usually following a publicannouncement known as a “call for proposals”, while the second one arepublic contracts, in order to buy services, goods or works and to ensurethe operations of the EU institutions or programs. Contracts are awardedthrough calls for tenders (public procurement) and involve a wide range ofareas: research, training and technical assistance, expert advices, confer-ence organization, Information Technologies equipment purchases, and soon. The EU has approved an Operational Program for Sicily (PO) with theaim of promoting the development of the region through aids to businessand intervention strategy for tourism sector, basic infrastructure and envi-ronmental protection. Common funding comes from the European RegionalDevelopment Fund (FESR), the European Social Fund (FSE) and the Eu-ropean Agricultural Guidance and Guarantee Fund (FEAOG). The mainactions planned for the FESR involve industry, crafts and business services(such as support for business start-ups, improving the facilities in industrialand craft areas, etc.), tourism (i.e. better accommodation, notably rural,touristic infrastructure, preservation of the cultural heritage), infrastructureto support economic activity (relating to water distribution and supply, en-ergy sources, scientific research and development, technological innovation,
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research facilities at universities and urban rail transport), the environment(as improving waste-water treatment capacity, treatment of solid waste fromurban centers and hospitals, measures to prevent coastal erosion and im-provement of protected natural areas), and technical assistance. Within thePO FESR 2007-2013, support action to industrial research and experimen-tal development activities have been activated in connection with supplychains, technological districts and production in potential excellence areasthat test a high degree of integration between universities, research centers,SMEs and large enterprises. Some projects funded by this grant have beendeveloped and conducted by using mathematical modeling and applicationto specific problems. Because of the multidisciplinary of the topic treated, itis crucial a joint work between mathematicians, computer scientists and en-gineers and it is noticeable the need for mathematical and numerical models.Some of these projects will be presented in this Mini-symposium, emphasiz-ing their industrial and technological application.
Motivation/Relevance to SIMAI:This Mini-symposium proposes to point out practical and concrete applica-tions of the mathematics from problems emerging from the SMEs needs andto underline the close relationship and connection between scientific researchdeveloped at the universities and the world of work and industry.
Confirmed speakers:
Dott. Giorgio Grasso (University of Messina);
Ing. Mauro De Marchis (University of Enna Kore);
Ing. Andrea Alaimo (University of Enna);
Ing. Luca Trefiletti (University of Enna Kore)
Other proposed speakers:
Ing. Giovanni Garaffo (Demetra S.r.l).
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Minisymposia
Models and applications of the theory ofconservation laws
Stefano BianchiniSISSA
Giuseppe CocliteUniversita di Bari
The aim of the minisymposium is to give an up to date account of differentaspects of conservation laws and their applications.
Speakers:
• Sara Daneri, Leipzig University
• Marco Di Francesco, Bath University
• Marco Sammartino, Universita di Palermo
• Laura Spinolo, CNR Pavia
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Minisymposia
Coherent Structures and Nonlinear Waves
Gaetana GambinoDepartment of Mathematic, University of Palermo
Maria Carmela LombardoDepartment of Mathematic, University of Palermo
Vincenzo SciaccaDepartment of Mathematic, University of Palermo
The goal of the mini-symposium is to provide a forum which brings togetherresearchers who study various aspects of nonlinear waves and pattern for-mation using analytical and numerical techniques among different fields ofapplication. The mini-symposium program will consist of presentations onsubjects ranging from basic mathematical research (existence and stabilityissues), to concrete applications.
Motivation/Relevance to SIMAI:Theoretical aspects of applied mathematical research on nonlinear wavesand coherent structures are relevant to subjects as fluid and solid mechan-ics, atmosphere and ocean dynamics, chemical reactions and biology, heattransfer and thermodiffusion effects of mixtures, high-energy particle andplasma physics. Remarkable agreement between theory and experimentscan be claimed in many of these fields.
Confirmed speakers:
1. Francesca Brini, Dipartimento di Matematica, Universita di Bologna,[email protected];
2. Giuseppe Maria Coclite, Dipartimento di Matematica, Universita diBari, [email protected];
3. Deborah Lacitignola, Dipartimento di Ingegneria Elettrica e dellInfor-mazione, Universita di cassino e del Lazio Meridionale, [email protected];
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4. Francesco Paparella, Dipartimento di matematica, Universita di Lecce,[email protected].
Other proposed speakers:
1. Andrea Giacobbe, Dipartimento di Matematica, Universita di Padova,[email protected];
2. Giovanni De Matteis, Dipartimento di Matematica, Universita di Mi-lano, [email protected].
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Minisymposia
Signal and image processing techniques, andapplications
Mariantonia CotroneiUniversita Mediterranea di Reggio Calabria
Via Graziella, loc. Feo di Vito, 89122 Reggio Calabria, Italy
Elisa FrancomanoUniversita di Palermo
Viale delle Scienze, 90128 Palermo, Italy
Francesca PitolliUniversita di Roma “La Sapienza”
Via Antonio Scarpa 16, 00161 Roma, Italy
The proposed mini-symposium is related to the activities of the SIMAIActivity Group “SIMAI-SIMA”, whose aim is to promote and coordinate re-search activities on mathematical models and numerical methods for experi-mental data analysis, CAGD, automation, animation, signal processing, im-age processing, scientific visualization, virtual reality. The mini-symposiumis intended to bring together researchers from different fields working onsignal and image processing with the aim of presenting and sharing noveltechniques, research results, and experience. A special emphasis will be puton the applications to real-world problems, principally including biomedicalapplications. In particular, the talks included in the mini-symposium willpresent research advances both in the aspects related to the constructionof suitable methods for data analysis (fuzzy tehniques, image fault detec-tion, radial basis functions, multiple MRA) and in the application of dataprocessing techniques to real problems (EEG, Electrocorticography, MEG,Functional Near Infrared Spectroscopy, magnetic tomography)
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Minisymposia
From computer aided geometric design toindustrial
CAD modeling and simulations
Carlotta GiannelliINdAM c/o University of Florence
Viale Morgagni 67/A, 50134 Firenze Italy
Carla ManniUniversity of Rome “Tor Vergata”
Via della Ricerca Scientifica 1, 00133 - Roma Italy
Short description Computer aided geometric design (CAGD) methodsare devoted to the mathematical foundations of modern modeling and pro-cessing applications connected to scientific visualization and manipulationof geometric entities. CAGD–oriented algorithms deal with the effectiveconstruction, representation and manipulation of curves, surfaces, volumesand (computational) grids. The resulting geometric model has a key rolefor the subsequent elaboration in different industrial applications, includingmanufacturing and engineering simulations.
Even if commercial CAD (Computer Aided Design) systems rely on ro-bust and accurate software libraries, the availability of highlevel technolo-gies open the path to innovative solutions able to face challenging require-ments emerging in industrial applications. Among others, representationsof curves and surfaces possessing suitable algebraic/geometric propertiesor spline models not confined to the tensor–product polynomial structureare key ingredients for powerful and brand–new technologies. Related de-velopments and their suitable interface with industrial geometric modelingstandards seems to be the challenge that the research and CAD communityhas to face.
The minisymposium will focus on emerging scientific results in the field,as well as on relevant applications of established techniques in the industrialenvironment.
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Motivation/relevance to SIMAI CAGD methods have a key role indifferent industrial applications, including manufacturing and engineeringsimulations and represent a relevant up–to–date topic in applied mathemat-ics. They constitute a natural bridge between academic research and thetechnological environment in industry.
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Minisymposia
High order semi-implicit schemes for evolutionarynon linear partial differential equations and
applications
Sebastiano BoscarinoUniversita degli Studi di Catania
viala A. Doria 6 95021 - Catania Italy
Several systems of evolutionary partial differential equations may containstiff terms, which require an implicit treatment. Typical examples are hy-perbolic systems with stiff hyperbolic or parabolic relaxation and kineticequations in regimes close to fluid dynamic limit. In many cases, the stiffterms are clearly identified. For example, in hyperbolic systems with hyper-bolic relaxation, the hyperbolic term is usually non stiff, while the relaxationterm is stiff. A natural way to treat such systems is to adopt implicit-explicitschemes, in which the relaxation is treated by an implicit scheme, while thehyperbolic part is treated explicitly. In several cases, however, such a dis-tinction is not so clear. For example, in the case of hyperbolic systems withdiffusive relaxation, a standard approach would lead to schemes, which inthe stiff limit suffer from classical parabolic CFL restriction. Such systemscan be treated by a penalization method, consisting in adding and subtract-ing the same term, so that the system appears as the limit relaxed systemplus a small perturbation. There are cases, however, in which stiff terms arenot just additive, and the penalization method is not particularly effective,since the limit system itself is not easily solvable by standard techniques.For many such systems, we present a new approach, which includes par-titioned and additive approach. It consists in identifying the linearly stiffdependence of the system on the unknown variable. Only this linear de-pendence will be treated implicitly, while the rest of the system is treatedexplicitly. This approach generalizes classical IMEX schemes based on ad-ditive or partitioned Runge-Kutta methods, and allows the construction ofhigh order linearly implicit schemes, which are much simpler to use thanfully implicit ones. Several examples will be presented.
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Minisymposia
Mathematical Problems from micro ansnano-electronics industry
Giovanni MascaliUniversita della Calabria
Organizers: Giuseppe Alı, Giovanni Mascali, Orazio Muscato, Vittorio Ro-mano
Modern electron devices require an increasingly accurate modeling of en-ergy transport in semiconductors in order to describe high-field phenomenasuch as hot electron propagation, impact ionization and heat generation.The standard drift-diffusion models cannot cope with high-field phenomenasince they do not comprise energy as a dynamical variable.
Also for many applications in optoelectronics it is necessary to describe thetransient interaction of electromagnetic radiation with carriers in complexsemiconductor materials and since the characteristic times are of order of theelectron momentum or energy flux relaxation times, some higher moments ofthe carrier distribution function must be necessarily involved. These are themain reasons why more general models have been sought which incorporateat least energy as a dynamical variable. In recent years new studies havebeen carried out whose main scientific achievements have been:
1. the development of physics based extended hydrodynamical modelsfor submicron devices which do not have any free phenomenologicalparameters;
2. the numerical implementation of the transient extended hydrodynam-ical models based on the exploitation of higher order conservativeschemes for hyperbolic systems of conservation laws;
3. the numerical implementation of the stationary extended hydrody-namical models by utilizing mixed finite elements;
4. the development of a deterministic (not Monte Carlo) solver of thesemiclassical Boltzmann transport equation for submicron devices;
5. the improved efficiency of Monte Carlo simulations.
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The use of new materials, and the transition from microtechnology to nan-otechnology undermine the reliability of the models classically used for thesimulation of semiconductors. This fact requires the development of inno-vative research in advanced mathematics.
The objective of this minisymposium is to present the latest developments,insights, methods and ideas in the above areas of research, and indicationsfor future research directions. An important aspect will be the involvementof researchers working for industries, which can provide a more timely indi-cation of the most relevant up-to-date problems and technique encounteredin real industrial environments.
Tentative list of speakers:
- Giuseppe Alı
- Roberto Beneduci
- Vito Dario Camiola
- Vincenza Di Stefano
- Concetta Drago
- Giovanni Mascali
- Orazio Muscato
- Vittorio Romano
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Minisymposia
Recent advances on the theory and applications ofSemi-Lagrangian methods
Maurizio FalconeDipartimento di Matematica “Guido Castelnuovo”
Universita degli Studi di Roma “La Sapienza”P. Aldo Moro, 2 - 00185 ROMA
Roberto FerrettiDipartimento di Matematica e Fisica
Universita degli Studi Roma TreVia Ostiense, 159, 00154 Roma
Large time-step or Semi-Lagrangian (SL) techniques have received a re-markable attention from the numerical PDE community in the last decade.In addition to the usual fields of application of such techniques, literaturereports successful application of schemes of this class to new models, espe-cially in nolinear/nonsmooth situations modeled by first and second orderHamilton-Jacobi equations. At the same time, a more complete theoreticalanalysis and a deeper understanding of the features of this approximationstrategy have been achieved. The minisymposium tries to give an updateof recent developments, on the side of both theory and applications, of SLschemes. Special focus will be given to second-order equations, flux-formand high-order schemes.
Motivation/Relevance to SIMAI:Current developments of SL schemes enlarge their range of use to new prob-lems and models, of great interest for applications. In particular, perspectivespeakers of this minisymposium work on a variety of topics like atmosphericCFD, dynamic programming, flow in porous media, image processing, ki-netic and multi-agent systems.
Speakers (confirmed):
- Luca Bonaventura (MOX Milano)
- Elisabetta Carlini (“Sapienza” Roma)
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- Silvia Tozza (“Sapienza” Roma)
- Giovanni Tumolo (ICTP Trieste)
Other possible speakers (to be included if possible):
- Giuseppe Straquadanio (Parma)
- Emiliano Cristiani (IAC-CNR)
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Contributed Talk
64
MSP - Contributed Talk
Development of a family of cost-optimizedprefactored high-order compact schemes for
low-speed aeroacoustics
Ivan SpissoCINECA, SuperComputing Application and Innovation Department
Aldo RonaUniversity of Leicester, Department of Engineering
Sergio PirozzoliUniversita degli Studi di Roma “La Sapienza”, Dipartimento di Meccanica e
Aeronautica
A new class of cost-optimized prefactored high-order compact schemes, de-veloped for shock-free error-bounded aeroacoustic applications, is presented.The cost-optimization theory of Pirozzoli (2007), based on the minimizationof the computational cost for a given level of numerical error, is applied toobtain a new class of time-explicit prefactored compact schemes. Suitablehigh-order prefactored boundary closures, which are accurate and stablewithin a selected Fourier space envelope, are coupled with the new interiorschemes. More conventional non-reflecting boundary conditions are shownto display an impedance mismatch, thus reducing the order of accuracy ofthe overall scheme. An eigenvalue analysis is performed, to verify the sta-bility of the prefactored cost-optimized schemes coupled with the boundaryclosures. A parallelization strategy, based on a finite-sized overlapping in-terface, is presented, and weak scalability tests results are shown. Goodagreement is shown between the predicted percentage cost-saving of theone-dimensional cost function and the measured savings in computationaltime for a one-dimensional monochromatic wave propagation test. Sampleapplications to broadband and two-dimensional space benchmark problemsclearly highlight the favourable properties of the baseline scheme for large-scale aeroacoustic applications.
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MSP - Contributed Talk
A Supermodular Generalized Nash EquilibriumProblem for Power Allocation in Cognitive Radio
Systems
Laura PratiUniversita degli Studi di Firenze
via S.Marta, 3 50139 - Firenze Italy
The use of radio resources like Internet services and mobile phones has beengrowing rapidly in recent years, leading to inefficiency of the traditionalassignment of the frequency band to the different communication systems.The use of Cognitive Radio systems allows a more flexible use of resources.In order to model the allocation of resources in a Cognitive Radio context, aGame-theoretical approach is efficient because it handles the radio resourceslike players which take their own decisions in a distributed way.
We discuss a Supermodular Generalized Nash Equilibrium Problem forpower allocation in a Dynamic Spectrum Access context, characterized bythe coexistence of primary and secondary users in the same frequency band.The secondary users are the true players of the game. We give mathematicalconditions to be fulfilled in order to guarantee the existence and uniquenessof the Generalized Nash Equilibrium by making use of the property of su-permodularity. The convergence of a Best Response-type algorithm to theGeneralized Nash Equilibrium is also guaranteed.
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MSP - Contributed Talk
The interaction of a uniform vortex with apointwise one
Giorgio RiccardiDepartment of Industrial and Information Engineering, Second University of
Naplesvia Roma 29, 81031 Aversa (CE), Italy
andCNR-INSEAN, Marine Technology Research Institute
via di Vallerano 139, 00128 Rome, Italy
The motion of a uniform vortex in presence of a pointwise one is inves-tigated. The fluid is assumed isochoric and inviscid and the flow planar.The shape of the uniform vortex is accounted for by means of the Schwarzfunction Φ of its boundary. A novel theoretical approach [1, 2] based onthe evolution equation: (∂t +U∂x)Φ = U is adopted, U and U being theanalytic continuations of the velocity and of its conjugate on the boundary.It leads to the integro-differential problem in the Schwarz function and inthe point vortex position. The analytical solution of the above problem isfaced by means of successive approximations. Results are compared withnumerical simulations of the vortex motion.
1. Riccardi, G., Durante, D. 2008 Velocity induced by a plane uniformvortex having the Schwarz function of its boundary with two simplepoles. J. Applied Mathematics, Hindawi Pub., ID 586567.
2. Riccardi, G. 2013 An analytical study of the self-induced inviscid dy-namics of two-dimensional uniform vortices. Acta Mechanica 224(2),307–326.
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MSP - Contributed Talk
Tensor Train Approximation of the First MomentEquation for the Lognormal Darcy Problem
Francesca BonizzoniFakultat fur Mathematik, Universitat Wien
Oskar-Morgenstern-Platz, 1 1090 - Wien Austria
Fabio NobileCSQI MATHICSE - Ecole Polytechnique Federale de Lausanne
Station, 8 - Lausanne Switzerland
We study the Darcy problem with lognormal permeability, which modelsthe fluid flow in a bounded heterogeneous porous medium. We adopt aperturbation approach, expanding the solution in Taylor series with respectto the Gaussian random field.
The approximation properties of the Taylor polynomial are analyzed([1,2]): we prove the local convergence of the Taylor polynomial to the solu-tion, whereas, in general, the global convergence is not guaranteed. Never-theless, for small values of the standard deviation of the random field, andsmall degree of the Taylor polynomial, the perturbation approach providesa good approximation of both the solution and its statistical moments.
The deterministic recursive problem solved by the expected value of thesolution (first moment equation) is derived, analyzed and discretized with afull tensor product finite element technique. High order correlations betweenthe derivatives of the solution and the random field are involved, which inthe discrete setting are represented by high order tensors.
To overcome the curse of dimensionality, we search for the solution in lowrank format, namely the Tensor Train format. An algorithm able to solvethe recursive first moment problem in Tensor Train format is presented, andits effectiveness is shown on few numerical examples ([1]).
1. Bonizzoni, F. 2013 Analysis and approximation of moment equationsfor PDEs with stochastic data. PhD thesis, Department of Mathemat-ics, Politecnico di Milano, Italy.
2. Bonizzoni, F. and Nobile, F. 2013 Perturbation analysis for the Darcyproblem with log-normal permeability. MATHICSE Technical ReportNr. 29.2013.
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MSP - Contributed Talk
Vortex merging in relativistic flows
Pierluigi VellucciUniversity of Rome La Sapienza
via A. Scarpa 14/16, 00161 Rome, Italy
Giorgio RiccardiDepartment of Industrial and Information Engineering, Second University of
Naplesvia Roma 29, 81031 Aversa (CE), Italy
In the present research the planar motion of an inviscid fluid (density ρ,pressure p and enthalpy h) at relativistic velocities is considered. In lightunits, the conserved variables are D = ρw, S = Dwµu and τ = Dwµ−D−p,w being the Lorentz factor, u = (u1, u2) the velocity and µ = 1+h the totalspecific enthalpy. The flow is described by a nonlinear hyperbolic differentialsystem, so that it is explained in terms of wave propagation and interaction[1]. Among the flows in which the vorticity ω = −∂2u1 + ∂1u2 plays animportant role, the merging between two initially uniform vortices will beinvestigated, by means of numerical integrations of the equations of motion[2,3].
1. Anile, A.M. 1989 Relativistic fluids and magneto-fluids. CambridgeUniversity Press.
2. Riccardi, G., Durante, D. 2008 Primitive variable recovering in Spe-cial Relativistic Hydrodynamics allowing ultra-relativistic flows. Int.Mathematical Forum, 3(42), 2081–2111.
3. Durante, D., Riccardi, G. 2010 An accurate and efficient Riemannsolver with tangent velocities for Godunov schemes in Special Rela-tivistic Hydrodynamics. Int. J. Numerical Methods in Fluids 64(1),1–22.
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MSP - Contributed Talk
Active stress as a local regulator of global size inmorphogenesis
Davide AmbrosiPolitecnico di Milano
piazza Leonardo da Vinci, 32 20133 - Milano Italy
Viola PettinatiPolitecnico di Milano
piazza Leonardo da Vinci, 32 20133 - Milano Italy
Pasquale CiarlettaCNRS and Institut Jean le Rond dAlembert
UMR 7190, Universite Pierre et Marie Curie - Paris 6, 4 place Jussieu, Case 162,75005 - Paris France
While a general consensus exists that the morphogenesis of living organismshas its roots in genetically encoded information, there is a big debate aboutthe physical mechanisms that actually mediate its control. In embryo de-velopment, cells stop proliferating at homeostasis, a target state in terms ofphysical conditions that can represent, for instance, the shape and size ofan organ. However, while control of mitosis is local, the spatial dimensionof a tissue is a global information. How do single cells get aware of thatat the same time? Which is their communication mechanism? While mor-phogen factors are demonstrated to play a key role in morphogenesis, and inparticular for shape emergence, they seem unable to produce a global con-trol on size by themselves and, conversely, many recent experiments suggestthat active mechanics plays an important role. In our work we focus on aparadigmatic larval structure: the imaginal disc that will become wing inthe fruit fly. By a formalization of theoretical conjectures in terms of simplemathematical models, we show that inhomogeneous stress, likely dictatedby morphogenetic patterns, is an admissible mechanism to convey locallythe global information of organ size.
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MSP - Contributed Talk
Numerical Simulations of Self-InducedThermodiffusion in Porous Media
Melania CarfagnaDISMA “G. L. Lagrange” Politecnico di Torino
Corso Duca degli Abruzzi, 29 I-10129 - Torino, Italy
Alfio GrilloDISMA “G. L. Lagrange” Politecnico di Torino
Corso Duca degli Abruzzi, 29 I-10129 - Torino, Italy
We consider a fluid-saturated porous medium exposed to a non-uniform tem-perature field, and describe it as a non-isothermal biphasic mixture compris-ing a solid and a two-constituent fluid. We model such a system by assumingthat the fluid free energy density depends on the gradient of the solute massfraction. This constitutive choice induces a coupling between the temper-ature gradient and the solute diffusive mass flux, which adds itself to thestandard Soret effect.
We present numerical simulations of a thermogravitational cell [1] and ther-mohaline flows [2] to show how the modified constitutive framework, whichis mandatory in diffuse-interface problems (c.f. Cahn-Hilliard model) [3],could be useful to emphasize some phenomenological features of the consid-ered benchmarks, depending on their settings and characteristics.
References:
1. Benano-Melly, L.B., Caltagirone, J.-P., Faissat, B., Montel, F., Coste-seque, P. (2001). Int. J. Heat and Mass Transfer, 44, 1285-1297.
2. Grillo, A., Lampe, M., Wittum, G. (2011). Journal of Porous Media,14(8), 671-690.
3. Lowengrub, J., Truskinovsky, L. (1997). Proc. R. Soc. Lond. A, 454,2617-2654.
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MSP - Contributed Talk
Considerations On Thermodiffusion In HigherOrder Binary Fluids
Alfio GrilloDISMA “G. L. Lagrange” Politecnico di Torino
Corso Duca degli Abruzzi, 29 I-10129 - Torino, Italy
Melania CarfagnaDISMA “G. L. Lagrange” Politecnico di Torino
Corso Duca degli Abruzzi, 29 I-10129 - Torino, Italy
We study a non-isothermal binary fluid system by selecting the mass fractionof one of the two fluids as the order parameter of the system. We assumethat the free energy of the system is of Cahn-Hilliard type, i.e. it features aterm depending on the order parameter, which may be non-convex in thisvariable (when the fluids are partially miscible [2]), and a term dependingon the gradient of the order parameter.We determine a model in which the chosen free energy induces a sponta-neous coupling between mass diffusion and thermal gradient. This couplingstems from the constitutive assumptions, rather than being a consequenceof Onsager’s relations [1], and leads to a non-standard Soret effect, whichadds itself to the standard one of thermodiffusion, if Onsager’s relations areinvoked.We present some implications of the non-standard Soret effect by discussingthe outcomes of numerical simulations.
References:
1. De Groot, S., Mazur, P., Non-equilibrium Thermodynamics, 2nd reprint,North-Holland, Amsterdam, 1969.
2. Lowengrub, J., Truskinovsky, L. (1997). Proc. R. Soc. Lond. A, 454,2617-2654.
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MSP - Contributed Talk
Uncertainty quantification analysis in engineeringdesign
Anna BassiEnginSoft SpA
Via Giambellino, 7 35129 - Padova, Italy
Manolo VenturinEnginSoft SpA
Via Giambellino, 7 35129 - Padova, Italy
Nowadays the use of uncertainty quantification tools is mandatory when de-veloping a new product, since they allow to monitor errors at each level andto control their propagation within the required tolerances.The Monte Carlo simulation approach has a drawback: it requires a hugenumber of simulations, making the convergence slow when the number ofparameters or dimensions increases, and this affects the possibility to intro-duce a new high quality product in the market.Among all stochastic methods, in engineering the non-intrusive ones aremore suitable, since it is not possible to modify kernels of well-known andstrengthened commercial tools.The Polynomial Chaos Expansion method is a good mathematical tool toperform this kind of analysis since it allows to drastically reduce the num-ber of simulations and, consequently, the amount of computational timeand resources. Furthermore, this method is suitable both for forward andbackward analysis, allowing to get many information about variables distri-butions and the related statistics.In this talk we propose the usage of the Polynomial Chaos Expansionsmethod with Scilab as main tool to study the robustness of a simulationof an Organic Rankin Cycle system.
References:
1. S. Poles and A. Lovison, 2009, A Polynomial Chaos Approach to Ro-bust Multiobjective Optimization, Schloss Dagstuh - Leibniz-Zentrumfuer Informatik
2. S. Poles and M. Venturin, Numerical simulation of an Organic RankineCycle, EnginSoft internal report
SIMAI 2014 73
MSP - Contributed Talk
Compressed solving: a model reduction techniquefor PDEs based on compressed sensing
Simone BrugiapagliaMOX - Politecnico di Milano
via Bonardi 9, 20133 - Milano, Italy
Stefano MichelettiMOX - Politecnico di Milano
via Bonardi 9, 20133 - Milano, Italy
Simona PerottoMOX - Politecnico di Milano
via Bonardi 9, 20133 - Milano, Italy
We present a model reduction method for 1D advection-diffusion-reactionproblems, motivated by the recent developments in the sparse representa-tion field, and particularly by compressed sensing: namely, the corsing(compressed solving) approach. The sparsity of the solution with respectto particular trial bases is exploited by a suitable choice of the test func-tions in the weak formulation, resulting in a underdetermined linear system(offline phase). Then, the solution is recovered using robust sparse opti-mization algorithms, like Basis Pursuit and Orthogonal Matching Pursuit(online phase). A Matlab implementation of the method, based on the tool-boxes SPGL1 and OMP-Box, verifies the robustness and the reliability ofthe proposed strategy. A comparison with an SVD-based model reductionapproach is provided. Finally, a preliminary generalization of the corsingapproach to the 2D case is applied to the classical Poisson problem.
SIMAI 2014 74
MSP - Contributed Talk
Long-term structure-preserving numericalmethods for Hamiltonian problems in Physics and
Medicine
Raffaele D’AmbrosioDipartimento di Matematica
University of SalernoVia Giovanni Paolo II, 132 - 84084 - Fisciano (SA), Italy
It is the purpose of this talk to analyze the structure preservation propertiesof multi-value methods for the numerical solution of Hamiltonian problems,originating from Celestial Mechanics, Molecular Dynamics and Immunology.
In particular, we aim to achieve accurate and efficient numerical energypreservation and orbits computation in the dynamics of Solar system plan-ets, by employing real data desumed by Nasa Horizons System, as well asnumerical modeling of T-cell dynamics by discretization of suitable modelsarising from Mechanical Statistics is object of the investigations.
It is known that, in the spirit of numerical conservation of the invariantsof Hamiltonian problems, the classical symplecticity property play a crucialrole. However, only certain Runge-Kutta methods are candidate for sym-plecticity. Even if multivalue methods cannot be symplectic, it is possibleto lead them possess a computationally cheap nearly preserving behaviorthrough the properties of G-symplecticity, symmetry and zero-growth pa-rameters for the parasitic components.
We are particularly interested in the long-time behavior of multi-valuemethods. Hence, we provide long-term error estimates by backward erroranalysis arguments, which permits to get sharp estimates for the parasiticsolution components and for the error in the Hamiltonian. We prove thatthe effects of parasitism on the numerical solution are then negligible ontime intervals of length O(h−2), where h is the stepsize of integration. Thetheoretical expectations are then confirmed by the numerical evidence.
References:
1. R. DAmbrosio, G. De Martino, B. Paternoster, Numerical integrationof Hamiltonian problems by G-symplectic methods, Adv. Comput.Math. 40(2), 553-575 (2014).
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2. R. DAmbrosio, E. Hairer, Long-term stability of multi-value methodsfor ordinary differential equations, J. Sci. Comput. doi: 10.1007/s10915-013-9812-y (2013).
3. R. DAmbrosio, E. Hairer, C. Zbinden, G-symplecticity implies conjugate-symplecticity of the underlying one-step method. BIT vol. 53, 867-872(2013).
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MSP - Contributed Talk
Irregularization accelerates iterative regularization
Paola BrianziUniversita di Genova
via Dodecaneso, 35 16146 - Genova Italy
Fabio Di BenedettoUniversita di Genova
via Dodecaneso, 35 16146 - Genova Italy
Andrea Di StefanoC.m.c. Sud
C.so Ferdinando Magellano, 1a/11 16149 - Genova Italy
Claudio EstaticoUniversita di Genova
via Dodecaneso, 35 16146 - Genova Italy
Luca SuraceUniversita di Genova
via Dodecaneso, 35 16146 - Genova Italy
When iterative methods are employed for the regularization of inverse prob-lems, a main issue is the trade-off between smoothing effects and compu-tation time, related to the convergence rate of iterations. Very often, thefaster is the method the lower is the obtained accuracy.A new acceleration strategy is presented here, inspired by the choice ofpenalty terms formerly used in the context of Tikhonov regularization.More precisely, we define a correction term proposed by Huckle and Sed-lacek in 2012 to enforce regularization capabilities, but with the oppositesign. This choice leads to an “irregularization” phenomenon, which speedsup the underlying basic method and can be controlled through a sequence ofdecreasing coefficients (as the iterations proceed, in order to prevent noiseamplification) tuning the weight of the correction term.Filter factor expansion and convergence are analyzed in the simplified con-text of linear inverse problems in Hilbert spaces, by considering modifiedLandweber iterations as a case study.
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Data assimilation: an illposed problem
78
MSP - Data assimilation: an ill posed problem
A Scalable Algorithm for Three Dimensional
Variational Data Assimilation
Luisa D’AmoreUniversita degli Studi di Napoli, Federico II
Complesso Universitario M.S.Angelo, Via Cintia, 80126 - Napoli Italy
Luisa CarracciuoloIstituto di Chimica e Tecnologia dei Polimeri, CNR
Via Campi Flegrei, 34 - 80078 Napoli Italy
Almerico MurliSPACI c/o
Universita degli Studi di Napoli, Federico II, Napoli, Italy
Rossella ArcucciImperial College of London, EEE Department
South Kensington Campus, London, SW7 2AZ, UK
A research collaboration between us and CMCC (Centro Euro Mediterra-neo per i Cambiamenti Climatici) give us the opportunity to use the DataAssimilation software called OceanVar [2]. OceanVar is based on a threedimensional variational scheme (3D-Var) and it is used in Italy to combineobservational data (Sea level anomaly, sea-surface temperatures, etc.) withbackgrounds produced by computational models of ocean currents for theMediterranean Sea (namely, the NEMO framework), within the Mediter-ranean Forecasting System (MFS)[3]. Here, we present a scalable approachfor variational DA: we introduce a decomposition of the global physical do-main into sub domains. On these sub domains we define local 3D-Var func-tionals and we prove that the minimum of the global 3D-Var functional canbe obtained by collecting the minimum of each local functional. The (global)regularization problem is decomposed into (local) regularization problems,in such a way. We perform a feasibility analysis of the related algorithm,analyzing its execution time and scalability [1]. Finally, our approach allowsto tackle the ill conditioning of DA inverse and ill posed problem withoutreducing the number of available data furthermore, as discussed in [4].
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1. L. D’Amore, R. Arcucci, L. Carracciuolo and A. Murli. 2014 A ScalableApproach for Data Assimilation, J. of Scientific Computing, to appear.
2. L. D’Amore, R. Arcucci, L. Marcellino and A. Murli. 2012 HPC com-putation issues of the incremental 3D variational data assimilationscheme in OceanVar software, J. of Num. An. Ind. and Appl. Math.7, 91–105.
3. S. Dobricic and N. Pinardi. 2008 An oceanographic threedimensionalvariational data assimilation scheme. Ocean Modell., 22, 89–105.
4. S. A. Haben, A. S. Lawless, N. K. Nichols. 2011 Conditioning ofincremental variational data assimilation, with application to the MetOffice system, Tellus, 782–792.
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MSP - Data assimilation: an ill posed problem
Variational Data assimilation in ComputationalHemodynamics: Applications to Parameter
Estimation
Luca BertagnaDepartment of Math & CS, Emory University
United States
Huanhuan YangDepartment of Math & CS, Emory University
United States
Alessandro VenezianiDepartment of Math & CS, Emory University
United States
With the progressive inclusion of numerical simulations in medical researchand clinical practice, accuracy and reliability of patient-specific computa-tional analyses need to be properly certified. This raises new challengeswhen estimating patient-specific parameters that may be too difficult oreven impossible to measure in practice. Data assimilation techniques arerequired to merge available data and numerical models to assess the relia-bility of a quantitative analysis. In this talk, variational procedures will beconsidered to estimate (a) vascular compliance; (b) cardiac conductivitiesfrom available measures of vessel displacement and electric potential respec-tively. We pursue a constrained minimization approach based on the solu-tion of the KKT system. In general, this leads to high computational costs,the constraint being represented by partial differential equations. Specifictechniques for the sake of computational efficiency are mandatory. We willaddress using simplified models (like the Monodomain equations for elec-trocardiology) and surrogate modeling techniques like Proper OrthogonalDecomposition (POD), based on an on-line/off-line paradigm. We will illus-trate successful experiences and pitfalls of this approach on the mentionedapplications.
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MSP - Data assimilation: an ill posed problem
Data Assimilation of Anthropogenic LandSubsidence
for the Compressibility Calibration in
Productive Hydrocarbon Reservoirs
Domenico BauColorado State University
Fort Collins, CO 80523, USA
Massimiliano Ferronato, Giuseppe Gambolati, Carlo Janna, PietroTeatini
Universita di PadovaVia Trieste 63, 35121 Padova, Italy
(ferronato,gambolati,janna,teatini)@dmsa.unipd.it
Claudia ZoccaratoUniversita di Padova
Via Trieste 63, 35121 Padova, Italy
Land subsidence is a major consequence of the pore pressure drawdowncaused by fluid withdrawal from productive hydrocarbon reservoirs. Deeprock compaction induced by field depletion is measurable on the ground sur-face in terms of land displacements. In this study, an Ensemble Smoother(ES) data assimilation technique is developed in order to reduce the uncer-tainty on the constitutive parameters that characterize the geomechanicalmodel. The procedure is tested for a real gas field seated at about 1500m depth. The uniaxial vertical compressibility in virgin conditions and theratio of the compressibility in loading/unloading have been calibrated asthe most influent parameters in controlling the vertical land displacements.The ES in geomechanics appears to be a quite promising approach to re-duce the compressibility uncertainty of the prior distribution by assimilatingvertical displacements data. On the other hand, the ratio of the compress-ibility in loading/unloading conditions is not much influenced by the dataassimilation, implying that the reservoir does not experience an importantunloading.
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MSP - Data assimilation: an ill posed problem
Conditioning of Incremental Variational DataAssimilation
Amos LawlessUniversity of Reading
United Kingdom
Nancy NicholsUniversity of Reading
United Kingdom
Stephen HabenUniversity of Oxford
United Kingdom
Adam El-SaidUniversity of Reading
United Kingdom
Four-dimensional variational data assimilation (4D-Var) is a method forassimilating observations into a numerical model by minimising a weightednon-linear least-squares objective function which measures the error betweenthe model forecast and the available observations. The problem is solved us-ing an iterative optimisation algorithm. In practice an incremental versionof 4D-Var is implemented in many operational forecasting centres, in whicha sequence of linear approximations to the nonlinear least-squares problemis solved. This is equivalent to using an approximate Gauss-Newton methodto solve the nonlinear minimisation problem.
The rate of convergence of the inner loop iteration scheme and the sensitiv-ity of the analysis to perturbations are proportional to the condition numberof the Hessian of the linear least-squares objective function. In this workwe examine the conditioning of the variational assimilation method theoret-ically. We derive bounds on the condition number of the Hessian and usethese examine the sensitivity of the conditioning to the length-scale in the
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correlation structures and to the density and accuracy of the observations.Theoretical results are illustrated using a simplified system and the Met Of-fice operational model. Finally we extend the bounds to the case where themodel constraint is not enforced exactly.
SIMAI 2014 84
MSP - Data assimilation: an ill posed problem
Variational Ocean Data Assimilation for the
Mediterranean Forecasting System
Nadia PinardiDepartment of Physics and Astronomy, University of Bologna
Via Berti Pichat 6/2, Bologna
Marina Tonani, Jenny Pistoia, Michelangelo Mariani, AlessandroGrandi
Istituto Nazionale di Geofisica e VulcanologiaVia Aldo Moro 44, 40127 Bologna, Italy
(marina.tonani,jenny.pistoia,michelangelo.mariani,alessandro.grandi)@bo.ingv.it
Srdjan DobricicJoint Research Centre
Via E. Fermi 2749, 21027 Ispra (VA), Italy.
Christopher K. WikleDepartment of Statistics, University of Missouri
146 Middlebush Hall, Columbia, MO 65211, USA
Ralph F. MilliffCooperative Institute for Research in Environmental Science, University of
ColoradoCampus Box 216 UCB, Boulder, CO 80309-0216, USA
Mark L. BerlinerDepartment of Statistics, The Ohio State University
1958 Neil Ave. Columbus OH 43210, USA
The Mediterranean Forecasting System produces analyses for sea level,temperature, salinity and currents in the entire Mediterranean Sea. Theyare produced with a three dimensional variational assimilation scheme thatconsiders both in situ and satellite data. The main characteristics of the data
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assimilation scheme is the description of the background error covariancematrix with a series of matrix operators that subdivide the vertical andhorizontal part of the error covariances and considers a fixed variability in theerror covariance spatial and temporal scales. Results indicate the robustnessof the data assimilation scheme for sparse in situ data and for dense satellitesampling data. Recently the temporal resolution of the error covariancematrix was changed to accommodate for higher temporal scale processeswhich can vary weekly and the results show improvements even if the spatialresolution is left to be coarse. Applications of the data assimilation scheme toObserving System Experiments for ARGO profiling float sampling strategieswill be shown.
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Numerical methods forinverse problems and image
processing
87
MSP - Numerical methods for inverse problems and image processing
Adaptive choice of the regularization parameterand matrix for the Arnoldi-Tikhonov methods
Silvia GazzolaUniversita degli Studi di Padova
via Trieste, 63 35121 - Padova Italy
Paolo NovatiUniversita degli Studi di Padova
via Trieste, 63 35121 - Padova Italy
Maria Rosaria RussoUniversita degli Studi di Padova
via Trieste, 63 35121 - Padova Italy
Krylov subspace methods have always played a central role in the regu-larization of large-scale linear discrete inverse problems: among them, theArnoldi-Tikhonov method [1] prescribes to project a Tikhonov-regularizedproblem into Krylov subspaces of increasing dimensions generated by theArnoldi algorithm. If compared to a purely iterative method, the Arnoldi-Tikhonov strategy can theoretically deliver more accurate reconstructions,since some known features of the desired solutions can be easily enforced.However, to successfully apply the Arnoldi-Tikhonov method, a proper reg-ularization parameter has to be chosen at each iteration of the Arnoldialgorithm, as well as an appropriate regularization matrix; furthermore, areliable stopping criterion has to be considered.
The goal of our talk is to introduce two new parameter choice rules[3,4], based on some reformulations of the discrepancy principle, in orderto adaptively set the regularization parameter; both these strategies aretailored to work in connection with the Arnoldi-Tikhonov methods, andthe first one can simultaneously act as a stopping criterion, too. We alsoaddress the issue of choosing the regularization matrix, and we introducetwo new strategies [2] that allow to approximate, into the Arnoldi-Tikhonovframework, regularization terms weighted in a generic norm .
We present the results of many meaningful numerical experiments re-garding the application of the above mentioned schemes to image deblurringand denoising problems.
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1. Calvetti, D. and Morigi, S. and Reichel, L. and Sgallari, F. 2000Tikhonov regularization and the L-curve for large discrete ill-posedproblems. J. Comput. Appl. Math. 123, pp. 423–446.
2. Gazzola, S. and Nagy, J. 2014 Generalized Arnoldi-Tikhonov methodfor sparse reconstruction. SIAM J. Sci. Comput. 36(2).DOI: 10.1137/130917673.
3. Gazzola, S. and Novati, P. 2014 Automatic parameter setting for Arnoldi-Tikhonov methods. J. Comput. Appl. Math. 256, pp. 180–195.
4. Gazzola, S. and Novati, P. and Russo, M.R. 2014 Embedded techniquesfor choosing the parameter in Tikhonov regularization. Numer. LinearAlgebra Appl.DOI: 10.1002/nla.1934.
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MSP - Numerical methods for inverse problems and image processing
A method for constrained L1/TV image denoising
Germana LandiUniversita degli Studi di Bologna
Piazza di Porta san Donato, 5 40126 - Bologna Italy
Total Variation (TV) minimization is a very popular image denoisingtechnique. When the noise degrading the image is impulsive, the data fi-delity term is usually expressed in the L1-norm, giving less importance to theso-called outliers. However, the non-differentiability of both the TV and theL1-fitting causes numerical difficulties. In order to reduce these difficulties,we consider the constrained formulation of the L1/TV denoising problemwhere the TV has to be minimized under a constraint expressing L1-datafidelity. The method we propose for the solution of this constrained prob-lem generates a sequence of strictly feasible points. The search direction isobtained by inexactly solving a proximal Newton-type subproblem. A line-search globalization strategy is employed. The global convergence of themethod can be proved. Numerical results show that the proposed approachis competitive with state-of-the-art L1/TV image denoising techniques interms of both restored image quality and computational efficiency.
SIMAI 2014 90
MSP - Numerical methods for inverse problems and image processing
Inexact Bregman Regularization for astronomicalimages corrupted by Poisson noise
Alessandro Benfenati,Valeria RuggieroUniversita degli Studi di Ferrara
Polo Scientifico Tecnologico, Blocco B, Via Giuseppe Saragat 1-Ferrara Italy
[email protected], [email protected]
Alessandro BenfenatiUniversita degli Studi di Ferrara
Polo Scientifico Tecnologico, Blocco B, Via Giuseppe Saragat 1-Ferrara Italy
The Bregman procedure is frequently employed in a contest of image restora-tion problems to obtain contrast enhancement ([1,2]). This procedure is aniterative scheme, where for each iteration it is required the computation ofan exact solution of a minimization problem, i.e. a minimizer of a function.In most applications (in a image reconstruction framework) the computa-tion of this exact solution is very expansive or, in some cases, impossible. Inorder to improve the efficency of the method and contemporaneously to pre-serve the convergence and the features of the Bregamn iterative procedurean inexact version of this scheme is proposed, where the inexactness of theinner subproblems’ solution is kept under control by the introduction of anew stopping criterion. Moreover, this procedure allows to obtain accuratereconstruction when an overestimation of the regularization parameter isknown. This is convenient when the data are corrupted by Poisson noise,since it makes possible to use the most advanced techniques and algorithmsfor minimizing the general Kullbach-Leibler divergence combined with a reg-ularization term. Numerical results are presented in order to evaluate theefficency of the Inexact Bregman iterative scheme, in a contest of imagerestoration, considering deblurring and denoising problems. A practical ap-plication is presented in an astronomical framework ([3]), in deconvolutionproblems of high contrast images consisting of very bright stars and smoothstructures underlying the stars, structures which don’t permit accurate re-constructions with classical deblurring algorithms.
1. C Brune, A Sawatzky, and M Burger. Primal and dual Bregman meth-ods with application to optical nanoscopy. Int. J. Comput. Vis.,92(2):211-229, 2010.
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2. A Benfenati and V Ruggiero. Inexact Bregman iteration with an ap-plication to Poisson data reconstruction, Inverse Problems, 29:065016,2013.
3. A La Camera, S Antoniucci, M Bertero, P Boccacci, D Lorenzetti, andB Nisini. Image reconstruction for observations with an high dynamicrange: LINC-NIRVANA simulations of a stellar jet. In F Delplancke,F J K Rajagopal, and F Malbet, editors, Optical and Infrared Inter-ferometry III, volume 8455 of Proc. SPIE, page 8455 3D, 2012.
SIMAI 2014 92
MSP - Numerical methods for inverse problems and image processing
Levenberg-Marquardt and Adaptive QuadraticRegularized methods for ill-posed nonlinear
systems
Stefania BellaviaUniversita degli Studi di Firenze
viale Morgagni, 40-44 50134 - Firenze Italy
Benedetta MoriniUniversita degli Studi di Firenze
viale Morgagni, 40-44 50134 - Firenze Italy
In this talk we will analyse a class of algorithms for ill-posed nonlinear sys-tems, which includes Levenberg-Marquadt [3] approaches as well as AdaptiveQuadratic Regularized (ARQ) methods. ARQ methods employ a model con-sisting of the Euclidean residual regularized by a quadratic term [1,4]. Localand global convergence properties of ARQ approaches for well-posed non-linear systems have been extensively studied [1,2]. Here, we will show thatsuitable modifications of these methods give rise to regularizing methodsfor ill-posed problems. The noise-free case as well as the realistic situationwhere noisy data are given will be considered. We will further show thatin the noise free case properly chosen regularizing terms also provide globalconvergent procedures. At this regard, we remark that global convergenceof regularizing approaches for ill-posed problems is still an open task.
1. Bellavia, S. and Cartis, C. and Gould, N.I.M and Morini, B. Toint,Ph. L., 2010, em Convergence of a Regularized Euclidean ResidualAlgorithm for Nonlinear Least-Squares. SIAM J. Numer. Anal., 48,1-29.
2. Bellavia, S. and Morini, B., 2014, em Strong local convergence proper-ties of adaptive regularized methods for nonlinear least-squares. IMAJ. Numer. Anal., to appear.
3. Hanke, M., 1997 A regularizing Levenberg-Marquardt scheme, withapplications to inverse groundwater ltration problems. Inverse Prob-lems, 13, 79-95.
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4. Nesterov, Yu., 2007, Modied Gauss-Newton scheme with worst-caseguarantees for global performance, Opt. Meth. and Soft., 22, 469-483.
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MSP - Numerical methods for inverse problems and image processing
Unsupervised tissue segmentation andclassification of three-dimensional 3T prostate
MRSI data by hierarchical non-negative matrixfactorization for automatic tumour detection and
visualisation
Teresa LaudadioIstituto per le Applicazioni del Calcolo “M. Picone” (IAC)
Consiglio Nazionale delle Ricerchevia Amendola 122/D, 70126 Bari, Italy
Anca R. Croitor Sava, Diana M. Sima, Sabine Van HuffelDepartment of Electrical Engineering (ESAT)
STADIUS Center for Dynamical Systems, Signal Processing and Data AnalyticsKU Leuven, Leuven, Belgium
Anca.Croitor, Diana.Sima, [email protected]
Alan J. WrightCancer Institute CRUKUniversity of Cambridge
Li Ka Shing Centre, Cambridge, UK
Arend HeerschapDepartment of Radiology
Radboud University Nijmegen Medical CenterNijmegen, Netherlands
A non-negative blind source separation technique, known as non-negativematrix factorization (NMF), is hierarchically applied to three-dimensional3T MRSI prostate data to extract characteristic patterns for tumour andbenign tissue, and to visualise their spatial distribution. Since several NMFalgorithms are available in the literature, in this study three different NMFimplementations are considered and embedded into the same kind of hierar-chical scheme, which allows to automatically retrieve the patterns of interestand to provide a tissue characterisation of the given MRSI data. Extensivesimulation and in vivo studies show that the hierarchical scheme provides
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higher quality tissue patterns compared to those ones obtained by perform-ing only one NMF level. Furthermore, the three implementations performsimilarly, although the one known as CONVEX-NMF provides a more reli-able tumour pattern when the MRSI data set is characterised by moderatelyaggressive tumour spectra.
SIMAI 2014 96
MSP - Numerical methods for inverse problems and image processing
Conjugate Gradient method for p-normminimization
Flavia LentiDepartment of Science and High Technology, University of Insubria
via Valleggio, 11 22100 - Como Italy
Claudio EstaticoDepartment of Mathematics, University of Genova
Via Dodecaneso, 35 16146 - Genova Italy
Serge GrattonCERFACS and ENSEEIHT, University of Toulouse
42 Avenue Gustave Coriolis, 31057 - Toulouse France
David Titley-PeloquinCERFACS
42 Avenue Gustave Coriolis, 31057 - Toulouse France
Many efforts to generalize the conjugate gradient method to non-quadraticfunctionals have been made in the recent literature, both in Hilbert andBanach spaces. Here we propose a generalization of the conjugate gradientmethod for the minimization of a p-norm cost functional Φ(x) = ||Ax−y||pp,related to the solution of the operator equation Ax = y, where A : X → Yis a linear operator between Lp Banach spaces. It is well known that thenew “geometry” of the Lp spaces, for values of the constant 1 < p < 2, cansubstantially reduce the over-smoothness effects of any iterative restorationprocess in L2 Euclidean space [1]. The high convergence speed of conven-tional conjugate gradient in L2 Hilbert space gives rise to a fast minimizationmethod in Lp Banach spaces too.The algorithm is applied to enhance the spatial resolution of microwave ra-diometer data. The problem which describes the relationship between thecoarse but partially correlated measurements and the brightness tempera-ture belongs to the class of Fredholm integral equation of the first kind.
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1. Scherzer, O., Grasmair, M., Grossauer, H., Haltmeier, M. and Lenzen,F. 2009 Variational Methods in Imaging, Series: Applied MathematicalSciences, vol. 167, Springer.
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MSP - Numerical methods for inverse problems and image processing
On the application of spectral projected gradientmethods in image segmentation*
Laura AntonelliICAR-CNR
Via P. Castellino, 111 - 80131 Napoli, Italy
Valentina De SimoneSeconda Universita degli Studi di NapoliViale A. Lincoln, 5 - 81100 Caserta, Italy
Daniela di SerafinoSeconda Universita degli Studi di NapoliViale A. Lincoln, 5 - 81100 Caserta, Italy
Image segmentation, as many problems in image processing, can be ad-dressed via the optimization of a cost functional. We consider a convexrelaxation of Chan-Vese’s active contour model [2]. In this case, the opti-mization problem takes the form
minu,c1,c2
E1(∇u) + λE2(u, c1, c2)
s.t. 0 ≤ u ≤ 1,(1)
where u is a continuosly differentiable function related to the segmentedimage, c1 and c2 are the mean intensity values of the objects and backgroundof the image, E1 is a regularization term, E2 is a fidelity term measuring insome sense the distance between the given image and a two-phase image withintensities c1 and c2, and λ is a positive parameter. A standard approach tosolve this problem consists in alternating the minimization with respect to uand (c1, c2); the latter minimization can be performed exactly, by expressingc1 and c2 as functions of u. We solve problem (1) by using a differentapproach, based on a nonmonotone spectral projected gradient method [1],where the minimization is carried out with respect to all variables, butthe steplength selection procedure is performed by taking c1 and c2 fixed.Numerical experiments show the effectiveness of our strategy.
* Work partially supported by INdAM-GNCS (2014 Project “First-order optimizationmethods for image restoration and analysis”).
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1. Birgin, E. G., Martinez, J. M. and Raydan, M. 2000 NonmonotoneSpectral Projected Gradient Methods on Convex Sets. SIAM J. Optim.10(4), 1196–1211.
2. Chan, T. F., Esedoglu, S. and Nikolova, M. 2006 Algorithms for findingglobal minimizers of image segmentation and denoising models. SIAMJ. Appl. Math., 66(5), 1632-1648.
SIMAI 2014 100
MSP - Numerical methods for inverse problems and image processing
Optimization methods for large-scaledeconvolution on HPC architectures with
applications in Microscopy
Riccardo ZanellaUniversita degli Studi di Ferrara
via Saragat, 1, 44122 - Ferrara Italy
Federica Porta, Luca ZanniUniversita degli Studi di Modena e Reggio Emilia
via Campi 213/b, 40122 - Modena Italy
[email protected], [email protected]
Gaetano ZanghiratiUniversita degli Studi di Ferrara
via Saragat, 1, 44122 - Ferrara Italy
A number of modern imaging applications require deconvolution techniquesto improve reconstruction accuracy by mitigating the distortion effects causedon the data by to the acquisition system. This can be computationallydemanding, mainly in the case of large-scale problems. In this talk wepresent an effective deconvolution approach based on an accelerated gradi-ent method, which is also able to exploit the power of some modern HPCarchitectures. The accelerated deconvolution algorithm is developed on thebasis of scaled gradient projection (SGP) method [1], which is particularlysuitable for the solution of constrained optimization problems coming fromthe maximum likelihood approach and, for the regularized version, by themaximum a posteriori approach. Advances on the use a new steplength se-lection rules based on Ritz coefficients will be also discussed. These ruleswere recently proposed by R. Fletcher in the unconstrained context [2]. Somemeaningful numerical experiments on large-scale 2D and 3D microscopy datawill show the benefits of the proposed approach and how it is able to exploitGPU architectures.
1. Bonettini S., Zanella R., Zanni L. (2009). A scaled gradient projectionmethod for constrained image deblurring. Inverse Problems 25, 015002(23pp).
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2. Fletcher R. (2012). A limited memory steepest descent method. Math.Program. A 135(1–2), pp. 413–436.
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New developments andapplications of Groebner
bases
103
MSP - New developments and applications of Groebner bases
Applications of Groebner bases to simple graphs
Maurizio ImbesiUniversita degli Studi di Messina
Via Nuova Panoramica dello Stretto, Contrada Di Dio, 98166 - Messina Italy
Monica La BarbieraUniversita degli Studi di Messina
Viale Ferdinando Stagno d’Alcontres, 31, 98166 - Messina Italy
Classes of simple graphs are studied using computational and algebraicmethods in order to give geometrical models in real connection problems.Let G be a simple graph. An algebraic object attached to G is the edge idealI(G) which is a monomial ideal of the polynomial ring in n variables, wheren is the number of vertices of G ([6]).We investigate algebraic properties of edge ideals via Groebner bases. Moreprecisely, we use the theory of Groebner bases to characterize monomial s-sequences that arise from G. We introduce some classes of acyclic graphsfor which, using the Grobner bases, we show that necessary and sufficientconditions hold in order that their edge ideals are generated by s-sequences.Moreover we establish a condition for which a monomial sequence of gener-ators associated to the edge ideal of a forest is an s-sequence ([2], [3], [4]).The notion of s-sequence is employed to compute algebraic invariants of thesymmetric algebra associated to I(G) such as the dimension, the multiplicityand the Castelnuovo-Mumford regularity ([1], [5]).
1. Herzog, J., Restuccia, G. and Tang, Z. 2001 s-sequences and symmetricalgebras. Manuscripta Math., 104, 479–501.
2. Imbesi, M. and La Barbiera, M. 2010 Edge ideals and connection prob-lems, Commun. Appl. Ind. Math., 1, 2, 127–134.
3. Imbesi, M. and La Barbiera, M. 2012 Invariants of symmetric algebrasassociated to graphs, Turk. J. Math., 36, 3, 345–358.
4. Imbesi, M., La Barbiera, M. and Tang, Z. Some Monomial SequencesArising From Graphs. Submitted.
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5. Tang, Z. 2004 On certain monomial sequences, J. Alg., 282, 2, 831–842.
6. Villarreal, R. H. 2001 Monomial Algebras. Marcel Dekker, Inc., Pureand Applied Mathematics, 238.
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MSP - New developments and applications of Groebner bases
Graphs of paths and associated monomial algebras
Gaetana RestucciaUniversita degli Studi di Messina
Viale Ferdinando Stagno d’Alcontres, 31 98166 - Messina Italy
Rosanna UtanoUniversita degli Studi di Messina
Viale Ferdinando Stagno d’Alcontres, 31 98166 - Messina Italy
We consider two classes of complete bipartite graphs of paths, studied in[2], with good algebraic properties. They are described by ideals of mixedproducts L = IrJs and L′ = IrJs−1 + Ir−1Js, in two sets of variables in thepolynomial ring K[X1, . . . , Xn;Y1, . . . , Ym], over the field K, where Ir is ther-th squarefree Veronese ideal in K[X1, . . . , Xn] and Js is the s-th squarefreeVeronese ideal in K[Y1, . . . , Ym]. We consider the case r = s = 2 and wedescribe phenomena that can be modeled by such graphs. The associatedmonomial algebras K[L] and K[L′] are algebras of Segre-Veronese type thatcan be intensively studied using the Groebner bases theory.
1. Restuccia, G. and Utano, R. 2014 Ideals of mixed products and asso-ciated monomial algebras. Preprint.
2. Restuccia, G. and Villarreal, R. H. 2001 On the normality of monomialideals of mixed products. Comm. Alg., 29(8), (2001) 3571-3580.
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MSP - New developments and applications of Groebner bases
Which Principal Borel ideals are Gotzmann?
Vittoria BonanzingaUniversita Mediterranea di Reggio Calabria
via Graziella (Feo di Vito) 89100 Reggio Calabria, Italy
Shalom EliahouUniv. Lille Nord de France, Calais, France
In this talk, I’ll present a joint work with S. Eliahou entitled Whichprincipal Borel ideals are Gotzmann? It is linked with papers [2] and [1]presented to SIMAI Congress in 2006. We denote by Sn the set of mono-mials in n variables, and by Sn,d those monomials in Sn of degree d. Foru ∈ Sn,d, we denote by 〈u〉 the principal Borel ideal generated by u. We saythat u is a Gotzmann monomial in Sn if the set 〈u〉 is a Gotzmann idealin Sn. Let u ∈ Sn, we denote by γn(u) the smallest exponent k ∈ N suchthat uxkn is Gotzmann. We focus here on Gotzmann monomials in Sn for nsmall. For n = 3, we obtain a complete answer for the function γn(u) andfor n = 4, we present a general conjecture.
References:
1. Bonanzinga, V. and Sorrenti, L. 2007 Gotzmann ideals and applica-tions to graphs II. Communications to SIMAI Congress, ISSN 1827–9015, vol. 2 DOI: 10.1685/CSC06024.
2. Bonanzinga, V. 2003 Principal Borel ideals and Gotzmann ideals, Arch.Math. (Basel) 81, n. 4, 385–396 MR 2057059 (2005b:13041).
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MSP - New Developments And Applications Of Groebner Bases
Algebraic and geometric models for business
Gioia FaillaUniversita Mediterranea di Reggio Calabria
via Graziella, Feo di Vito, 89125 - Reggio Calabria Italy
In integer programming the classical transportation problem TP de-scribes the exchange among n factories F1, . . . , Fn which produce a respec-tive supply of U1, . . . , Un units of an indivisible good and m stores S1, . . . , Smwhich have respective demands of V1, . . . , Vm units. TP is modelized by thealgebraic-geometric (1-1) Segre-model, given by a semigroup homomorphismπ, or by a k-algebra homomorphism h that lifts π, constructed by the Segreproduct of two polynomial rings on a field k (i.e the real number field R)in n and m variables respectively. In this research we improve the classi-cal model TP and we propose a new algebraic-geometric model called (1-2)Segre-Veronese model for describing the exchange among the n factories andthe
(m2
)groups of 2 stores, coming by the aggregations of the m stores. The
enumeration problem for elements of a fiber of π with moderate size can besolved using Groebner bases theory.
1. G.Failla, Projective Toric Varietes and associated fibers, Rendicontidel Circolo Matematico di Palermo, Serie II, Suppl. 77 (2006),pp267-280.
2. B.Sturmfels, Groebner bases and Convex polytopes,Univ.Lect.Series,Vol.8,Amer.Math.Soc., 1995
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MSP - New developments and applications of Groebner bases
On the Birkhoff model for ranking problems
Gaetana RestucciaUniversita degli Studi di Messina
Viale Ferdinando Stagno d’Alcontres, 31 98166 - Messina Italy
The problem of ranking a number of alternatives based on scores or pref-erences assigned by multiple voters (or under multiple criteria) has becomeexceptionally important in modern applications.In addition to well-knownexamples such as rankings of colleges, sport teams, stocks, or webpages,ranking methodologies have been used in novel surprising ways. Concerningthe mathematical tools, let Sn := the symmetric group of the set of data1, 2, ..., n = [n], of cardinality n! and let π ∈ Sn any permutation.Let S = K[Xπ, π ∈ Sn] the polynomial ring with variables indexeded bypermutations in Sn, whose coefficients are in any infinite field K of charac-teristic zero (the field of real numbers < ).Let T = K[Y1, Y2, ..., Yn] a polynomial ring , where the indeterminates areviewed as a system of parameters.
Definition: A STATISTICAL RANKING MODULE is an homomorfismf : S −→ T .The BIRKHOFF MODEL studies SAMPLING PROBLEMS FROM STATIS-TIC.
The homomorfism f : S −→ T is such that T = K[Yij , 1 ≤ i ≤ j ≤ n],where Yij is the entry of a generic matrix and f(xπ) =
∏Yi,π(i)
RESULTS: Our results concern the Byrkhoff ranking model for subsets ofthe full set of permutations.
1. B. Sturmfels, V.Welker - Commutative algebra of statistical ranking,J. Algebra 361, 264-286 (2012)
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MSP - New Developments And Applications Of Groebner Bases
Simplicial complexes, convex polytopes and art
Vincenzo IorfidaUniversita degli studi della Calabria
Arcavacata di Rende (CS) Italy
Many objects of convex geometry and geometric combinatoric appear inproducts of art. We define a simplicial complex on a vertex set 1, 2, . . . , nand a convex polytope on set of points v1, . . . , vm of Rn, from the point ofview of commutative algebra and polyhedral geometry. By using the Groeb-ner bases theory, we obtain new simplicial complexes and new polytopes,that could be interesting subject of the art. More precisely, we introducea term order < on the monomials of the polynomial ring K[X1, . . . , Xn],K a field, and for special classes of binomial ideals we determine their ini-tial complex, hence the convex polytope. We recovery them in products ofart as painting and sculpture during the XX- XXI centuries ( see the Dalıhypercube).
1. B. Sturmfels, Groebner bases and convex polytopes, Univ. Lect. Se-ries, Amer. Math. Soc.,Vol.8 ,1995
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Complex Systems(SisCo-SIMAI Activity
Group)
111
MSP - Complex Systems (SisCo-SIMAI Activity Group)
Modeling altruism and selfishness in welfaredynamics
Marina DolfinUniversita degli Studi di Messina
Contrada Di Dio, Vill. S. Agata, Messina, 98166, Italy
Miros law LachowiczUniversity of Warsaw
ul. Banacha, 2, Warsaw, 02–097, Poland
Social systems need to be viewed as complex evolutive systems, includ-ing nonlinear interactions and learning phenomena, where collective com-portment appear and appropriate mathematical structures suitable to catchthese features are needed. In this talk a mathematical structure is proposedmodeling welfare dynamics in societies viewed as complex evolutive systemssubject to different policies of wealth distribution [1]. Interactions amongagents are modeled as stochastic games triggered by a threshold. The ap-proach contains the whole path from modeling to simulations, through aqualitative analysis of the initial value problem. Simulations are developedto put in evidence by visualization the dynamical behavior of the followingfeatures:
• Influence of the dynamics of the threshold µ on the trend, asymptoticin time, of the solutions, by comparison with the case of constantthreshold.
• Influence of the initial conditions by understanding how the dynamicsdiffer depending on the initial distribution of wealth; for instance bycomparing the dynamics of a population where the initial conditionsare concentrated on poor classes to that of a population characterizedby a higher presence of wealthy classes.
• Interplay between the influence of µ and that of the initial conditions.
• Role of a ”selfishness” parameter γ.
1. Dolfin, M. and Lachowicz, M. 2014 Modeling altruism and selfishnessin welfare dynamics: the role of non linear interactions. Math. ModelsMethods Appl. Sci. 24.
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MSP - Complex Systems (SisCo-SIMAI Activity Group)
A kinetic approach to traffic flow on road networks
Luisa FermoUniversita degli Studi di Cagliari
viale Merello, 92 09123 - Cagliari Italy
Andrea TosinConsiglio Nazionale delle Ricerche
via dei Taurini, 19 00185 - Roma Italy
This talk deals with a new kinetic model describing traffic flows on networksof different interconnected roads. According to the author’s knowledge, thisis the first attempt to model such system by means of kinetic equations.
The idea is to use the generalized kinetic and stochastic game theoryof active particles together with discrete representation of the microscopicstates of vehicles. This way the model successfully captures both the im-plicit stochasticity of human behaviors, hence ultimately of microscopic carinteractions, and the intrinsic microscopic granularity of the distribution ofvehicles along a road, which indeed do not properly form a continuum evenin congested situations.
More precisely, we present the modeling of two basic types of junctions:a junction with one incoming and two outgoing roads, which introduces theconcept of flow distribution and the dual junction with two incoming andoutcoming road which introduce the concept of right of way.
Finally, we show some numerical simulations and we discuss a qualitativeanalysis of the initial/boundary value problem on such networks.
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MSP - Complex Systems (SisCo-SIMAI Activity Group)
Nonlocal interaction equations with two species
Simone FagioliUniversita degli Studi dell’Aquilavia Vetoio, 67100 - L’Aquila Italy
We presents a systematic existence and uniqueness theory of weak mea-sure solutions for systems of nonlocal interaction PDEs with two species,which are the PDE counterpart of systems of deterministic interacting par-ticles with two species, see [3]. The main motivations behind those modelsarise in cell biology, pedestrian movements, and opinion formation. In caseof symmetrizable systems (i.e. with cross-interaction potentials one multi-ple of the other), we provide a complete existence and uniqueness theorywithin (a suitable generalization of) the Wasserstein gradient flow theoryin [1], which allows to consider interaction potentials with discontinuousgradient at the origin, see [2]. In the general case of non symmetrizablesystems, we provide an existence result for measure solutions which usesa implicit-explicit version of the JKO scheme, which holds in a reasonablenon-smooth setting for the interaction potentials. Uniqueness in the nonsymmetrizable case is proven for smooth potentials using a variant of themethod of characteristics. One-dimensional local nonlinear stability for anonlocal predator-prey model is discussed, both at particles and PDE levelsproviding some numerical results.
1. Ambrosio, L.; Gigli, N. and Savare, G. 2008 Gradient flows in metricspaces and in the space of probability measures. Lectures in Mathe-matics ETH Zurich, Birkhauser Verlag, Basel.
2. Carrillo, J. A., Di Francesco, M., Figalli, A., Laurent, T. and Slepcev,D. 2011 Global-in-time weak measure solutions and finite-time aggrega-tion for nonlocal interaction equations. Duke Math. J., 156, 229–271.
3. Di Francesco M. and Fagioli, S. 2013 Measure solutions for non-localinteraction PDEs with two species. Nonlinearity, 26, 2777–2808.
SIMAI 2014 114
MSP - Complex Systems (SisCo-SIMAI Activity Group)
A Kinetic Model of Crowd Evacuation fromBounded Domains
Juan Pablo Agnelli (1), Francesca Colasuonno (2), Damian Knopoff (1)
(1) FaMAF - CIEM, Universidad Nacional de Cordoba, (2) Politecnico di Torino
[email protected], [email protected],
Francesca ColasuonnoPolitecnico di Torino
Corso Duca degli Abruzzi, 24, 10129 - Torino Italy
The presentation is based on [1], in which we propose a kinetic modelfor the evacuation of crowds from bounded domains, such as a room withone or more exit doors. We use a hybrid representation of the crowd, withcontinuous-discrete features, that is position is assumed to be a continuousvariable, while velocity direction is a discrete variable.
The modeling approach considers dynamics caused by interactions ofwalking people at the micro-scale with all the other pedestrians and withthe geometry of the domain (i.e. position of walls and of exit doors). In-teractions are non-local and trigger a decision process which modifies thevelocity direction of people in a stochastic manner, whereas for simplicitythe velocity modulus is assumed to depend deterministically on the localdensity.
Numerical simulations are developed to study evacuation time dependingon the size of the exit zone, on the initial distribution of the crowd and ona parameter which weighs the unconscious attraction of the stream and thesearch for less crowded walking directions.
[1 ] Agnelli, J.P., Colasuonno, F. and Knopoff, D. 2014 A kinetic theoryapproach to the dynamics of crowd evacuation from bounded domains,accepted for publication in Math. Models Methods Appl. Sci.
SIMAI 2014 115
MSP - Complex Systems (SisCo-SIMAI Activity Group)
An Easy-to-Use Approach for SimulatingTraffic Flow on Networks
Gabriella BrettiIAC–CNR
Via dei Taurini, 19 00185 - Roma Italy
Maya BrianiIAC–CNR
Via dei Taurini, 19 00185 - Roma Italy
Emiliano CristianiIAC–CNR
Via dei Taurini, 19 00185 - Roma Italy
In this talk we present a model for traffic flow on networks based on a hy-perbolic system of conservation laws with discontinuous flux. Each equationdescribes the density evolution of vehicles having a common path along thenetwork. We consider a Godunov-based approximation scheme for the sys-tem which exhibits surprising properties, being able to select automatically areasonable solution without requiring external procedures at junctions (e.g.,maximization of the flux via a Linear Programming method [2,4]). Sinceusers do not have to deal with vehicle dynamics at junction, the numericalcode can be implemented in minutes.
We also show how the scheme can be recast in the framework of theclassical theory of traffic flow on networks, where a conservation law has tobe solved on each arc of the network. This is achieved by deducing a modifiedanalytical problem which is correctly solved by the numerical algorithm.Numerical comparisons with standard schemes [2,4] are also presented.
Reference papers are [1,3].
1. Bretti, G., Briani, M. and Cristiani, E. 2014 An easy-to-use approachfor simulating traffic flow on networks: Numerical experiments, Dis-crete Contin. Dyn. Syst. Ser. S 7, 379–394 (arXiv:1310.8329).
2. Bretti, G., Natalini, R. and Piccoli, B. 2007 A fluid-dynamic trafficmodel on road networks, Arch. Comput. Methods Eng. 14, 139–172.
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3. Briani, M. and Cristiani, E. 2014 An easy-to-use approach for simulat-ing traffic flow on networks: Theoretical study, submitted (arXiv:1401.1651).
4. Garavello, M. and Piccoli, B. 2006 Traffic flow on networks, AIMS onApplied Math. Vol. 1, American Institute of Mathematical Sciences.
SIMAI 2014 117
MSP - Complex Systems (SisCo-SIMAI Activity Group)
Some remarks on the risk driving index definition:mathematical models
Paolo FregugliaUniversita degli Studi dell’Aquila
Via Giovanni Di Vincenzo, 16/B 67100 - L’Aquila Italy
Beginning from well-known model of traffic we add another equationwhich represents some aspects of safety driving. This equation can be or aPDE or a suitable equation based on the generalized kinetic theory for activeparticles, in which short range interactions among drivers are modeled asstochastic games. Our analysis considers two different parts: objective andsubjective. Namely, the objective part concerns an analysis of the drivingconditions which do not depend on the driver and the subjective part regardsthe physical and psychological conditions of the driver. Of course, whenan individual drives he is liable to both parts. We wish to introduce someconsiderations in order to define a risk driving index (or, in symmetric way, asafe driving index ). This index could be utilized as tool for the governance ofvehicular traffic, with regard both the intrinsic difficulty of the road course,the weather conditions and the state of a driver. In other words, we proposea measure which enables to establish when a road can be covered with adegree of care. We give also an attempt of data validation.
SIMAI 2014 118
MSP - Complex Systems (SisCo-SIMAI Activity Group)
Kinetic description of optimal control problemsand applications to consensus modeling
Giacomo AlbiTechnische Univirsitat Munchen,
BoltzmannStraße, 3 85748 - Garching, Germany
Michael HertyRTWH Aachen University
Templergraben, 55 52056 - Aachen, Germany
Lorenzo PareschiUniversita di Ferrara, via Machiavelli, 35 44121, Ferrara
In this talk we will discuss an optimal control problem for a large systemof interacting agents using a kinetic perspective. As a prototype we firstintroduce a microscopic model of consensus formation under constraints. Inorder to investigated the mean–field description of this problem, we proposea Boltzmann-type equation based on a model predictive control formulation.In particular, the receding horizon strategy allows to embed the minimiza-tion of suitable cost functional into binary particle interactions acting asinstantaneous control. We derive the corresponding Fokker-Planck asymp-totic limit of the consensus dynamic and we show that stationary solutionscan be computed explicitly. Finally we report several numerical resultsshowing the robustness of the present approach.
SIMAI 2014 119
MSP - Complex Systems (SisCo-SIMAI Activity Group)
On the Modeling of Learning Dynamics in LargeLiving Systems
Silvana De LilloUniversita degli Studi di Perugia
Via Vanvitelli,1 06123 Perugia, Italy
Our presentation deals with the modeling of learning dynamics in a largesystem of in- teracting entities. The mathematical approach is based on thekinetic theory of active particles. Their microscopic state is modeled bya scalar variable called activity, which is assumed to be heterogeneouslydistributed among the particles. Nonlinear interactions lead to collectivephenomena of learning. The structure allows the derivation of specific mod-els and of numerical simulations related to real systems. The leading ideaproposed in this theory is that individuals learn by interactions, whose fre-quency depends on a suitable metric distance. The learning process is char-acterized by nonlinear interactions among individuals. We introduce thereference mathematical structure,discuss existence and uniqueness proper-ties of the solution of the initial value problem in a suitable functional spaceand then discuss a practical examples constructing the so called table ofgames and showing the results of the related numerical simulations.
SIMAI 2014 120
MSP - Complex Systems (SisCo-SIMAI Activity Group)
On a Model of Darwinian Dynamics andCompetition between Tumor and Immune Cells
Elena De AngelisDISMA - Politecnico di Torino
corso Duca degli Abruzzi 24, 10129 - Torino Italy
The talk concerns the modeling of the early stage of cancer phenomena,namely mutations, onset, progression of cancer cells, and their competitionwith the immune system. The mathematical approach is based on the ki-netic theory of active particles developed to describe the dynamics of largesystems of interacting cells, called active particles. Their microscopic stateis modeled by a scalar variable which expresses the main biological func-tion. The modeling focuses on an interpretation of the immune-hallmarksof cancer.
1. Bellomo, N. and Carbonaro, B. 2011 Toward a mathematical theoryof living systems focusing on developmental biology and evolution: Areview and perspectives. Phys. Life Rev. 8, 1–18.
2. Bellouquid, A. De Angelis, E. and Knopoff, D. 2013 From the modelingof the immune hallmarks of cancer to a black swan in biology. Math.Models Methods Appl. Sci. 23, 949–978.
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MSP - Complex Systems (SisCo-SIMAI Activity Group)
Transient states and congestion in trafficdynamical models on road networks
Armando Bazzani, Marco Di Cristina, Mattia Guidetti, EleonoraAndreotti, Sandro Rambaldi
Department of Physics and Astronomy - Bologna Univesity and INFN - Sezione diBologna
via Irnerio, 46 40126 - Bologna Italy
Armando BazzaniDepartment of Physics and Astronomy - Bologna University and INFN - Sezione
di Bolognavia Irnerio, 46 40126 - Bologna Italy
The complex networks have been extensively used to cope with the problemof extracting relevant information from the big data-base that new technolo-gies allow to collect on complex systems. Biological systems, social systemsand economics are the main application research fields. Statistical Physicshas developed suitable methods to characterize the equilibrium or statesand the existence of phase transitions. Recently the data base have beenenriched by dynamical properties of the considered systems opening the pos-sibility of studying the transient states and the transitions to critical statesunder a dynamical point of view. As a consequence there has been newmotivations to study stochastic dynamical systems on network-like interac-tions structures. Being inspired by the traffic dynamics we propose a classof models defined on a network topology whose nodes are characterize by astate x ∈ [0, 1] which evolves according
xk =∑j
πkj(t)Φ(xj , xk)−∑k
πjk(t)Φ(xk, xj)
where πkj ∈ [0, 1] is a stochastic random matrix which defines the weights ofthe network links (i.e.πkj weights the directed link between the nodes j andk and
∑k πkj = 1). The functions Φ(nj , nk) define the ’particles’ flows on
the link j → k which is a nonlinear function of the node states (and possibleof the node features) and satisfies the conditions
φ(0, xk) = 0 limxk→1
φ(xj , xk) = 0 limxj→1
φ(xj , xk) ≥ 0
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and for any value xk there exists a critical point such that ∂φ/∂xj = 0,which corresponds to a local maximum for the xj state. According to ourassumptions when the state of a node tends to 1, the node is congestedand it prevents other particles from entering in the node. This gives riseto a congestion spreading in the network following a backward cascade. Wehave studied the existence of equilibrium points for the average dynamicsand their stability, the transition probabilities to congested states and thestatistics of the first congestion time and the effect of a delay time for thepropagation of the information on the network on the dynamics in congestedstates. We have also considered possible local strategies to control the con-gestion development and the congestion spreading in the system. Theseresults have been applied to the study of traffic congestion formation ona road network using the traffic data recorded by 300 magnetic spires inthe road network of Emilia Romagna region in Italy. This system allowsto record microscopic information on vehicle dynamics (transit time andvelocity) on the main road network covering an area of order 20000 km2.The theoretical model suggests the existence of new observables that mayforecast the development of traffic congestion.
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MSP07 - Complex Systems (SisCo - SIMAI Activity Group)
A 2-population kinetic model for vehicular traffic
Matteo SempliceUniversita degli Studi di Torino
via Carlo Alberto, 10 10123 - Torino Italy
Gabriella PuppoUniversita degli Studi dell’Insubria
via Valleggio, 11 22100 - Como Italy
Giuseppe ViscontiUniversita degli Studi dell’Insubria
via Valleggio, 11 22100 - Como Italy
In the study of vehicular traffic we measure quantities like density, flux andaverage speed experimentally. However, the diagrams that relate these vari-ables can have different interpretations. Starting from a model of vehiculartraffic, based on kinetic theory, in which the space of microscopic veloc-ity is discrete, we try to understand the nature of experimental diagrams.Although the models with 1-population provide an equilibrium curve thatreflects the charachteristics of traffic, the real data seem to suggest a depen-dence of the asymptotic distribution on the initial one. Extending the modelto 2-population, we can show that we obtain the scattering of real data ifwe consider the presence of vehicles with mixed features (like average lengthand maximum speed): what has been suggested as a result of stochastichuman behavior, seems predicted in a deterministic way.
1. Fermo, L. and Tosin, A. 2013 A fully-discrete-state kinetic theory ap-proach to modeling vehicular traffic.. SIAM J. Appl. Math. 73(4),1533-1556.
2. Kerner, B. S. 2004 The Physics of Traffic. Springer, Berlin.
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Mathematical Models andComputational Methods in
Biomedicine
125
MSP - Mathematical Models and Computational Methods in Biomedicine
Compartmental Models for Nuclear MedicineData: an Inverse Problems Perspective
Michele Piana, Sara Garbarino, Fabrice Delbary, Valentina Vivaldiand Giacomo Caviglia
Dipartimento di Matematica, Universita di Genovavia Dodecaneso 35 I-16146 Genova Italy
Michele PianaDipartimento di Matematica, Universita di Genova and CNR - SPIN, Genova
via Dodecaneso 35 I-16146 Genova Italy
Compartmental analysis is a computational tool for the modeling of nu-clear medicine data that, in its most recent applications, exploits spatio-temporal information provided by Positron Emission Tomography (PET).This talk introduces two novel compartmental models describing the excre-tion of 18Fluoro-deoxyglucose (FDG) in the renal and hepatic systems. Thefirst model accounts for variations in FDG concentration due to water re-absorption in renal tubules and for increase of bladder’s volume during theexcretion process. The second model accounts for the dual blood supplyproper of the liver circulatory system and uses tracer concentration in thegut to describe the flow in the portal vein at the liver entrance. The com-putational reduction of both models is performed by using inverse problemstechniques: in the first case we used a non-stationary steepest descent ap-proach that explicitly accounts for the Poisson nature of nuclear medicinedata; in the second case, a regularized multi-dimensional Newton algorithmwith an ad hoc rule for the optimal selection of the regularization parameter.The applications considered illustrate new insights about the role of met-formin in cancer metabolism and utilizes data recorded by a PET systemfor small animal models.
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MSP - Mathematical Models and Computational Methods in Biomedicine
A Small Angle X-ray Scattering Technique forDetermining Nanoscale Particle Size Distributions
Federico BenvenutoINRIA/Ecole Polytechnique
Route de Saclay, 91128 Palaiseau Cedex, France
Houssem HaddarINRIA/Ecole Polytechnique
Route de Saclay, 91128 Palaiseau Cedex, France
The determination of a protein’s scale size is a difficult problem that istypically addressed by means of crystallography. Small angle X-ray scatter-ing (SAXS) may offer an alternative approach, which does not require theavailability of a crystalline sample. Further, SAXS allows dynamic measure-ments and provides access to information not limited to the surface of thesample, being able to measure inside the material without sophisticated sam-ple preparation. A SAXS experiment typically produces a one-dimensionalscattering intensity obtained by circular averaging the two-dimensional scat-tering pattern observed in the experiment. In order to determine the sizeinformation from this intensity, one needs to solve an ill-posed inverse scat-tering problem. This talk briefly introduces the SAXS modeling under theassumption that all nanoparticles in the system of interest are equally sizedand shaped, and presents a statistical method to determine the size of thenanoparticles. SAXS data are obtained by an azimuthal regrouping of scat-tered photons acquired by a charged coupled device and therefore are Poissondistributed. The talk will show the effectiveness of Expectation Maximiza-tion, when coupled with an appropriate stopping rule, to retrieve positiveparameters from SAXS data.
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MSP - Mathematical Models and Computational Methods in Biomedicine
The Hough Transform and a Novel PrognosticIndex for Chronic Leukemia
Anna Maria Massone, Cristina CampiCNR - SPIN
via Dodecaneso, 33 16146 - Genova Italy
[email protected] - [email protected]
Annalisa Perasso, Mauro Carlo Beltrametti, Michele PianaDipartimento di Matematica, Universita degli Studi di Genova
via Dodecaneso, 35 16146 - Genova Italy
[email protected] - [email protected] -
Anna Maria MassoneCNR - SPIN
via Dodecaneso, 33 16146 - Genova Italy
It has been recently proved that a computational analysis of Positron Emis-sion Tomography/Computerized Tomography (PET/CT) images allows theassessment of alteration of bone structure and bone marrow metabolism inadult patients with advanced chronic lymphocytic leukemia and that thiskind of analysis may even offer prognostic potentials [2]. The crucial re-quirement for the reliability of this study is the application of a patternrecognition method able to accurately segment the intra-bone space in clin-ical CT images of the human skeleton. The talk shows how this task can beaccomplished by a procedure based on the definition of Hough Transform forspecial classes of algebraic curves [1]. The idea is the one to introduce a cat-alogue of curves that satisfy some specific algebraic geometry conditions, tocompute their Hough Transform and apply a standard recognition approachbased on the optimization of an accumulator function. The effectivenessof this method will be proved against low-resolution clinical CT data andlead to the recognition of complex profiles in many different districts of thehuman skeleton.
1. Beltrametti M.C., Massone A.M. and Piana M. 2013 Hough transformof special classes of curves. SIAM J. Imag. Sci. 6, 391-412.
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2. Sambuceti G. et al. 2012 Estimating the whole bone marrow asset inhumans by a computational approach to integrated PET/CT imaging.Eur. J. Nucl. Med. Mol. Imaging 39, 1326-1338.
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Mathematical Models and Computational Methods in Biomedicine
Sequential Monte Carlo Samplers for thedetermination of neural activity from
neurophysiological data
Alberto SorrentinoUniversita degli Studi di Genova
Via Dodecaneso 35, 16146 - Genova Italy
Riccardo AraminiUniversita degli Studi di Genova
Via Dodecaneso 35, 16146 - Genova Italy
Gianvittorio LuriaUniversita degli Studi di Genova
Via Dodecaneso 35, 16146 - Genova Italy
Magnetoencephalography records non-invasively the magnetic fields pro-duced by the brain. In the dipolar approximation, the neural current ismodeled as an uknonwn number of point sources, termed current dipoles.We consider the problem of estimating the number of dipoles, their locationsand strength, from a single spatial distribution of magnetic field. We usea Bayesian approach, with uninformative priors for all parameters but thenumber of sources, which is assigned a Poisson prior with low mean. Weset up a sequential Monte Carlo sampler, that samples from a temperingsequence (a one-parameter family) of distributions, that closely reminds theregularization path. From the so-obtained posterior distribution we computepoint estimates of the source parameters. Simulated data show very goodlocalization properties, and experimental data evoked by somato-sensorystimulation confirm that the method can localize sources in real scenarios.
1. Sorrentino A., Luria G. and Aramini R. 2014. Bayesian Multi-DipoleModeling of a Single Topography in MEG by Adaptive Sequential MonteCarlo Samplers Inverse Problems 30 045010
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New Perspectives onApplicabilities in Graph
Theory
131
MSP - New Perspectives on Applicabilities in Graph Theory
Graphs & Neuro-Fuzzy Approaches to SolveInverse Problems in Non Destructing Testing and
Evalutation
Mario VersaciUniversita “Mediterranea” degli Studi di Reggio Calabriavia Graziella Feo di Vito, 89122 - Reggio Calabria Italy
Non-Destructive Testing in the eld of defects identication in metallic ele-ments plays a remarkable role with special regard to those sectors wherethe integrity of the material is strictly required. As a consequence, thedetection of defects and discontinuous deformations in metallic plates andbars, together with the relevant shape classication, provides to the operatoruseful information on the actual mechanical integrity of the specimen [1].When transformations are being studied, the loss of uniquess in the solu-tion, together with the relevant fragmentation of the strain elds inside thesolid can be observed, the equilibrium coming out as a solution presentedfrom a ne mixture among phases. In this context, starting from a theoreticalcharacterization of physical models with respect to computational aspects, acomparison with data from experimental investigation based on eddy currenttechnology is carried out. Finally, a new approach by neuro-fuzzy inferencesystem exploiting a network structure represented by graphs is proposed tosolve the inverse problem. In particular, Mamdani and Sugeno fuzzy infer-ence systems and fuzzy similarities [2], [3] have been exploited to investigateany discontinuities of the specimen subject to plastic deformation obtain-ing a map of mechanical stress (not obtainable by measurement campaign)calculated by application of the constitutive laws.
1. Pedregal, P. 2000 Variational Methods in Non Linear Elasticity. SIAMPress.
2. Chaira, T. and Ray, A.K. 2010 Fuzzy Image Processing and Applica-tions with MatLab. CRC Press.
3. Postorino, M.N., Versaci, M. 2013 Modelling user mode choices byan ellipsoidal fuzzy approach. International Journal of Modelling andSimulation, ActaPress, 33, 235-243.
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MSP - New Perspectives on Applicabilities in Graph Theory
Vertex covering optimizationin Veronese bi-type graph ideals
Maurizio ImbesiUniversity of Messina, Department of Civil Engineering and Applied Mathematics
Via Nuova Panoramica dello Stretto, Contrada Di Dio, 98166 - Messina Italy
Monica La BarbieraUniversity of Messina, Department of Mathematics and Computer Sciences
Viale F. Stagno d’Alcontres, 31, 98166 - Messina Italy
In [1], [5] monomial ideals of the ring R = K[X1, . . . , Xn;Y1, . . . , Ym]were introduced and their link with bipartite graphs was studied. Wedeal with ideals of Veronese bi-type, namely monomial ideals of R gen-erated in the same degree: Lq,s =
∑k+r=q Ik,sJr,s, with k, r > 1, s 6 q,
where Ik,s is the ideal of Veronese type generated on degree k by the setXai1
1 · · ·Xainn |
∑nj=1 aij = k, 0 6 aij 6 s, s ∈ 1, . . . , k and Jr,s is the
ideal of Veronese type generated on degree r by Y bi11 · · ·Y bim
m |∑m
j=1 bij = r,0 6 bij 6 s, s ∈ 1, . . . , r.For s=2 and q>3, the ideals Lq,2 are associated to the walks of length q−1 ofcomplete bipartite graphs having loops in all their vertices x1, . . . , xn, y1, . . . , ym,the so-called strong quasi-bipartite graphs K′n,m , and correspond to the gen-eralized graph ideals Iq(K′n,m).
The ideals of Veronese bi-type Lq,2 can be considered as bi-polymatroidalideals in R that derive from a special class of discrete bi-polymatroids,namely monomial ideals generated in a single degree such that for any twominimal generators u, v with degXi(u) > degXi(v) or degYk(u) > degYk(v)there exist j ∈ [n] with degXj (u) < degXj (v) or l ∈ [m] with degYl(u) <degYl(v) for which Xj(u/Xi) or Yl(u/Yk) are minimal generators.Algebraic properties, such as the monomial localization of the bi-polymatroidalideal Iq(K′n,m), are examined in [3]. It is also pointed out an algebraic aspectconcerning a generalization of the notion of minimal vertex covers, given in[2], [4], [6], that is the ideal of vertex covers for the generalized graph idealof K′n,m . Such ideal, denoted by (Iq)c(K′n,m), is generated by all monomialsXi1 · · ·XikYj1 · · ·Yjh such that (Xi1 , . . . , Xik , Yj1 , . . . , Yjh) is an associated
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prime ideal of Iq(K′n,m). Finally, the structure of (Iq)c(K′n,m), n > m, isfully described.The study of all these facts is devoted to find specific useful tools for im-proving actual critical situations for the connections in the field of commu-nications and transport.
1. Imbesi, M. and La Barbiera, M. 2013 Algebraic properties of non-squarefree graph ideals. Math. Reports, 65(15), 107–113
2. Imbesi, M. and La Barbiera, M. 2014 Monomial ideals of graphs withloops. Anal. Stiint. Univ. Al. I. Cuza din Iasi, Sect. Mat., In press
3. Imbesi, M. and La Barbiera, M. On algebraic properties of Veronesebi-type ideals arising from graphs. Submitted
4. Imbesi, M. and La Barbiera, M. Vertex covers in graphs with loops.Submitted
5. Imbesi, M., La Barbiera, M. and Stagliano P.L., On generalized graphideals of complete bipartite graphs. Submitted
6. Villarreal, R.H. 2001 Monomial Algebras. Dekker Inc., Pure and Appl.Math., 238
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MSP - New perspectives on applicabilities in graph theory
Graphs of paths and applications
Anna Maria StanganelliUniversita degli Studi di Palermo
Piazza Marina , 61 90133 - Palermo Italy
Our attention is fixed to a simply graph G3 of paths of lenght 2 of a completegraph G3 on a vertex set 1, 2, ..., n that can be employed to modelisedifferent fields of the life. More precisely we consider the polynomial ringA = K[X1, X2, ..., Xn] , K a field, and the monomial squarefree ideal I3 ofA, generated by
(n3
)monomials Xi1Xi2Xi3 , 1 ≤ i1 < i2 < i3 ≤ n, so called
3-Veronese square free ideal of A. For a bounded set of variables, westudy:
1. The monomial algebra K[G3] = K[Tijk, 1 ≤ i ≤ j ≤ k ≤ n]
2. The Groebner basis of the presentation ideal J3 of K[G3]
3. Algebraic invariants of K[G3]
In particular we study for a bounded set of variables,all possible monomialorders on K[Tijk, 1 ≤ i ≤ j ≤ k ≤ n] that give a quadratic binomial Groeb-ner basis for J3.
Theorem: There exists a term order < onK[Tijk, 1 ≤ i ≤ j ≤ k ≤ n] suchthat the sorted monomials are precisely the< − standardmonomialsmodulo J3.The initial ideal in<(J3) is generated by square free monomials. TheoremIn the second part of the talk we consider an application of obtained re-sults to problems of traffic,where many graphs of the type introduced beforenaturally arise,when some corners of the streets are whithout obstacles.
1. Sturmfels B., Groebner bases and convex polytopes , Univ. Lect. Series,Vol. 8, Amer. Math. Soc., 1995.
2. Miller E., Sturmfels B. Combinatorial commutative algebra. GraduateTexts in Mathematics, Springer Verlag, New York, 2004.
3. Stanganelli A.M., Graphs of paths and applications (work in progress,2014).
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MSP - New Perspectives on Applicabilities in Graph Theory
On Ideals Associated to Complete BipartiteGraphs
Maurizio ImbesiUniversity of Messina, Department of Civil Engineering and Applied Mathematics
Via Nuova Panoramica dello Stretto, Contrada Di Dio, 98166 - Messina Italy
Monica La BarbieraUniversity of Messina, Department of Mathematics and Computer Sciences
Viale F. Stagno d’Alcontres, 31, 98166 - Messina Italy
Paola Lea StaglianoUniversity of Palermo, Department of Energy, Engineering and Mathematical
ModelsViale delle Scienze, Edificio 7, 90128 - Palermo Italy
It is known that graphs are useful symbolic representations for several con-nection problems. We consider complete bipartite graphs, Kn,m, and westudy good properties for the generalized graph ideals Iq(Kn,m). These ide-als are monomial ideals in two sets of variables generated by square-freemonomials of fixed degree q, associated to the paths of length q−1 of Kn,m.In particular, they are ideals of mixed products and various results aboutthem are known [3], [4]. However, some problems arise when we want tostudy algebraic and geometric properties for them and for some algebras re-lated to them [1], [2]. Using computational and algebraic methods, we inves-tigate on Iq(Kn,m), in order to study when they have a linear resolution, andto compute standard invariants for the symmetric algebra Sym(Iq(Kn,m)).Moreover, the structure of minimal vertex cover of Iq(Kn,m) is fully de-scribed.
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1. La Barbiera, M. and Stagliano, P. L. 2014 Generalized graph ideals oflinear type. Turk. J. Math. 38, 203–211.
2. Imbesi, La Barbiera, M. and Stagliano, P. L. 2014 On generalized graphideals of complete bipartite graphs. Submitted.
3. Restuccia, G. and Villarreal, R. H. 2001 On the normality of monomialideals of mixed products. Comm. in Algebra 29-8, 3571–3580.
4. Villarreal, R. H. 2001 Monomial Algebras. M. Dekker Inc, 238.
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Numerical methods forcoupled problems
138
MSP - Numerical methods for coupled problems
ELECTROMECHANICAL MODELLING ANDIN SILICO ANALYSIS OF A RAT CARDIAC
SYNCYTIUM
Fabrizio Del BiancoDepartment of Industrial and Information Engineering, University of Pavia
via Ferrata, 1 27100 - Pavia Italy
Piero Colli FranzoneDepartment of Mathematics, University of Pavia
via Ferrata, 1 27100 - Pavia Italy
Simone ScacchiDepartment of Mathematics, University of Milano
via Saldini, 50 20133 - Milano Italy
Lorenzo FassinaDepartment of Industrial and Information Engineering, University of Pavia
via Ferrata, 1 27100 - Pavia Italy
We performed a study on the mechanics and electrophysiology occurringduring the contraction of a 2D syncytium made of rat cardiomyocytes bycarrying out numerical simulations of an electromechanical model for itscell and tissue components. From the online database CellML 1.1 we tookthree different models describing rat ventricular phenomena at the cell scale,which had already been corrected and integrated into the so-called PHN(Pandit-Hinch-Niederer) model: Pandit et al. electrical activity model [8],Hinch et al. calcium dynamics model [3] and Niederer et al. active tension(or contraction force) generation model [7]. Then, in order to simulate theelectromechanical response of our 2D sheet of cardiac tissue, we added aMonodomain model [1] to allow the propagation of the action potentialand a quasi-static finite elastic model [4][9] to simulate the biomechanicalresponse at the tissue scale. The discretization of the complete model wasachieved by using finite elements in space and semi-implicit finite differencesin time. At last we performed a set of simulations changing the values ofsome relevant parameters in order to match the experimental results foundin the literature [2][5][6].
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1. Colli Franzone, P. and Pavarino, L. F. 2004 A parallel solver forreaction-diffusion systems in computational electrocardiology. Math-ematical Models and Methods in Applied Sciences. 14, 883–911.
2. Fassina, L. et al. 2011 Video evaluation of the kinematics and dynam-ics of the beating cardiac syncytium: an alternative to the Langendorffmethod. Int. J. Artif. Organs. 34, 546–558.
3. Hinch, R. Greenstein, J. L. Tanskanen, A. J. Xu, L. and Winslow, R. L.2004 A simplified local control model of calcium-induced calcium releasein cardiac ventricular myocytes. Biophysical Journal. 87, 3723–3736.
4. Holzapfel, G. A. and Ogden, R. W. 2004 Constitutive modelling ofpassive myocardium: a structurally based framework for material char-acterization. Phil. Trans. R. Soc.. 367, 3445–3475.
5. Janssen, P. M. L. Stull, L. B. and Marban, E. 2002 Myofilament prop-erties comprise the rate-limiting step for cardiac relaxation at bodytemperature in the rat. Am. J. Physiol. Heart Circ. Physiol.. 282,H499–H507.
6. Layland, J. and Kentish, J. C. 1999 Positive force- and [Ca2+]i-frequencyrelationships in rat ventricular trabeculae at physiological frequencies.Am. J. Physiol. Heart Circ. Physiol.. 276, H9–H18.
7. Niederer, S. A. Hunter, P. J. and Smith, N. P. 2006 A quantitativeanalysis of cardiac myocyte relaxation: a simulation study. Biophysi-cal Journal. 90, 1697–1722.
8. Pandit, S. V. Clark, R. B. Giles, W. R. and Demir, S. S. 2001 Amathematical model of action potential heterogeneity in adult rat leftventricular myocytes. Biophysical Journal. 81, 3029–3051.
9. Pathmanathan, P. and Whiteley, J. P. 2009 A numerical method forcardiac mechanoelectric simulations. Annals of Biomedical Engineer-ing. 37, 860–873.
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MSP - Numerical methods for coupled problems
Interface Control Domain Decomposition (ICDD)Method for Stokes Darcy coupling
Marco DiscacciatiLaCaN - ETSECCPB - UPC BarcelonaTech
Campus Nord UPC - C2, E-08034 Barcelona, Spain
Paola GervasioDICATAM - Universita degli Studi di Brescia
via Branze, 38. 25123 - Brescia Italy
Alo QuarteroniMATHICSE - CMCS - Ecole Polytechinque Federale de Lausanne
Station 8, CH-1015 - Lausanne Switzerland
We present the Interface Control Domain Decomposition (ICDD) methodto address heterogeneous and multiphysics problems by overlapping subdo-main splitting. Interface controls are unknown functions used as Dirichletboundary data on the interfaces of an overlapping decomposition designedfor solving boundary value problems. The controls are computed throughan optimal control problem with interface observation [1], [2]. The mainadvantage of applying this approach to heterogeneous problems is to avoidsharp interfaces which would require an in depth knowledge of the localphysical behavior (interface conditions) of the specific problem. In this talkwe consider the Stokes/Darcy problem modeling the filtration of incom-pressible fluids through porous media, aiming at discussing both theoreticaland computational aspects of the ICDD method, as well as at comparingthis approach with classic coupling techniques based on the Beavers-Joseph-Saffman interface conditions [3].
1. M. Discacciati, P. Gervasio, and A. Quarteroni. The interface controldomain decomposition (ICDD) method for elliptic problems. SIAM J.Control Optim., 51(5):3434-3458, 2013.
2. M. Discacciati, P. Gervasio, and A. Quarteroni. The interface controldomain decomposition (ICDD) method for the Stokes problem. J.Coupled Syst. Multiscale Dyn., 1(5):372-392, 2013.
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3. M. Discacciati, P. Gervasio, and A. Quarteroni. Heterogeneous math-ematical models in uid dynamics and associated solution algorithms,volume 2040 of Lecture Notes in Mathematics, chapter 2, pages 57-123. Springer, 2011. Lectures given at the C.I.M.E. Summer Schoolheld in Cetraro, July 2009. Edited by G. Naldi and G. Russo.
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MSP - Numerical methods for coupled problems
Finite elements for Immersed Boundary Method
Daniele BoUniversita degli Studi di Pavia
Dipartimento di Matematica “F. Casorati” - via Ferrata, 1 - 27100 Pavia Italy
Nicola CavalliniUniversita degli Studi di Pavia
Dipartimento di Matematica “F. Casorati” - via Ferrata, 1 - 27100 Pavia Italy
Lucia GastaldiUniversita degli Studi di Brescia
DICATAM - via Branze, 43 - 20123 Brescia Italy
The finite element method has been applied with success to the ImmersedBoundary Method, for the numerical treatment of fluid-structure interac-tion problems [2] [1]. Recently a new variational formulation based on theintroduction of a Lagrange multiplier has been introduced. We show underreasonable assumptions that the scheme results to be inconditionally stablewith respect to the time discretization.
1. Bo, D., Gastaldi, L., Heltai, L. and Peskin, C.S. 2008 On the hyper-elastic formulation of the immersed boundary method. Comput. Meth-ods Appl. Mech. Engrg. 197, 2210-2231.
2. Bo, D., Cavallini, N. and Gastaldi, L. 2011 Finite element approach toimmersed boundary method with dierent uid and solid densities.Math.Models Methods Appl. Sci. 21, 2523-2550.
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MSP - Numerical methods for coupled problems
A hybrid level set/front tracking approach forfluid-structure interaction with large structural
displacements
Steen BastingDepartment of Mathematics, Friedrich-Alexander-University Erlangen-Nuremberg
Cauerstr. 11, 91058 Erlangen - Germany
Annalisa Quaini, Suncica Canic, Roland GlowinskiDepartment of Mathematics, University of Houston
4800 Calhoun Rd, Houston TX 77204 - USA
quaini,canic,[email protected]
We present a numerical method to simulate the movement of a thin inex-tensible beam immersed in an incompressible viscous fluid. Our approachcombines the flexibility of mesh moving/front tracking techniques with anadditional level set description of the interface. The computational mesh isautomatically aligned to the interface by minimizing a nonlinear, constrainedfunctional [1]. This optimization based mesh adjustment does not changethe topology of the mesh while guaranteeing optimal mesh quality. Dueto the mesh alignment, discontinuities of the solution variables (pressure)across the interface can be captured accurately. This approach allows forvery large structural displacements. To solve the fluid-structure interactionproblem, we adopt the classical Dirichlet-Neumann method with an accel-eration technique [3]. To simulate the motion of the inextensible beam weuse an augmented Lagrangian method, whose resulting saddle point prob-lem is solved with an Uzawa-Douglas-Rachford algorithm [2]. Our approachis assessed through various 2D numerical tests. We also show that whenthe structural displacement is small the results are in good agreement withArbitrary Lagrangian Eulerian simulations.
1. Basting S. and Weismann M. 2013 A hybrid level set-front trackingfinite element approach for fluid-structure interaction and two-phaseflow applications. J. Comput. Physics 255, 228–244.
2. Glowinski R. and Tallec P.L. 1988 Augmented Lagrangian and operator-splitting methods in nonlinear mechanics, SIAM, Philadelphia.
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3. Mok D., Wall W. and Ramm E. 2001 Accelerated iterative substruc-turing schemes for instationary fluid-structure interaction,. In Com-putational Fluid and Solid Mechanics (ed. K. Bathe), pp. 1325–1328,Elsevier.
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Numerical methods for coupled problems
An implicit high-order Discontinuous Galerkinsolver for hybrid RANS-LES simulations
Alessandro ColomboUniversita degli Studi di Bergamo
viale Marconi, 5 24044 - Dalmine(BG) Italy
Francesco Bassi, Lorenzo Botti, Nicoletta Franchina, Francesco CarloMassa
Universita degli Studi di Bergamoviale Marconi, 5 24044 - Dalmine(BG) Italy
[email protected], [email protected],
[email protected], [email protected]
Antonio Ghidoni, Stefano RebayUniversita degli Studi di Brescia
Via Branze, 38 25123 - Brescia Italy
[email protected], [email protected]
Turbulent flows are characterized by a wide range of length and time scales.In fact, while the largest eddies dimension is comparable to that of the bodythat generated turbulence, the smallest eddies length-scale dramatically de-creases with increasing the Reynolds number. For problems of industrialrelevance the simulation of all the turbulent scales, i.e., Direct NumericalSimulation (DNS), is nowadays not feasible and some modelling has to beintroduced. The governing equations, i.e., Navier–Stokes (NS) equations,can be averaged in time obtaining the Reynolds-Averaged Navier-Stokes(RANS) equations where all the scales are modelled by means of a turbu-lence model, e.g., k−ω. Although the solution of RANS equations is feasibleeven for high Reynolds numbers, it can be inaccurate in the prediction ofsome flow features such as massive separation and laminar recirculation bub-bles. Large Eddy Simulation (LES) and Detached Eddy Simulation (DES)aim to bridge the gap between no (DNS) and full (RANS) modelling ofturbulent scales by solving the large scales of turbulence and modelling theeffects of smaller scales by means of subgrid scale (SGS) models. In this workwe propose an implicit implementation of the DES-type eXtra-Large EddySimulation (X-LES) model of Kok et al.[1] in the Discontinuous Galerkin(DG) solver MIGALE. An accurate space discretization on hybrid type,
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highly-stretched and curved, elements is obtained by using hierarchical andorthonormal polynomial basis functions local to each element and definedin the physical space. The time-accurate integration of the fully coupledsystem of equations is performed by means of linearly implicit Rosenbrock-type Runge–Kutta methods [2], where the exact Jacobian is derived analyt-ically. Assessment and validation of our implementation will be performedby computing external aerodynamics problems that involve massively sepa-rated flows, e.g., the flow around a cylinder and a delta wing.
1. J. C. Kok, H. S. Dol, B. Oskam and H. van der Ven. Extra-large eddysimulation of massively separated flows. AIAA paper, 2004-264, 2004.
2. E. Hairer and G. Wanner. Solving Ordinary Differential EquationsII: Stiff and Differential-Algebraic Problems (2nd revised edition),Springer Series in Computational Mathematics, 1996.
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MSP - Numerical methods for coupled problems
Patient-specific model of the electrical activity inthe heart: generation of Purkinje networks driven
by clinical measurements
Simone PalamaraMOX, Dipartimento di Matematica, Politecnico di Milano
Piazza Leonardo da Vinci 32, I-20133, Milano, Italy
Domenico CatanzaritiDivisione di Cardiologia, Ospedale S. Maria del Carmine
Corso Verona 4, 38068, Rovereto (TN), Italy
Maurizio CentonzeU.O. di Radiologia di Borgo-Pergine
Viale Vicenza 9, 38051 Borgo Valsugana (TN), Italy
Elena FaggianoMOX, Dipartimento di Matematica, Politecnico di Milano
Piazza Leonardo da Vinci 32, 20133, Milano, Italy
Fabio NobileCSQI - MATHICSE, Ecole Polytechnique Federale de Lausanne
Station 8, CH-1015, Lausanne, Switzerland
Alfio QuarteroniSB SMA MATHICSE - CMCS, Ecole Polytechnique Federale de Lausanne
Station 8, CH-1015, Lausanne, Switzerland
Christian VergaraDipartimento di Ingegneria, Universita di Bergamo
Viale Marconi 5, 24044, Dalmine (BG), Italy
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A key aspect of the heart modeling is the study of electrical activation,that triggers the heart contraction. In particular, the ventricular activationis regulated by the Purkinje fibers (PF), which is the peripheral part of thecardiac conduction system. The PF are isolated from the surrounding mus-cle except at their endpoints, called Purkinje muscle junctions (PMJ), fromwhich the electrical signal enters the muscle.The focus of our work is to provide a computational algorithm for the gen-eration of a patient-specific Purkinje network, driven by clinical measures ofthe electrical activation in the ventricle. The proposed algorithm is basedon searching the optimal locations of the PMJ to best fit the measures,computing the activation times in the PF and in the ventricles by solvingEikonal problems.We tested the accuracy of our method considering five patient-specific ge-ometries with clinical measures acquired during normal and pathological ac-tivations. As pathologies, we considered two case of Wolff-Parkinson-Whitesyndrome, one of heart failure and one of Left Bundle Branch Block.The numerical results proved the essential role of a patient-specific Purkinjenetwork, both in modeling the healthy and the pathological activations ofthe patients under consideration.
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MSP - Numerical methods for coupled problems
Analysis and optimization of the generalizedSchwarz method for elliptic problems withapplication to fluid-structure interaction
Giacomo GiganteDip. di Ingegneria, Universita di Bergamo
viale Marconi 5, 24044 - Dalmine (BG) Italy
Christian VergaraDip. di Ingegneria, Universita di Bergamo
viale Marconi 5, 24044 - Dalmine (BG) Italy
We propose a unified convergence analysis of the generalized Schwarz methodapplied to a linear elliptic problem for a general interface (flat, cylindrical orspherical) in any dimension. In particular, we provide the exact convergenceset of the interface symbols related to the operators involved in the trans-mission conditions. We also provide a general procedure to obtain estimatesof the optimized interface symbols within the constants. Finally, we applysuch general results to a fluid-structure interaction model problem, and weassess the effectiveness of the theoretical findings through three-dimensionalnumerical experiments in the haemodynamic context.
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Numerical methods for coupled problems
Multiscale model of rift dynamics
Miglio EdieMox, Dept. of Mathematics, Politecnico di Milano
P.zza L. da Vinci 32, 20133 Milano, Italy
Mattia PenatiMox, Dept. of Mathematics, Politecnico di Milano
P.zza L. da Vinci 32, 20133 Milano, Italy
In this talk a mathematical model for the simulation of the mid-ocean ridgewill be developed. At the beginning a dimensional analysis is performedon the general conservation laws of continuum mechanics, in order to esti-mate the magnitude of each term; this is a necessary step which can not beavoided before introducing other hypotheses. The dimensionless model willbe then particularized for shallow domains, this kind of approximation willbe very useful for the mathematical modeling of large portion of lithosphere.The derived models will be coupled together to define a simplified model ofmid-ocean ridge. The analysis will allow also to define suitable boundaryconditions for the problem at hand.
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MSP - Numerical Methods for Coupled Problems
Coupling Micro-Scale Dynamics to CollectiveBehaviors: The Case of Living, hence Complex,
Systems
Nicola BellomoPolitecnico di Torino
This communication refers to the modeling of living systems and shows ina number of applications the micro-scale dynamics is transferred to collec-tive behaviors. The first part deals with a methodological approach, whilethe second part proposes a number of case-studies focusing on biological(multicellular systems) [1],[2],[3], and life sciences.
[1 ] N. Bellomo, D. Knopoff, and J. Soler: On the Difficult InterplayBetween Life, “Complexity”, and Mathematical Sciences, Math. Mod.Meth. Appl. Sci. 23 (2013), 1861-1913.
[2 ] G. Ajmone Marsan, N. Bellomo, and A. Tosin, Complex Systems andSociety, Springer Briefs in Mathematics, (Springer, 2013).
[3 ] N. Bellomo and A. Bellouquid, Derivation of new chemotaxis modelsby asymptotic analysis of kinetic models for large binary cell mixtures,to be published.
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MSP - Numerical Methods for Coupled Problems
Optimized partitioned procedures for theStokes-Darcy coupled problem
Luca Gerardo-GiordaBCAM - Basque Center for Applied Mathematics
Mazarredo 14,. 48009 Bilbao, Basque Country, Spain
Marco DiscacciatiLaCaN - ETSECCPB - UPC BarcelonaTech
Campus Nord UPC - C2, E-08034 Barcelona, Spain
We consider a coupled Stokes-Darcy system for the filtration of an incom-pressible fluid through a porous medium. The model couples the solutionof the Stokes equation in the fluid region, with the solution of the Darcyequation in the porous medium region through the surface separating thetwo physical domains. Partitioned procedures are modular algorithms com-monly used for the solution of coupled multiphysics problems. They involveseparate solvers for the different subproblems, that interact in an iterativeframework through the exchange of suitable transmission conditions at themultiphysics interface. In the framework of domain decomposition methods,the Robin-type interface conditions introduced in [1] guarantee convergencein the absence of overlap between the different subregions. Following theideas developed in [2] for Fluid-Structure Interaction problems, we optimizethe performance of the corresponding algorithm, both in term of an iterativesolver and as a preconditioner for the fully coupled problem [3].
1. M. Discacciati, A. Quarteroni and A. Valli 2007 Robin-Robin domaindecomposition methods for the Stokes-Darcy coupling. SIAM J. Nu-mer. Anal., Vol. 45 (3), pp. 2193-2213.
2. L. Gerardo-Giorda, F. Nobile, and C. Vergara 2010. Analysis andoptimization of Robin-Robin partitioned procedures in Fluid-StructureInteraction problems. SIAM J. on Num. Anal., Vol. 48 (6), pp. 2091-2116.
3. M. Discacciati, L. Gerardo-Giorda 2014 Optimized Schwarz Methodsfor the Stokes-Darcy coupling. In preparation.
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MSP - Numerical methods for coupled problems
Fluid-Structure-Interaction in Hemodynamicsusing Nonlinear, Anisotropic Hyperelastic Wall
Models
Daniel BalzaniInstitute of Mechanics, Universitat Duisburg-Essen, Germany
Simone DeparisChair of Modeling and Scientific Computing, EPFL, Switzerland
Simon FaustenInstitute of Mechanics, Universitat Duisburg-Essen, Germany
Davide FortiChair of Modeling and Scientific Computing, EPFL, Switzerland
Alexander HeinleinMathematical Institute, Universitat zu Koln, Germany
Axel KlawonnMathematical Institute, Universitat zu Koln, Germany
Alfio QuarteroniChair of Modeling and Scientific Computing, EPFL, Switzerland
Oliver RheinbachInstitut fur Numer. Math. und Optim., Technische Universitat Bergakademie
Freiberg
Jorg SchroderInstitute of Mechanics, Universitat Duisburg-Essen, Germany
We consider the fluid-structure-interaction problem in a blood vessel using amonolithic coupling approach [1], first using a Convective Explicit approachfor the fluid. We believe that the prediction of transmural stresses requiresthe use of sophisticated nonlinear material models for the vessel wall. For-tunately, such models have been developed in the past and their parame-ters have been adapted to experimental data. Here, we use an anisotropic,polyconvex hyperelastic material model for the structure [2]. The coupledsimulations build on the LifeV software library [3] and FEAP [4]. Absorbingboundary conditions on the outflow are imposed to reduce reflections.
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1. D. Balzani, P. Neff, J. Schroder, G.A. Holzapfel, A polyconvex frame-work for soft biological tissies. Adjustment to experimental data.IJSS, 43(20), p. 6052–6070, 2006.
2. P. Crosetto, S. Deparis, G. Fourestey, A. Quarteroni, Parallel al-gorithms for fluid structure-interaction problems in haemodynamics.SISC, 33(4), 1598-1622, 2011.
3. LifeV Software Library, www.lifev.org
4. R.L. Taylor, Finite Element Analysis Program,http://www.ce.berkeley.edu/projects/feap/
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MSP - Numerical methods for coupled problems
A novel implementation of the H-basedformulation of the eddy current model
Ana Alonso RodrıguezDipartimento di Matematica, Universita di Trento
Via Sommarive, 14 I-38050 POVO
Enrico BertolazziDipartimento di Ingegneria Industriale, Universita di Trento
Via Mesiano 77, I-38050 Trento, Italy
Riccardo GhiloniDipartimento di Matematica, Universita di Trento
Via Sommarive, 14 I-38123 POVO
Alberto ValliDipartimento di Matematica, Universita di Trento
Via Sommarive, 14 I-38123 POVO
Eddy current equations are a well-known approximation of Maxwell equa-tions obtained by disregarding the displacement current term (see e.g., [2]).The typical setting for an eddy current problem distinguishes between a con-ducting region, ΩC, and the surrounding non-conducting air region, ΩI. Theunknowns of the formulation based on the magnetic field can be reduced tothe magnetic field in the conductor HC, the scalar magnetic potential ΨCin the insulator and, if the insulator is not simply connected, the loop fieldρI, a curl-free vector field whose line integral on some loops contained in ΩIis different from 0. We present a novel implementation of the finite elementapproximation of the H-based formulation of the eddy current model thatuses an alternative procedure for the construction of a basis of the space ofloop fields. The proposed method works for general topological configura-tions and it does not need the determination of “cutting” surfaces (see e.g.,[3]). The procedure is based on the explicit knowledge of a maximal set ofnon bounding cycles on the boundary of the insulator (see [4]), and it usesan explicit formula for expressing the discrete loop fields in terms of linkingnumbers (see [1]).
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1. A. Alonso Rodrıguez, E. Bertolazzi, R. Ghiloni and A. Valli. Con-struction of a finite element basis of the first de Rham cohomologygroup and numerical solution of 3D magnetostatic problems, SIAM J.Numer. Anal., 51 (2013), 23802402.
2. A. Alonso Rodrıguez and A. Valli. Eddy Current Approximation ofMaxwell Equa- tions, Springer-Verlag Italia, Milan, 2010.
3. P. W. Gross and P. R. Kotiuga. Electromagnetic Theory and Compu-tation. A Topo- logical Approach, Cambridge University Press, NewYork, 2004.
4. R. Hiptmair and J. Ostrowski. Generators of H1(Γh, Z) for triangu-lated surfaces: construction and classification, SIAM J. Comput., 31(2002), 14051423.
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Computational models fornatural hazards and extreme
events simulation
158
MSP - Computational models for natural hazards and extreme events simulation
A finite-difference ghost-point method for ellipticequations with application to Cauchy-Navier
equations
Giovanni RussoUniversita degli Studi di Catania
viale Andrea Doria, 6 95125 - Catania Italy
Armando CocoBristol University
Queens Road, Bristol BS8 1RJ - United Kingdom
Elliptic problems in arbitrary (possibly infinite) domain and general bound-ary conditions are center to many applications, like diffusion phenomena,fluid dynamics, charge transport in semiconductors, crystal growth, electro-magnetism and many others. In this talk the finite-difference ghost-pointmethod proposed in [1] and its applications are described. The arbitrarydomain is defined by a suitable level-set function. The equations are dis-cretized by classical central differences on interior points, while boundaryconditions with high order reconstructions are enforced to define the solu-tion at ghost points, which are grid nodes outside the domain with a neigh-bor inside the domain. The linear system arising from the discretization issolved by a suitable multigrid approach. The numerical method has beensuccessfully employed in several contexts: from fluid-dynamic (incompress-ible Navier-Stokes and compressible Euler equation) to Elasticity problems(Cauchy-Navier equations). The latter application constitutes the main fo-cus of the present talk, with application to volcanology for computing thedisplacement caused by pressure sources [2]. In this case the method is ex-tended to treat with infinite domains, by a technique based on a smoothcoordinate transformation, which maps an unbounded domain into a unitsquare.
1. Coco, A. and Russo, G. 2013 Finite-Difference Ghost-Point MultigridMethods on Cartesian Grids for Elliptic Problems in Arbitrary Do-mains. In Journal of Computational Physics, vol. 241, pp. 464–501.
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2. Coco. A., Currenti, G., Del Negro, C. and Russo, G. 2014 A SecondOrder Finite-Difference Ghost-Point Method for Elasticity Problemson unbounded domains with applications to Volcanology. In Commu-nications in Computational Physics, accepted.
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MSP - Computational models for natural hazards and extreme events simulation
An accurate and efficient DG framework foradaptive numerical weather prediction
Giovanni TumoloThe Abdus Salam ICTP
Strada Costiera 11, 34151 - Trieste Italy
Luca BonaventuraMOX - Politecnico di Milano
Via Bonardi 9, 20133 - Milano Italy
The overwhelming evidence that climate is changing, including the charac-teristics of extreme phenomena, poses a challenge to the next generation ofnumerical weather prediction (NWP) models. The study of the origin andmechanisms determining the location, intensity and frequency of extremes,and how these may change in the future, will indeed require NWP modelsto be adaptive in order to be able to accurately represent and predict suchextremes.
We have introduced an accurate and efficient discretization approach forthe shallow water equations on the sphere (extending the technique proposedin [1]), as well as for the non-hydrostatic Euler equations on a vertical slice,that can be effectively applied to all geophysical scale flows [2]. Numericalsimulations of classical shallow water and non-hydrostatic benchmarks val-idate the method and demonstrate its accuracy and efficiency, making it agood candidate for providing the basis of an accurate and efficient adaptiveclimate and weather prediction system.
We combine a semi-Lagrangian approach with a novel TR-BDF2 basedsemi-implicit time integrator and with a spatial discretization based onadaptive discontinuous finite elements on hierarchical bases. The resultingmethod is unconditionally stable and has full second order accuracy in time,thus improving standard off-centered trapezoidal rule discretizations with-out any major increase of the computational cost nor loss in stability, whileallowing the use of time steps up to 50 times larger than those required bystability for explicit methods applied to corresponding DG discretizations.
The method also has arbitrarily high order accuracy in space and caneffectively adapt the number of degrees of freedom employed in each element
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in order to balance accuracy and computational cost. The p-adaptivity ap-proach employed does not require remeshing and hence is especially suitablefor NWP applications, where a large number of physical quantities has tobe reconstructed on the mesh from the available data. Furthermore the p-adaptivity approach can cure the pole problem by reducing the polynomialdegree in polar elements, yielding a reduction in the computational costcomparable to that achieved with reduced Gaussian grids.
1. Tumolo G., Bonaventura L., Restelli M. 2013 A semi-implicit, semi-Lagrangian, p-adaptive discontinuous Galerkin method for the shallowwater equations. J. Comput. Phys. 232, 46–67.
2. Tumolo G., Bonaventura L. 2014 An accurate and efficient numericalframework for adaptive numerical weather prediction. Report MOX18/2014 (submitted to Quarterly J. Royal Met. Soc.).
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MSP - Computational models for natural hazards and extreme events simulation
Numerical-based deterministic methods forearthquake risk analysis in large urban areas
Ilario MazzieriPolitecnico di Milano
Piazza L.da Vinci, 32 20133 - Milano Italy
Paola AntoniettiPolitecnico di Milano
Piazza L.da Vinci, 32 20133 - Milano Italy
Alfio QuarteroniCMCS, Ecole Polytechnique Federale de Lausanne (EPFL)
Station 8, 1015 Lausanne, Switzerland
In this talk we provide an overview of the recent advances on numericalmethods for the simulations of earthquake events. We show that numerical-based deterministic methods can be effectively employed to provide realisticearthquake ground shaking maps to be used as the key ingredient to developearthquake risk scenarios.We present a set of realistic (and physically plausible under the local geolog-ical and seismological constraints) extreme earthquake scenarios in key loca-tions worldwide performed with SPEED (http://mox.polimi.it/it/progetti/speed),a new parallel open source code for the simulation of complex wave prop-agation phenomena jointly developed by the Laboratory for Modeling andScientific Computing MOX (Department of Mathematics, Politecnico di Mi-lano) and the Engineering Seismology Group (Department of Civil and En-vironmental Engineering, Politecnico di Milano).From the methodological viewpoint, SPEED is based on a spectral elementformulation enhanced by the Discontinous Galerkin approach for treatingnon-conforming approximations. After illustrating the SPEED code, wepresent different case studies and we derive some interesting considerationson the pros and on the limitations of deterministic approaches. This workhas been carried out in collaboration with Munich RE (Germany).
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MSP - Computational models for natural hazards and extreme events simulation
Assessing volcanic hazard by using multiphaseflow simulations
Augusto Neri, Tomaso Esposti Ongaro, Mattia de’Michieli VitturiIstituto Nazionale di Geofisica e Vulcanologia, Sezione di Pisa
Via della Faggiola 32, 56126 Pisa
Since the 70s volcanologists have successfully described several key fea-tures of the dynamics of volcanic eruptions by using mathematical mod-els. First, simple 1D steady-state homogeneous flow models were used toinvestigate the different eruptive mechanisms of explosive eruptions and toexplore the first-order effect of different input parameters. Nowadays, thecontinuous evolution of those early models has led to the development ofa variety of transient, 2D/3D, homogeneous/multiphase flow models of vol-canic phenomena implementing state-of-the-art formulations of the underly-ing physics, new-generation experimental data, as well as high-performancenumerical techniques. These numerical models have proved to provide use-ful insights in the dynamics of explosive eruptions, as well as to represent avaluable tool for the assessment and representation of volcanic hazards. Inthis talk we will illustrate the application of some multiphase flow models tospecific volcanic phenomena (e.g. volcanic jet, pyroclastic density current,ballistic ejecta), to the reconstruction of past events, such as the famous Mt.St. Helens eruption in 1980, as well as to the 2D/3D numerical simulationof possible eruptive scenarios at high-risk explosive volcanoes such as CampiFlegrei and Vesuvius (Italy). We will discuss the challenges and limitationsof the different mathematical models as well as of the approach adopted toquantify the volcanic hazard on a probabilistic basis and considering someof the uncertainties affecting the volcanic system.
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MSP - Computational models for natural hazards and extreme events simulation
Lessons learnt from recent earthquakes and theimportance of 3D physical modeling in insurance
and (re)insurance market
Marco SupazziniGeo Risk, Munich RE,
Koniginstr. 107, 80802 Munich, Germany.
With the ongoing progress of computing power made available not onlyby large supercomputer facilities but also by relatively common worksta-tions and desktops, physics-based source-to-site 3D numerical simulationsof seismic ground motion will likely become the leading and most reliabletool to construct earthquake ground shaking scenarios.This contribution aims at providing an overview of recent progress on thissubject, by taking advantage of the experience gained during a recent re-search contract between Politecnico di Milano, Italy, and Munich RE, Ger-many, with the objective to construct ground shaking scenarios from hy-pothetical earthquakes in large urban areas worldwide. Within this con-tract, the SPEED (SPectral Elements in Elastodynamics with Discontinu-ous Galerkin) computer code was developed, based on a spectral elementformulation enhanced by the Discontinous Galerkin approach to treat non-conforming meshes.Different earthquake scenarios will be overviewed, e.g., Emilia-Romagna,Italy 2012 and Christchurch, New Zealand 2011. The comparison withstrong motion records allows one to derive some interesting considerationson the pros and present limitations of such approach. Finally, some furtherdevelopment will be presented aiming at drawing the future perspective forthis research project.
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Variational inequalities,immune systems and localminimizers of functionals
166
Variational inequalities, immune systems and local minimizers of functionals
Multiscale modelling of living systems: amathematical and computational perspective
Francesco PappalardoUniversita degli Studi di Catania
Piazza Universita, 2 95131 - Catania Italy
Filippo CastiglioneCNR, Italy
Piazzale Aldo Moro, 7 00185 - Roma Italy
Carlo BiancaSorbonne Universites
4, Place Jussieu 75252 Paris Cedex 05, France
Giulia RussoUniversita degli Studi di Catania
Piazza Universita, 2 95131 - Catania Italy
giuliarusso @tiscali.it
Marzio PennisiUniversita degli Studi di Catania
Piazza Universita, 2 95131 - Catania Italy
Santo MottaUniversita degli Studi di Catania
Piazza Universita, 2 95131 - Catania Italy
The language of mathematics has been extensively used to describe nat-ural phenomena of the physical sciences in terms of models based on equa-tions. The mathematical language allows logical reasoning over a repre-sentation of the physical entities involved in the phenomenon and makespossible to account for the observations made through experimentation.
It is coming nowadays more clear that in order to obtain a unified de-scription of the different mechanisms governing the behavior and causality
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relations among the various parts of a living system, the development ofcomprehensive computational and mathematical models at different spaceand time scales are required. This is one of the most formidable challengesof modern biology characterized by the availability of huge amount of highthroughput measurements.
In this work, we draw attention to the importance of multi-scale model-ing in the framework of studies of biological systems in general and of theimmune system in particular.
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MSP - Variational inequalities, immune systems and local minimizers of functionals
Duality theory for dynamic vaccination games
Annamaria BarbagalloUniversity of Naples “Federico II”
via Cintia 80126 - Naples Italy
Antonino MaugeriUniversity of Catania
viale A. Doria, 6 95125 - Catania Italy
Maria Alessandra RagusaUniversity of Catania
viale A. Doria, 6 95125 - Catania Italy
The talk is devoted to an infinite dimensional duality theory finalized tostudy the existence of a strong duality between a convex optimization prob-lem connected with the management of vaccinations and its Lagrange dual(see [1]). Specifically, the authors show the solvability of a dual problemusing as basic tool an hypotheses known as Assumption S (see for details[2], [3], [4]). By using this theory, it is possible to overcome the difficulty ofthe voidness of the interior of the ordering cone which defines the cone con-straints. Moreover, applying the duality theory to the dynamic vaccinationgame, the Lagrange multipliers associated to the problem are obtained andthe behavior of the problem is better understood.
1. Barbagallo, A., Maugeri, A. and Ragusa, M. A. On strongly dualitytheory with applications to vaccination games. Submitted.
2. Daniele, P. and Giuffre, S. 2007 General infinite dimensional dualityand applications to evolutionary network equilibrium problems. Optim.Lett. 3, 227-243.
3. Daniele, P., Giuffre, S., Idone, G. and Maugeri, A. 2007 Infinite di-mensional duality and applications. Math. Ann. 339, 221-239.
4. Maugeri, A. and Raciti, F. 2010 Remarks on infinite dimensional du-ality. J. Global Optim. 46, 581-588.
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Variational inequalities, immune systems and local minimizers of functionals
Approximate symmetries of differential equations.
Marianna RuggieriUniversita degli Studi di Enna KOREvia delle Olimpiadi, 94100 - Enna Italy
Maria Paola SpecialeUniversita degli Studi di Messina
Contrada Papardo, Salita Sperone - Messina Italy
In many problems of physical interest differential equations contain termsinvolving ”small” parameters. The combined treatment of the theory of Liegroups and perturbation analysis leads to the development of the Theory ofapproximate symmetries. We consider the above coupled KdV equations
ut + uxxx + 2uux + ε [2e1vvx + e2(uxv + uvx) + e3vxxx] = 0
c1vt + vxxx + 2vvx + c2vx + ε c3[e1(uxv + uvx) + 2e2uux + e3uxxx] = 0,(2)
in terms of approximate symmetry reduction approach. The model [1],describes two resonantly interacting normal modes of internal-gravity-wavemotion in a shallow stratified liquid. In (2), u(t, x) and v(t, x) represent thedesplacement from the horizontal of the fluid interfaces, ei (i = 1, 2, 3) andcj (j = 1, 2, 3) are arbitrary constants, while ε << 1 is a small parameter.When ε = 1 some recent results can be found in [2]. In this paper we performthe approximate symmetry reduction of (2) and approximate solutions arecomputed by means of the approximate generator of the first order.
1. Gear J. A. and Grimshaw R. 1984. Weak and strong interactionsbetween internal solitary waves. In Stud. Appl. Math., 70(3), 235258.
2. Ruggieri M. and Speciale M. P. 2013, Similarity Reduction and ClosedForm Solutions for a Model Derived from Two Layer Fluids, in Ad-vances in Difference Equations, 355(1), Springer.
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MSP - Variational inequalities, immune systems and local minimizers of functionals
General Financial Equilibrium Problem withMemory Term and Adaptive Constraints
Annamaria BarbagalloUniversity of Naples
via Cintia, 80126 - Naples Italy
Patrizia DanieleUniversity of Catania
viale A. Doria, 6 95125 - Catania Italy
Mariagrazia LorinoUniversity of Catania
viale A. Doria, 6 95125 - Catania Italy
Antonino MaugeriUniversity of Catania
viale A. Doria, 6 95125 - Catania Italy
Cristina MirabellaUniversity of Catania
viale A. Doria, 6 95125 - Catania Italy
This talk is devoted to the study of a general financial equilibrium prob-lem. The problem is modeled by means of an evolutionary variational in-equality. In the previous papers [1] and [5], three interesting formulas (deficitformula, balance law, liability formula) were given. These formulas are ofgreat importance for the theory of equilibrium problems evolving in timeand they could be of great utility for the management of the world econ-omy. Papers [3] and [4] were the sequel of the previous papers [1] and [5]: weobtained that the solution of the evolutionary inequality is continuous andLipschitz continuous with respect to time and we illustrated the achieved re-sult through numerical examples. In paper [2] the risk assessment dependedon previous equilibria and adaptive constraints were considered. All these
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previous papers and results are the basis of this talk in which the utilityfunction includes a memory term and adaptive constraints depending onthe expected solution are considered. An existence theorem is proved andsignificant examples are provided.
1. Barbagallo, A., Daniele, P., Giuffre, S. and Maugeri, A. 2014 Varia-tional approach for a general financial equilibrium problem: the Deficitformula, the Balance law and the Liability formula. A path to the econ-omy recovery. European J. Oper. Res. 237, 231–244.
2. Barbagallo, A., Daniele, P., Maugeri, A., Mirabella, C., A Varia-tional approach to the evolutionary financial equilibrium problem withmemeory terms and adaptive constraints. In press in Network Modelsin Economics and Finance. Springer Optimization and Its Applica-tions.
3. Barbagallo, A., Daniele, P., Maugeri, A. and Mirabella, C. 2013 Fur-ther results for general financial equilibrium problems via variationalinequalities. Journal of Mathematical Finance 3, 33–52.
4. Barbagallo, A., Daniele, P., Maugeri, A. and Mirabella, C. 2013 Re-cent Results on a General Financial Equilibrium Problem. In 11thInternational Conference of Numerical Analysis and Applied Mathe-matics 2013: ICNAAM 2013 (eds. T.E. Simos, G. Psihoyios and Ch.Tsitouras). AIP Conference Proceedings, vol. 1558, pp. 1789–1792.
5. Barbagallo, A., Daniele, P. and Maugeri, A. 2012 Variational formu-lation for a general dynamic financial equilibrium problem. Balancelaw and liability formula. Nonlinear Anal. 75, 1104-1123.
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MSP - Variational inequalities, immune systems and local minimizers of functionals
A bilevel model of the continuous-time optimalpollution emission price problem
Laura ScrimaliUniversita degli Studi di Catania
viale Andrea Doria, 6 95125 - Catania Italy
We consider the problem of the optimal pollution emission price in acontinuous-time setting and give a formulation as a bilevel programmingproblem. In particular, we suppose that control policies are imposed tothe end of regulating the pollution emissions of manufacturers in a supplychain. Therefore, the government chooses the optimal price of the pollutionemission with consideration to manufacturers’ response to the price. On theother hand, the manufacturers choose the optimal quantities of productionto maximize their profits, given the price of pollution emission. Inspiredby [1] and [2] and using some new recent results on variational inequalitiesand infinite dimensional duality, we reformulate the bilevel programmingproblem into a one level optimization problem. Moreover, the existence ofsolutions is investigated. Finally, a numerical example is provided.
1. Dempe, S. 2002. Foundations of Bilevel Programming. Kluwer,Dordrecht.
2. Wang G-M., L-M. Ma and L-L. Li. 2011. An application of bilevelprogramming problem in optimal pollution emission price. J. Serv.Sci. Mang. 4, 334–338.
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MSP - Variational inequalities, immune systems and local minimizers of functionals
Inverse variational inequalities and applications toan economic equilibrium problem
Annamaria BarbagalloUniversity of Naples “Federico II”
via Cintia 80126 - Naples Italy
Paolo MauroUniversity of Catania
viale A. Doria, 6 95125 - Catania Italy
The talk deals with the behavior of control policies whose aim is to reg-ulate the exportation through the adjustments of supply taxes or incentiveson the firms (see [1], [2]). Then, we are concerned with a policy-makeroptimization problem. This aspect is studied with the help of an inverseevolutionary variational formulation. And, hence, a characterization of theinverse variational inequality with an appropriate evolutionary variationalinequality is given. Here the possibility of presence of production and de-mand excesses is explored. We remark that the definition of equilibrium forthe firms is given by using the infinite dimensional duality theory. In orderto illustrate theoretical results, we present a numerical example.
1. Barbagallo, A. and Mauro, P. and Ragusa, M. A. 2014 An inverseproblem for the dynamic oligopolistic market equilibrium problem inpresence of excesses. Procedia Soc. Behav. Sci. 108, 270–284.
2. Barbagallo, A. and Mauro, P. Inverse variational inequality approachand applications. Accepted on Num. Funct. Anal. Optim.
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Modeling, simulation andoptimization of complex
systems using PartialDifferential Equations
175
Modeling, simulation and optimization of complex systems using Partial Differential
Equations
Flow Optimization in Vascular Networks
Radu C. CascavalUniversity of Colorado Colorado Springs, USA
1420 Austin Bluffs Pkwy, Colorado Springs, CO 80918 - USA
Ciro D’ApiceUniversity of Salerno
via Giovanni Paolo II, 132, 84084 - Fisciano(SA) Italy
Maria Pia D’ArienzoUniversity of Salerno
via Giovanni Paolo II, 132, 84084 - Fisciano(SA) Italy
Rosanna ManzoUniversity of Salerno
via Giovanni Paolo II, 132, 84084 - Fisciano(SA) Italy
The study of mathematical models for vascular networks is very impor-tant because of its applications in medicine and pharmacology. The best wayto study the arterial system would be to use a 3-D model, but it requiresa very high computational power, so we use a 1-D reduced model based onNavier-Stokes equations with appropriate boundary conditions, which stillallows to capture the major features under study, such as arterial bloodpressure and flow. The simulation is limited by the computational power,so, instead of considering an entire human network, we simulate portions ofthe network and use inflow and outflow conditions which must realisticallymimic the behavior of the network that has been removed from the model.The system is solved numerically using the discontinuos Galerkin schemeand the two-steps method of Adam-Bashfort. The aim is to study the effectof truncation to the flow in the root edge in the case of a fractal network,the effect of adding or subtracting an edge to a given network, the effectof growing a given network in order to obtain the same amount of flow,and optimal control strategies on a network in the event of a blockage orunblockage of an edge or of an entire subtree.
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1. Alastruey J. 2006, Numerical modelling of pulse wave propagation inthe cardiovascular system: development, validation and clinical appli-cation, PHD thesis.
2. Cascaval R.C. 2012, A Boussinesq model for pressure and flow velocitywaves in arterial segments, Math Comp Simulation, 82(6), 1047-1055.
3. Ottesen J.T., Olufsen M.S., Larsen J.K. 2004, Applied MathematicalModels in Human Physiology, SIAM, 403–422.
4. Formaggia L., Lamponi D., Quarteroni A. 2003, One-dimensional mod-els for blood flow in arteries, J Eng Math 47: 251-276.
5. Reymond P., Merenda F., Perren F., Rufenacht D., Stergiopulos N.2009, Validation of a one-dimensional model of the systemic arterialtree, Am J Physiol Heart Circ Physiol 297, H208–H222.
6. Steele B.N., Valdez-Jasso D., Haider M.A., Olufsen M.S. 2011,Predict-ing Arterial Flow and Pressure Dynamics Using a 1D Fluid DynamicsModel with a Viscoelastic Wall, SIAM Journal of Applied Mathemat-ics, 1123-1143.
7. Pozrikidis C. 2009, Numerical Simulation of Blood Flow Through Mi-crovascular Capillary Networks Bulletin of Mathematical Biology, 71,1520-1541.
8. Cheng Y., Shu C.W. 2008, A discontinuous Galerkin finite elementmethod for time dependent partial differential equations with higheroder derivatives Mathematics of Computation, 77, 262, 699-730.
9. Antonopoulos D.C., Dougalis V.A. 2012, Numerical solution of the’classical’ Boussinesq system, Math. and Computers in Simulation,82, 984-1007.
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MSP - Modeling, simulation and optimization of complex systems using Partial
Differential Equations
Optimization of the input flow of a supply chain
Ciro D’ApiceUniversity of Salerno
via Giovanni Paolo II, 132, 84084 - Fisciano(SA) Italy
Carmine De NicolaUniversity of Salerno
via Giovanni Paolo II, 132, 84084 - Fisciano(SA) Italy
Rosanna ManzoUniversity of Salerno
via Giovanni Paolo II, 132, 84084 - Fisciano(SA) Italy
The mathematical modeling of supply chains and the development of tech-niques for simulation and optimization purposes is of great interest in orderto reduce bottlenecks, dead times at queues, and so on. Depending on thescale, one can distinguish different modeling approaches. For a recent reviewsee [1].Here we focus attention on a continuous model for supply chains proposed in[4], according to which a supply chain consists of processors with constantprocessing rate and a queue in front of each processor. The dynamics ofparts on a processor is described by a conservation law, while the evolutionof the queue buffer occupancy is given by an ordinary differential equation.We deal with the optimal control problem, where the control is given bythe input flow to the supply chain and the cost functional is the sum ofthe time-integral of queues and quadratic distance from a preassigned de-sired outflow (see [2, 3]). In particular the controls are the locations of thediscontinuities of the input flow of piecewise constant type, while the fluxvalues are fixed. Simulations are performed to show results for the proposednumerical algorithm in some case studies.
1. D’Apice C., Gottlich S., Herty H., Piccoli B. 2010 Modeling, Simula-tion & Optimization of Supply Chains A Continuous Approach, SIAM,Society for Industrial and Applied Mathematics.
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2. D’Apice C., Manzo R., Piccoli B. 2012 Optimal input flows for a PDE-ODE model of supply chains. Communications in Mathematical Sci-ences, 10(36), 1226-1240.
3. D’Apice C., Manzo R., Piccoli B. 2013 Numerical schemes for theoptimal input flow of a supply-chain. SIAM Journal on NumericalAnalysis, 51(5), 2634-2650.
4. Gottlich S., Herty M., Klar A. 2005 Network Models for Supply Chains.Communication in Mathematical Science, 3, 545-559.
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Modeling, simulation and optimization of complex systems using Partial Differential
Equations
A problem of train scheduling on the rail lineVerona-Monaco of Bavaria
Martina MazzantiPhoops srl
via della Torretta, 14, 50137 - Firenze Italy
Viola PungettiAlmavivA S.p.A
Via di Casal Boccone, 188, 00137 - Roma Italy
Vincenzo VespriUniversity of Firenze
viale Morgagni, 67/a, 50134 - Firenze Italy
As part of a project Industria 2015 called SIFEG (Sistema Integrato TrasportoMerci Ferro Gomma) one of the Promoters, Bertolotti S.p.A, asked to theMaster’s candidates Mazzanti and Pungetti to investigate the impact of afreight car of new generation, much faster than those currently in use, aboutthe transport of goods by rail. In collaboration with Trenitalia the railwayline on the route Verona-Monaco of Bavaria has been analyzed . The choiceof this trait arises from the fact that this route is a real bottleneck for theentry and the exit of goods between Italy and Germany. Applying Opera-tions Research techniques rail traffic was simulated and the impact of thefreight wagon of new generation was assessed.
1. Crainic T.G. 2002, A Survey of Optimization Models for Long-HaulFreight Transportation, Montreal: Centre for Research on Transporta-tion.
2. Crainic T.G., Ferland J.-A., Rousseau J.-M. 1984, A Tactical Plan-ning Model for Rail Freight Transportation, Transportation Science,18, 165-184.
3. Harrod S. 2007, Railway Capacity Management and Planning, Univer-sity of Cincinnati.
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4. Lindner T., Zimmermann U.T. 2003, Train Schedule Optimization inPublic Rail Transport, Mathematics-Key Technology for the Future,703-716.
SIMAI 2014 181
Modeling, simulation and optimization of complex systems using Partial Differential
Equations
Kernel estimates for Schrdinger type operatorswith unbounded diffusion and potential terms
Anna CanaleUniversity of Salerno
via Giovanni Paolo II, 132, 84084 - Fisciano(SA) Italy
Abdelaziz RhandiUniversity of Salerno
via Giovanni Paolo II, 132, 84084 - Fisciano(SA) Italy
Cristian TacelliUniversity of Salerno
via Giovanni Paolo II, 132, 84084 - Fisciano(SA) Italy
Schroedinger equation gives the quantum description of a particle in a elec-tric filed. The ground state of the particle is of relevant importance ant itcan be related to the heat kernel of the operator. The study of the kernel,furthermore, can be useful for the investigation of spectral properties andpointwise bounds of eigenfunctions of the operator. For this reason we studythe kernel of the semigroup generated by a Schroedinger type operator withunbounded coefficient. We consider an operator whose coefficients have apolynomial grow of degree greater than 2 as regards the diffusion part and alower degree as regards the potential term. We estimate the first eigenvalueof the operator and give heat kernel estimate using the equivalence betweenthe ultracontractivity of the semigroup and a weighted Nash inequality.
1. Bakry D., Bolley F., Gentil I., Maheux P. 2012 Weighted Nash in-equalities. Revista Matematica Iberoamericana, 28, 3, 879-906.
2. Davies E.B. 1989 Heat Kernels and Spectral Theory, Cambridge Uni-versity Press.
3. Canale A., Rhandi A., Tacelli C. 2013, Schroedinger type operatorswith unbounded diffusion and potential terms, preprint.
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4. Canale A., Rhandi A., Tacelli C. 2013, Kernel estimates for Schroedingertype operators with unbounded diffusion and potential terms, preprint.
5. Lorenzi L., Rhandi A. 2012 On Schroedinger type operators with un-bounded coefficients: generation and heat kernel estimates, preprint.
6. Metafune G., Spina C., Tacelli C. 2014, Elliptic operators with un-bounded diffusion and drift coefficients in L p spaces, Preprint, Ad-vances in Differential Equations,19, 5-6. 473-526.
7. Shen Z. 1995, L p estimates for Schrdinger operators with certain po-tentials, Annales de linstitut Fourier, 45, 2, 513546.
8. Wang F.Y. 2002, Functional inequalities and spectrum estimates: theinfinite measure case, J. Funct. Anal., 194, 288-310
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GASVA on MathematicalModelling in Environmental
and Life Sciences
184
MSP - GASVA on Mathematical Modelling in Environmental and Life Sciences
Quasi Steady-State Approximations (QSSAs)in the CME-based stochastic framework
A. Borri F. Carravetta G. Mavelli P. PalumboIstituto di Analisi dei Sistemi e Informatica,
Italian National Research Council (IASI-CNR),Rome, Italy
alessandro.borri,francesco.carravetta,gabriella.mavelli,[email protected]
A. M. BersaniDipartimento di Metodi e Modelli Matematici,
Universita La Sapienza di Roma,Rome, Italy
The Chemical Master Equation (CME) provides an accurate stochastic de-scription of complex biochemical processes in terms of probability distri-bution of the underlying chemical population. In contrast to deterministicmethods, CMEs are therefore considered fruitful stochastic methods for theanalysis of biochemical reactions. In the deterministic framework, reactionsare usually described by directly expressing the time-evolution of the concen-tration for each of the involved species, thus leading to having to handle anOrdinary Differential Equation (ODE) system, often of great dimension. Toface the analysis of complex processes, the practice to exploit Quasi-SteadyState Approximations (QSSAs) has been introduced in literature with theaim of reducing the dimensionality of the system, thus speeding numericalsimulations. In this work, we perform a preliminary investigation of the ap-plicability of QSSAs to the stochastic method based on CMEs. To this end,the CME description is applied to the original chemical network, as well asto the standard and total QSS Approximations. The contribution confirmsby simulations the effectiveness and superiority of the latter approximationwith respect to the former one, also from a stochastic point of view.
SIMAI 2014 185
MSP - GASVA on Mathematical Modelling in Environmental and Life Sciences
A semi-analytical study intransdermal drug delivery systems
Giuseppe PontrelliIAC – CNR
Via dei Taurini, 19 - 00185 Roma
Mathematical models for drug delivery are extensively used in bioengi-neering and provide important contributions to the medical practice, be-cause constitute a powerful predictive tool for a fundamental understandingof biotransport processes. For example, many studies have been carried outto investigate the release properties of a therapeutic drug from a vehicleacross the skin, through a transdermal patch.
In order to investigate such a process, a two-phase mathematical modeldescribing the dynamics of a substance between two coupled media of dif-ferent properties and extents is presented. The first layer is a polymericplatform where the drug is initially contained, and the other one is the skinwhere the drug is directed to. A set of coupled non-homogeneous partialdifferential equations describes the diffusion and the reversible binding andunbinding in both layers. Additional flux continuity at the interface andan absorbing condition at the biological medium limit are imposed. Aneigenvalue problem is solved and a concentration closed-form solution of thetwo-phase two-layer model is given in the form of an infinite series expansion.
The typical drug dynamics, the concentration levels, the optimal deliv-ery rate are shown as outcomes of simulations and discussed in some casestudies. The results are used to discuss the roles of the diffusion and reac-tion parameters, to evaluate drug release efficacy and to assess an optimalcontrol strategy in the rational design of advanced delivery systems.
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MSP - GASVA on Mathematical Modelling in Environmental and Life Sciences
A hybrid mathematical model for self-organizingcells in the zebrafish lateral line primordium
Ezio Di CostanzoDipartimento di Scienze di Base e Applicate per l’Ingegneria - Sezione di
Matematica, Sapienza University of RomeVia A. Scarpa, 16 00161 - Rome Italy
Roberto NataliniIstituto per le Applicazioni del Calcolo “M. Picone”, Consiglio Nazionale delle
RicercheVia dei Taurini, 19 00185 - Rome Italy
Luigi PreziosiDipartimento di Scienze Matematiche, Politecnico di Torino
Corso Duca degli Abruzzi, 24 10129 - Turin Italy
Lateral line is a sensory system, which is present in fish and amphibians,that is used to detect movement and vibration in the surrounding water,together with other fundamental functions. Zebrafish lateral line representsa model organ which has contributed to a deeper understanding in manyfundamental biological issues: interactions between multiple signaling, col-lective migration during morphogenesis, response of an organ to injury. Inthis talk [1] we propose a discrete in continuous mathematical model for themorphogenesis of the posterior lateral line system in zebrafishes. Our modelfollows closely the results obtained in recent biological experiments, [2], [3],[4]. Our description is discrete for the cellular level and continuous for themolecular level. We prove the existence of steady solutions consistent withthe formation of particular biological structure, the neuromasts. Dynamicalnumerical simulations are performed to show the behavior of the model andits qualitative and quantitative accuracy to describe the evolution of thiscell aggregate.
1. Di Costanzo, E., Natalini, R. and Preziosi, L. 2013 A hybrid mathe-matical model for self-organizing cell migration in the zebrafish lateralline. Journal of Mathematical Biology, DOI: 10.1007/s00285-014-0812-9, arXiv:1311.2255 [q-bio.CB].
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2. Haas, P. and Gilmour, D. 2006 Chemokine Signaling Mediates Self-Organizing Tissue Migration in the Zebrafish Lateral Line. Develop-mental Cell 10, 673–680.
3. Lecaudey, V., Akdogan, G. C., Norton W. H. J. and Gilmour, D. 2008Dynamic Fgf signaling couples morphogenesis and migration in thezebrafish lateral line primordium. Development 135, 2695–2705.
4. Nechiporu, A. and Raible, D., 2008 FGF-Dependent MechanosensoryOrgan Patterning in Zebrafish. Science 320, 1774–1777.
SIMAI 2014 188
MSP - GASVA on Mathematical Modelling in Environmental and Life Sciences
Ago-Antagonist Theory in Darwinian Evolution
Armando BazzaniDept. of Physics and Astronomy (DFA),
University of Bologna, Italy
Paolo FregugliaDept. of Information Engineering, Computer Science and Mathematics (DISIM),
University of L’Aquila, Italy
In this talk we analyse our proposal on the essential structural aspects ofDarwinian Evolution Theory. Using this point of view we apply a mathe-matical ago-antagonist theory inspired by Y.Cherruault (1998) ideas, whichwe have extended. In the ago-antagonist model, the phenotype charactersmeasure the individual propensity to perform an innovative x(t) (agonist)or conservative y(t) (antagonist) action with respect to mutations and tospeciation process. We have mathematically introduced the conflict conceptand we present a model that takes into account the environmental effects bymean of a stochastic multiplicative process. We shortly discuss the proper-ties of the related stochastic differential equations.
SIMAI 2014 189
MSP - GASVA on Mathematical Modelling in Environmental and Life Sciences
Wind-Blown Sand: AnErosion-Transport-Sedimentation-Sliding Model
Luca BrunoDipartimento di Architettura e Design Politecnico di Torino
Corso Duca degli Abruzzi 24 , Torino
Davide FransosOptiflowMarseille
Luigi PreziosiDipartimento di Scienze Matematiche Politecnico di Torino
Corso Duca degli Abruzzi 24
Four phenomena are involved in sand movement: erosion, wind trans-port, sedimentation, sliding. The main reason of erosion of a sand bed isthe shear stress exerted by wind on the surface. This is the origin of aphenomenon called saltation, that consists in the raising of sand particlesfrom the soil that then follow a ballistic trajectory influenced by drag andgravity, eventually impacting again on the surface and inducing new parti-cles to detach from the surface. Sand is then transported by the wind andsediment under the action of gravity.
In this talk we will propose a comprehensive multiphase model for sanderosion, transport, sedimentation, and sliding that is then solved in a mov-ing boundary domain. Luckily, the motion of sand grains and the evolutionof dune shapes occur on very different time scales which allows the problemto be split and solved in cascade: first determining the flow field, possiblyinfluenced by the presence of grains, then the transport of sand in the do-main, and then the evolution of the surface as a consequence of erosion,deposition of sand and redistribution of sand due to the formation of sandavalanches.
SIMAI 2014 190
MSP - GASVA on Mathematical Modelling in Environmental and Life Sciences
Numerical modelling of initial formation inmultispecies biofilms
Berardino D’AcuntoUniversity of Naples
via Claudio 21, 80125 - Napoli, Italy
Luigi FrunzoUniversity of Naples
via Claudio 21, 80125 - Napoli, Italy
Maria Rosaria MatteiUniversity of Cassino and the Southern Laziovia Di Biasio, 43, 03043 Cassino (FR), Italy
The work presents a mathematical modelling able to model the attachmentphenomena in the initial phase of biofilm growth. In the framework of contin-uum model, the biofilm growth depends on two main phenomena: biomassgrowth and substrate diffusion into biofilm [1]. The first is described by aset of nonlinear hyperbolic partial differential equations, the second by aset of semi-linear parabolic partial differential equations. As the physicalphenomena, the two sets of equation are mutually connected. The resultingmathematical problem is a free boundary value problem, which is essentiallyhyperbolic [2,3]. The model has been applied to the biological competitionof heterotrophic-autotrophic bacteria in a multi-specie biofilm. The effectsof different attachment rates on the biofilm dynamic performances predict-ing biofilm thickness, volume fractions of bacterial species and substrateconcentration trends have been investigated.
1. Wanner, O. and Gujer, W. 1986 Multispecies biolm model Biotechnol.Bioeng. 28, 314-328.
2. Dacunto, B. and Frunzo, F. 2011 Qualitative analysis and simulationsof a free boundary problem for multispecies biolm models Math. Com-put. Model. 43, 1596-1606.
3. Dacunto, B. and Frunzo, F. 2012 Free boundary problem for an initialcell layer in multispecies biolm formation Appl. Math. Letters. 25,20-26.
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MSP - GASVA on Mathematical Modelling in Environmental and Life Sciences
A Multidomain Mathematical Model about theIntracellular Transport of Naked DNA Plasmids
Maria Grazia NotarangeloDipartimento di Scienze di Base e Applicate per l’Ingegneria - Sezione di
Matematica, Sapienza University of RomeVia A. Scarpa, 16 00161 - Rome Italy
Roberto NataliniIstituto per le Applicazioni del Calcolo “M. Picone”, Consiglio Nazionale delle
RicercheVia dei Taurini, 19 00185 - Rome Italy
We propose a spazio-temporal model to describe and analyze the intracel-lular trafficking of naked DNA plasmids.The naked DNA plasmid is extra-chromosomal genetic material used in gene therapy to vehiculate therapeuticvectors, that will be transfected into the nucleus. The DNA size of plasmidvectors is between 5 kb and 20 kb, corresponding to 3300-13200 kDa, respec-tively. The large size of this plasmid not permits the free diffusion in thecytoplasm and the pass across the nuclear envelope. For this reason, we havefocused the attention about the role of microtubules in the cytoplasm, andthe RAN cycle and the importin through nuclear envelope. Our model ishence a multidomain model: cytoplasm and nucleus in two dimensions, andmicrotubule in one dimension. Through numerical simulations, we demon-strate and support the experimental data for which the microtubules and theimportin are necessary to transport the plasmids into the nucleus. Thereforeour results may help to explain how , under certain conditions, the DNAplasmid passes through the cytoplasm and across the nuclear envelope.
1. Notarangelo, MG. Natalini, R. and Signori, E. 2014 Gene Therapy:The Role of Cytoskeleton in Gene Transfer Studies Based On Biologyand Mathematics. Current Gene Therapy, Vol 14, 2, 121-127
2. Vaughan, E.E. DeGiulio, J.V and Dean, D.A. 2006 Intracellular Traf-ficking of Plasmids for Gene Therapy: Mechanisms of CytoplasmicMovement and Nuclear Import. Current Gene Therapy. 6, 671-681.
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MSP - GASVA on Mathematical Modelling in Environmental and Life Sciences
Time Scale Separation, Normal Modes andQuasi-Steady State Approximations in Enzyme
Kinetics
Pierluigi VellucciSapienza Universita di Roma
Dipartimento SBAI - via Antonio Scarpa, 16 00161 - Rome Italy
Alberto Maria BersaniSapienza Universita di Roma
Dipartimento SBAI - via Antonio Scarpa, 16 00161 - Rome Italy
The mathematical treatment of enzyme kinetics, based on quasi-steady stateapproximations, relies on the separation of two different time scales, relatedto a fast transient phase and a slow phase, where the reactants can beapproximately considered in a quasi equilibrium. Several authors have de-termined sufficient and necessary conditions for the separation of the twotime scales in a single reaction, in the framework of the so-called standardquasi-steady state approximation (sQSSA). In the Nineties a new type ofquasi-steady state approximation, called total (tQSSA), has been proposed;it is valid in a very large range of parameters and initial conditions, muchlarger with respect to the standard QSSA. As the classical QSSA, the tQSSAcan be interpreted as the leading term of an asymptotic expansion in terms ofa suitable parameter. Starting from some papers by Palsson and coauthorsin Eighties, we link the tQSSA to the normal modes of the system of non-linear EDOs governing the reactions, aiming at determining a general ruleallowing the detection of sufficient conditions guaranteeing the separation oftime scales in more general reactions and, consequently, the determinationof the appropriate parameters for the corresponding asymptotic expansions.
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Numerical Methods andModels for Multiscale
Kinetic Equations
194
MSP - Numerical Methods and Models for Multiscale Kinetic Equations
High Order Semi-Lagrangian Schemes for theBGK Model
Maria GroppiUniversita degli Studi di Parma
Parco Area delle Scienze, 53/A 43124 - Parma [email protected]
Giovanni RussoUniversita degli Studi di Catania
Viale Andrea Doria, 6 95125 - Catania Italy
Giuseppe StracquadanioUniversita degli Studi di Parma
Parco Area delle Scienze, 53/A 43124 - Parma Italy
This talk focuses on the investigation and implementation of high ordernumerical methods for the solution of the BGK equation in kinetic theoryof rarefied gases. This equation governs the evolution of the distributionfunction of a monatomic gas, and it is a consistent approximation of theBoltzmann equation. The numerical methods are based on a semi-lagrangianformulation [3], that allows us to use larger time steps. The High order intime is obtained in two ways, namely by using Runge-Kutta methods of highorder DIRK type, or by using multi-step methods of BDF type. The latterone has the advantage of requiring less interpolation than the DIRK schemes.The High order in space is obtained by using an interpolation technique ofWENO type, preventing oscillations. Some applications of these numericalschemes will be presented. One dimensional (in space and velocity) and 3D(in velocity) problems, treated by means of the Chu reduction [1], have beeninvestigated to test the rate of convergence. The methods have been alsoextended to BGK models for mixtures of inert and reactive gases [1], [2],and reflective and diffusive boundary conditions have been also included,with high order treatment of the boundary.
1. Aimi, A. and Diligenti, M. and Groppi, M. and Guardasoni, C. 2007On the numerical solution of a BGK-type model for chemical reactions,EUR J MECH B-FLUID 26, 455-472.
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2. Andries, A. and Aoki, K. and Perthame, B. 2002 A consistent BGK-type model for gas mixtures, J. Stat. Phys. 106, 993–1018.
3. Russo, G. and Santagati, P. and Yun, S. B. 2012 Convergence of asemi-lagrangian scheme for the BGK model of the Boltzmann equation,SIAM J NUMER ANAL 50 1111-1135.
SIMAI 2014 196
MSP - Numerical Methods and Models for Multiscale Kinetic Equations
Kinetic relaxation models for reacting gasmixtures
Maria GroppiUniversita degli Studi di Parma
Parco Area delle Scienze 53/A 43124 - Parma Italy
Giampiero SpigaUniversita degli Studi di Parma
Parco Area delle Scienze 53/A 43124 - Parma Italy
Recent relaxation time-approximation models of BGK type for the kineticdescription of chemically reacting gas mixtures are briefly reviewed [1,4].In spite of their simplicity, their capability in retaining the most signifi-cant mathematical and physical properties of the Boltzmann-type kineticequations made them useful and tractable tools of investigation of chemicalreactions in rarefied gas dynamics.
As well known, the main drawback of the BGK approach is an uncorrectprediction of transport coefficients in the continuum limit. To overcomethis problem, ellipsoidal (ES) BGK models for inert mixtures have beeninvestigated [2,3]. Moving towards this direction, in this talk we presentan ES-BGK model for a slowly reacting binary gas mixture, which is ableto correctly reproduce, in the hydrodynamic limit, Fick’s law for diffusionvelocities and Newton’s law for the viscous stress.
1. Bisi, M., Groppi, M and Spiga, G. 2010 Kinetic Bhatnagar-Gross-Krook model for fast reactive mixtures and its hydrodynamic limit.Phys. Rev. E 81, 036327 1–9.
2. Brull, S., Pavan, V. and Schneider, J. 2012 Derivation of a BGK modelfor mixtures. Eur. J. Mech. B–Fluids 33, 74–86.
3. Groppi, M., Monica, S. and Spiga, G. 2011 A kinetic ellipsoidal BGKmodel for a binary gas mixture. EPL 96, 64002 1–6.
4. Groppi, M. and Spiga, G. 2004 A Bhatnagar–Gross–Krook–type ap-proach for chemically reacting gas mixtures. Phys. Fluids 16, 4273–4284.
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MSP - Numerical Methods and Models for Multiscale Kinetic Equations
Derivation of BGK models for gas mixtures
Stephane BrullUniversite Bordeaux 1
351, cours de la Liberation 33405 Talence Cedex FRANCE
This paper is devoted to the construction of a BGK operator for gas mix-tures. The construction is based as in introduced in some previous works onthe introduction of relaxation coefficients and a principle of minimizationof the entropy under constraints of moments. These free parameters arecom pared with the free parameters introduced in the Thermodynamics ofIrreversible Processes approach of the Navier-Stokes system. At the end theBGK model is proved to satisfy Fick and Newton laws.
SIMAI 2014 198
MSP - Numerical Methods and Models for Multiscale Kinetic Equations
Oxygen transport properties estimation byDSMC-CT simulations
Domenico Bruno1, Aldo Frezzotti2, Gian Pietro Ghiroldi21Istituto di Metodologie Inorganiche e dei Plasmi, Consiglio Nazionale delle
Ricerche - Via G. Amendola, 122 - 70125 Bari, Italy2Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano - Via La
Masa, 34 - 20156 Milano, Italy
Abstract. Coupling DSMC simulations with classical trajectories calcu-lations is emerging as a powerful tool to improve predictive capabilities ofcomputational rarefied gas dynamics. The considerable increase of com-putational effort oulined in the early application of the method [1] can becompensated by running simulations on massively parallel computers. Inparticular, GPU acceleration has been found quite effective in reducing com-puting time [2, 3] of DSMC-CT simulations. The aim of the present workis to study rarefied oxygen flows by modeling binary collisions through anaccurate potential energy surface, obtained by molecular beams scattering[4]. The accuracy of the method is assessed by calculating molecular oxygentransport properties following three different DSMC-CT simulation meth-ods. In the first one, non-equilibrium zero and one-dimensional rarefied gasdynamic simulations are adopted and the transport properties are computedfrom the non-equilibrium fluxes of momentum and energy. In the secondmethod, transport properties are obtained from DSMC-CT simulations ofspontaneous fluctuation of an equilibrium state [5]. In the third method thecollision trajectory calculation has been incorporated with a Monte Carlointegration procedure to evaluate the Taxman’s expressions for the trans-port properties of polyatomic gases [6]. In Figure 1, preliminary results forthe shear viscosity are compared with the experimental results by Lemmondet al. [7]. The three methods provide very close values of shear viscosity,their estimated statistical error not exceeding 3%. The experimental valuesare slightly understimated, the percentage deviation being, again, around3%.
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200 400 600 800 1000T [K]
1e-05
2e-05
3e-05
4e-05
5e-05
η [
Pa s
]
Figure 1: Shear viscosity. Solid line: Experimental results [7], © Non-equilibrium simulations, N Spontaneous fluctuations simulations, ∗ MonteCarlo evaluation of Taxman’s collision integrals.
1. K. Koura, Phys. Fluids, 9, 3543-3549 (1997).
2. D. Ferrigni, Simulation of rotational relaxation in diatomic gas byclassical trajectories on GPU’s, Masters thesis, Politecnico di Milano(2012), URL http://hdl.handle.net/10589/57042.
3. P. Norman, P. Valentini and T. Schwartzentruber,J. Comp. Phys.247, 153-167 (2013).
4. V. Aquilanti, D. Ascenzi, M. Bartolomei, D. Cappelletti, S. Cavalli,M. de C. Vitores and F. Pirani, J. Am. Chem. Soc., 121, 10794-10802(1999).
5. D. Bruno and V. Giovangigli, Physics of Fluids,, 23, 093104 (2011).
6. N. Taxman, Physical Review, 110, 1235-1239 (1958).
7. E. W. Lemmon and R. T. Jacobsen Int. J. Thermophys., 25, 21-69(2004).
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MSP - Numerical Methods and Models for Multiscale Kinetic Equations
A kinetic BGK model for a multi-componentmixture
Marlies PirnerDept. of Mathematics
Wurzburg University, Germany
Christian KlingenbergDept. of Mathematics
Wurzburg University, Germany
Gabriella PuppoUniversita degli Studi dell’Insubria
via Valleggio, 11 22100 - Como Italy
We consider a multi component gas mixture without chemical reactions as-suming that the number of particles of each species remains constant. Wewill illustrate the derived model in the case of two species. The two speciesmixture is modelled by a system of kinetic BGK equations featuring twointeraction terms on the right hand side and is motivated by physical con-siderations. We prove consistency of our model: conservation properties,H-theorem and convergence to a global equilibrium in the shape of a globalMaxwell distribution. Thus, we are able to derive the usual macroscopicconservation laws. Finally, by considering a mixture composed of ions andelectrons, we derive the macroscopic equations of ideal MHD from our model.This is joint work with Christian Klingenberg (Wurzburg University) andGabriella Puppo (Universita Insubria).
Keywords: multi-fluid mixture, kinetic model, BGK approximation, plasmaflow
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MSP - Numerical Methods and Models for Multiscale Kinetic Equations
Binary interaction algorithms for the simulation ofself-organized systems
Giacomo AlbiTechnische Univirsitat Munchen,
BoltzmannStraße, 3 85748 - Garching bei Munchen, Germany
Lorenzo PareschiUniversita di Ferrara, via Machiavelli, 35 44121, Ferrara
Microscopic models for self-organized systems take into account large num-bers of interacting individuals. Numerical resolution of large multi-agentsystems implies huge computational costs. Typically for N interacting in-dividuals we have a cost of O(N2). We tackle the problem numerically byconsidering approximated binary interaction dynamics described by kineticequations and simulating such equations by suitable stochastic methods.This approach permits us to compute approximate solutions as functions ofa small scaling parameter ε at a reduced complexity of O(Ns) operations,with Ns the sample size used to reconstruct the kinetic density. Several nu-merical results show the efficiency of the algorithms proposed and possibleextensions.
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The mathematics of learningfrom data
203
MSP - The mathematics of learning from data
Learning a set by kernel methods
Francesca OdoneDIBRIS, Universita degli Studi di Genovavia Dodecaneso, 35 16146 - Genova, Italy
Lorenzo RosascoDIBRIS, Universita degli Studi di Genovavia Dodecaneso, 35 16146 - Genova, Italy
Alessandro RudiDIBRIS, Universita degli Studi di Genovavia Dodecaneso, 35 16146 - Genova, Italy
AlessandroToigoDipartimento di Matematica, Politecnico di di Milano
Piazza Leonardo da Vinci, 32 - 20133 Milano, Italy
Ernesto De VitoDIMA, Universita degli Studi di Genovavia Dodecaneso, 35 16146 - Genova, Italy
In this talk I will present a new class of learning algorithms, which allow toestimate the minimal set where the data live on. The main idea is to embedthe data, originally described by vectors in Rd into a bigger Hilbert spaceH by means of a feature map in such a way that any closed subset of Rd isrepresented by a closed subspace in H. This closed space is hence estimatedfrom the empirical data as the linear span of the first k-eigenvectors of theempirical covariance matrix, or a smoother version of it. I will presentsome general results about the statistical consistency of the algorithm anddiscuss the role of the zero mean condition. Furthermore, I will commenton the algorithmic implementation and will present a few experiments bothon synthetic and real data.
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MSP - The mathematics of learning from data
A Unifying Framework for Multi-task Learning
Carlo CilibertoIstituto Italiano di Tecnologia
via Morego 30 16163 - Genova Italy
Youssef MrouehMassachusetts Institute of Technology
77 Massachusetts Avenue - Cambridge, USA
Tomaso PoggioMassachusetts Institute of Technology
77 Massachusetts Avenue - Cambridge, USA
Lorenzo RosascoUniversita degli Studi di Genovavia Balbi, 5 16126 - Genova Italy
Multi-task learning is widely acknowledged to be a key approach in re-ducing the amount of supervision required when distinct but related learn-ing tasks need to be solved simultaneously. The underlining idea is that thesystem should leverage on task relatedness (structure) to reduce the samplecomplexity and the amount of necessary labeled data.
In this context, a fundamental question is to develop a framework thatallows to incorporate prior information about the tasks, when available, andlearn it otherwise. A challenge is to develop the aforementioned frameworkin such a way as to induce convex learning problems that can be prov-ably solved. To this end, we investigate a regularization approach based onvector-valued reproducing kernels [?] and formulated as a kernel learningproblem. We recover most previously proposed methods as special cases.
We introduce a barrier method and notice that, by applying results fromoptimization theory, the output kernel learning problem can be solved byalternating minimization [?] or inexact block coordinate decent [?]. Thiscan be interpreted as a two step process alternating between supervised andunsupervised learning phases.
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MSP - The mathematics of learning from data
A stochastic iteration process with applications tosplitting and learning
Patrick Louis CombettesLaboratoire Jacques-Louis Lions Faculte de Mathematiques
Universite Pierre et Marie Curie - Paris 6
Jean-Christophe PesquetLaboratoire d’Informatique Gaspard Monge
Universite Paris-Est
This work investigates the properties of stochastic quasi-Fejr monotone se-quences in Hilbert spaces and emphasizes their pertinence in the study of theconvergence of block-coordinate fixed point methods. The iterative meth-ods under investigation feature random sweeping rules to select the blocksof variables that are activated over the course of the iterations and allow forstochastic errors in the evaluation of the operators. Algorithms using quasi-nonexpansive operators or compositions of nonexpansive averaged operatorsare constructed. The results are shown to yield novel block-coordinate oper-ator splitting methods for solving structured monotone inclusion and convexminimization problems. In particular, the proposed framework leads to thedesign of random block-coordinate versions of the Douglas-Rachford andforward-backward algorithms and some of their variants. Applications tolearning are discussed.
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MSP - The mathematics of learning from data
Dictionary Identification
Karin SchnassUniversity of Sassari, Computer Vision Laboratory
Porto Conte Ricerche 07041 Alghero, Italy
In this talk we give an overview over the why and how of dictionary learn-ing. After motivating two flavours of research, sparse coding, from the dataprocessing side and sparse component analysis, from the data analysis side,we focus on the theoretical results for 3 optimisation principles for dictio-nary identification. We further discuss the local and global efficiency ofthe corresponding algorithms and draw some conclusions for their use inpractice.
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MSP - The Mathematics of Learning from Data
Spectral k-Support Norm Regularization
Massimiliano PontilUniversity College London
Malet Place, WC1E, London, U.K.
The k-support norm is a regularizer which has been successfully appliedto sparse vector prediction problems. We show that it belongs to a gen-eral class of norms which can be formulated as a parameterized infimumover quadratics. We further extend the k-support norm to matrices, andwe observe that it is a special case of the matrix cluster norm. Using thisformulation we derive an efcient algorithm to compute the proximity op-erator of both norms. This improves upon the standard algorithm for thek-support norm and allows us to apply proximal gradient methods to thecluster norm. We also describe how to solve regularization problems whichemploy centered versions of these norms. Finally, we apply the matrix regu-larizers to different matrix completion and multitask learning datasets. Ourresults indicate that the spectral k-support norm and the cluster norm givestate of the art performance on these problems, signicantly outperformingtrace norm and elastic net penalties.
1. A.M. McDonald, M. Pontil, D. Stamos. New Perspectives on k-Supportand Cluster Norms. arXiv:1403.1481, 2014.
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MSP - The mathematics of learning from data
Stochastic proximal methods
Lorenzo RosascoDIBRIS, Universita di Genova
Via Dodecaneso, 35 16146 Genova - Italy
Silvia VillaLaboratory for Computational and Statistical Learning, IIT & MIT
Bldg. 46-5155, 43 Vassar Street, Cambridge, MA
Bang Cong VuLaboratory for Computational and Statistical Learning, IIT & MIT
Bldg. 46-5155, 43 Vassar Street, Cambridge, MA
In this talk I will present recent advances on the convergence properties ofa class of stochastic proximal gradient algorithms for solving minimizationproblems. These algorithms are easy to implement and suitable for solv-ing high dimensional problems thanks to the low memory requirement ofeach iteration. Moreover, they are particularly suitable for composite op-timization, where a convex objective function is the sum of a smooth anda non-smooth component. I will show that this algorithm can be naturallyapplied to solve standard online machine learning algorithms and I will focuson convergence in expectation and convergence almost surely of the iterates.
References:
• L. Rosasco, S. Villa, B.C. Vu, Convergence of a stochastic proximalgradient algorithm, arxiv:1403.5074
• L. Rosasco, S. Villa, B.C. Vu, A Stochastic forward-backward split-ting method for solving monotone inclusions in Hilbert spaces, arxiv:1403.7999
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Mathematical Applicationsfunded by the European
Union
210
MSP - Mathematical Applications funded by the European Union
Kore Hexacopter
Andrea AlaimoUniversita degli Studi di Enna Kore
Via delle Olimpiadi 94100 - Enna Italy
Valeria ArtaleUniversita degli Studi di Enna Kore
Via delle Olimpiadi 94100 - Enna Italy
Cristina MilazzoUniversita degli Studi di Enna Kore
Via delle Olimpiadi 94100 - Enna Italy
Angela RicciardelloUniversita degli Studi di Enna Kore
Via delle Olimpiadi 94100 - Enna Italy
This talk concerns the Mathematical Problems arisen within the activity ofa Project supported by the PO FESR 2007/2013 subprogram 4.1.1.1 Ac-tions to support the research and experimental development in connectionwith the production sectors, technological and production districts in areasof potentiality excellence that test high integration between universities, re-search centers, SMEs and large enterprises. The title of the Project is MezzoAereo a controllo remoto per il Rilevamento del TErritorio - MARTE and itsobjective is the realization of a multirotors system. The multirotor systemtaken into account is a hexarotor. Assuming the hexacopter as a rigid body,its dynamics is described by the Newton-Euler equations, in which rotationsare parameterized in terms of quaternions. Unlike the classical Euler-angleparameterization, they avoid gimbal lock and guarantee more efficiency andstability. A novel PID control, based on quaternions with a linear and simpleerror, is implemented on an Arduino board with a GPS system to navigateby waypoints and it is maneuvered in manually or automatically way on aselected path or according to its mission.
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MSP - Mathematical Applications funded by the European Union
A MATHEMATICAL DYNAMIC NUMERICALMODEL FOR ENERGY RECOVERY IN
WATER DISTRIBUTION NETWORK USINGPUMP AS TURBINE
Gabriele FreniUniversita degli Studi di Enna Kore
Cittadella Universitaria, 94100 - Enna Italy
Mauro De MarchisUniversita degli Studi di Enna Kore
Cittadella Universitaria, 94100 - Enna Italy
In the framework of the project SESAMO (Integrated information system forthe acquisition, management and sharing of environmental data for decisionsupport), founded European Research Project POR FESR Sicily 2007-2013– Measure 4.1.1.1, a mathematical model for analyzing water distributionnetworks, based on the Method Of Characteristic (MOC) was developed.The model is able to simulate the initial filling process, based on the hy-potheses that the air pressure inside the network is always equal to theatmospheric pressure and that the water column can not be fragmented, aswell as the steady state condition. The network model is integrated with anode demand model based on the node pressure- consumption law, whichdefines flow drawn from the network for filling the users’s tank. In complexsystems characterized by the presence of private tanks and water scarcityconditions, water managers usually apply intermittent distribution, tryingto reduce the water volumes supplied to the users and pipe leakages, or usePressure Reduction Valves (PRV) for controlling pressure in the network.The application of Pumps As Turbines (PATs) appears as an alternative andsustainable solution to either control network pressure as well as to produceenergy. In the present paper, the hydrodynamic model, already presentedby [1] was further developed introducing a specific dynamic module ableto reproduce the PATs behavior. The model was applied to a district ofPalermo network (Italy) characterized by intermittent distribution and byinequities among the user in terms of supplied water volumes. The analysisof energy recovery, carried out for a number of different scenarios, shows
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that PATs installation can lead to a very attractive economical benefit interm of energy production.
1. Freni, G., De Marchis, M. & Napoli, E. 2014 Implementation of pres-sure reduction valves in a dynamic water network model. Journal ofHydroinformatics 16(1), 207–217.
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MSP - Mathematical Applications funded by the European Union
upGraded REnewable ENergy system project
Andrea AlaimoUniversita degli Studi di Enna ”Kore”
Cittadella Universitaria, 94100 - Enna Italy
Antonio EspositoUniversita degli Studi di Enna ”Kore”
Cittadella Universitaria, 94100 - Enna Italy
Giovanni PipitoneUniversita degli Studi di Enna ”Kore”
Cittadella Universitaria, 94100 - Enna Italy
The aim of the G.RE.EN (upGraded REnewable ENergy system) project isto develop new components which are able to improve the electrical efficiencyof photovoltaic and wind power system. The project is granted by POFESR 2007 - 2013 Asse IV, Obiettivo Operativo 4.1.1 - Linea di Intervento4.1.1.2. In this project a new bucket configuration for a Darrieus helicalwind turbine with three blades is proposed. Numerical analysis was carriedout to estimate the performance of the proposed configuration by means ofthe commercial code ANSYS Fluent. Mathematical problems related to thissimulations concern the integration of the Navier-Stokes equations. Theseequations are solved by using appropriate boundary conditions along all thecontrol volume. The turbulence model adopted is the Transition SST modelbased on the Menter’s formulation. Parametric studies are performed for afixed angle of twist (30, 60and90); the results show that for 60 angle oftwist, the performance of the rotor is improved and evidence a better startingtorque. This circumstance is confirmed by static analyses performed on theproposed Darrieus wind turbine configuration.
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MSP - Mathematical Applications funded by the European Union
IPSE Project: Real Time Multi-View VideoTracking of People in Industrial Environments
Giorgio M. GrassoUniversita degli Studi di Messina
via Concezione 6-8, 98121 - Messina Italy
Alessio PlebeUniversita degli Studi di Messina
via Concezione 6-8, 98121 - Messina Italy
Within the 7th European Framework a video analysis project has been pro-posed together with industrial partners aimed at improuving safety of work-ers in chemical plants. The system designed in this project is based ona series of processing stages, based on a state-of-the-art image processingsolution specific for each stage.
The overall set of algorithmic tasks can be divided into three maingroups, according to their time scheduling, as follows:
Set 1. includes the construction of the geometric models of the cam-eras, performed in two separated steps. Both procedures are based on theminimization of the error between the computed transformation of calibra-tion points in the scene, and the corresponding image projections. The setof parameters that minimize the error are estimated with the Levenberg-Marquardt optimization algorithm.
The procedure in set 2. is performed continuously in real time, and hasthe purpose to provide a reliable model of the background. The algorithmused computes a model in the Hue-Saturation-Intensity color space, andadapts automatically the model based on a noise estimation.
The real-time analysis is by itself a sequence of several processing steps.We can again identify two groups of algorithms, depending on their schedul-ing:
• continuous running analysis;
• multi-camera fusion analysis.
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Coherent Structures andNonlinear Waves
216
MSP - Coherent Structures and Nonlinear Waves
Systems with moving boundaries
Giuseppe CocliteUniversita degli Studi di Bari
Via E. Orabona 4, 70125 Bari, Italy
We consider a system of scalar balance laws in one space dimension coupledwith a system of ordinary differential equations. The coupling acts throughthe (moving) boundary condition of the balance laws and the vector fieldsof the ordinary differential equations. We prove the existence of solutionsfor such systems passing to the limit in a vanishing viscosity approximation.The results were obtained in collaboration with Professor Mauro Garavello.
SIMAI 2014 217
MSP - Coherent Structures and Nonlinear Waves
Coherent structures and large-scale instabilities infingering convection
Francesco PaparellaUniversita del Salento
via Arnesano Km 1.2 73100 - Lecce Italy
Fingering convection is a peculiar form of convection with two buoyancy-changing scalars with different diffusivities in which the fluid is unstableeven if the overall density decreases upward. Using both direct numeri-cal simulations and analytical theory we show that the fluid self-organizesin blobs that carry the buoyancy anomalies. The appearance of the blobsis responsible for non-Gaussian tails in the probability distribution of thebuoyancy fluctuations.
At higher Reynolds number, blobs cluster together and form larger-scalestructures which are able to effectively stir the fluid. This phenomenon leadsto the formation of step-like profiles in the horizontal averages of density andof the two scalars. The formation of steps has often been attributed vaguelyto some form negative diffusion process, due to the fact that fingering con-vection carries density up-gradient. A mathematical model that describesthe dynamics of the horizontally-averaged scalar fields and the staircase-forming instabilities elucidates the proposed process of staircase formation,while avoiding the ill-posedness of naive negative-diffusion approaches.
1. von Hardenberg J. and Paparella F. 2010 Non-Gaussian buoyancystatistics in ngering convection. Phys. Lett. A 374, 2646-2653.
2. Paparella F. and von Hardenberg J. 2012 Clustering of Salt Fingers inDouble-Diusive Convection Leads to Staircaselike Stratication. Phys.Rev. Lett. 109, 014502.
3. Paparella F. and von Hardenberg J. 2014 A Model for Staircase For-mation in Fingering Convection. Acta Appl. Math. In press.
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MSP - Coherent Structures and Nonlinear Waves
Oscillating Turing patterns and spiral wavebehavior in a mathematical model for alloy
electrodeposition
Benedetto BozziniUniversita del Salento
via Monteroni, 73100 Lecce - Italy,
Deborah LacitignolaUniversita degli Studi di Cassino e del Lazio Meridionale
via di Biasio 43, 03043 Cassino - Italy
Ivonne SguraUniversita del Salento
via per Arnesano, 73100 Lecce - Italy,
Metal growth by an electrochemically controlled process is known to exhibitpeculiar instabilities that have a crucial impact on the quality of the ma-terial and on its functional properties. We consider a novel mathematicalmodel for alloy electrodeposition which accounts for the coupling betweensurface morphology and surface composition as a means for understandingthe formation of morphological patterns found in electroplating. We studyTuring and Hopf instabilities and analyse the codimension-2 Turing-Hopfbifurcation. As a result, we detect and characterize classical Turing pat-terns as well as oscillating Turing patterns. In the Hopf region, we provethe existence of spiral wave behavior and observe the emergence of complexspatio-temporal behavior via spirals break up. We investigate the modelspatio-temporal dynamics from both the analytical and numerical points ofview obtaining classes of morphogenetic scenarios in good qualitative accor-dance with experiments.
1. Bozzini B., Lacitignola D., Sgura I., 2013 Spatio-temporal organizationin alloy electrodeposition: a morphochemical mathematical model andits experimental validation. J. Solid State Electrochem. 17, 467-479.
2. Lacitignola D., Bozzini B., Sgura I., 2014 Spatio-temporal organizationin a morphochemical electrodeposition model: analysis and numericalsimulation of spiral waves. Acta Applicandae Matematicae, to appear.
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3. Lacitignola D., Bozzini B., Sgura I., Spatio-temporal organization in amorphochemical electrodeposition model: Hopf and Turing instabilitiesand their interplay, submitted.
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MSP - Coherent Structures and Nonlinear Waves
Second-grade nematic fluids and nematoacoustics
Giovanni De MatteisDepartment of Mathematics and Information Sciences
Northumbria UniversityNewcastle Upon Tyne, England, UK
There is plenty of experimental evidence that the propagation of an ultra-sonic wave in a nematic liquid crystal affects the director n, which representsthe average molecular orientation, thus producing detectable optical effects.There have been several attempts to explain these observations on the basisof a coherent variational theory. We present here a general theory for ne-matoacoustics that incorporates flow effects. Applications of the proposedtheory are also provided. Firstly, an explicit application to a simple com-putable case is given in order to estimate phenomenological parameters in-volved in the theory and by using available experimental data. In particular,propagation of plane waves is considered via linearization of the governingequations stemming from the general theory. Secondly, we introduce theequations that have been derived from the basic theory and that govern thenematoacoustic streaming in liquid crystals. Thirdly, travelling wave solu-tions are also shown in a simple one-dimensional nonlinear reduced model.Finally, if time permits, we sketch the solution for the so-called Freederickstransition by considering the coupling with an electric field.
Keywords: wave propagation, nematic liquid crystals, acoustics, varia-tional theory, Freedericks transition
References:
1. E. G. Virga, Physical Review E, Variational theory for nematoacous-tics 80, 031705 (2009)
2. G. De Matteis and E. G. Virga, Director libration in nematoacoustics,Physical Review E 83: 1-8, 011703 (2011)
3. G. De Matteis, Acoustic torque acting upon nematic liquid crystals,Acta Applicandae Mathematicae, Vol. 122, Issue 1, pag. 205-223,December (2012)
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4. G. De Matteis and L. Martina, Lie point symmetries and reductionsof one-dimensional equations describing perfect Korteweg-type nematicuids, Journal of Mathematical Physics, 53, 033101 (2012)
5. G. De Matteis and G. Napoli, Electric-field-induced density modula-tions in a nematic liquid crystal cell, SIAM Journal on Applied Math-ematics, Vol. 73, Issue 2, pag. 882-903 (2013)
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MSP - Coherent Structures and Nonlinear Waves
Heat Transfer problems in ExtendedThermodynamics
Elvira BarberaUniversita degli Studi di Messina
V.le F. DAlcontres 31 98166 - Messina Italy
Francesca BriniUniversita degli Studi di Bologna
via Saragozza, 8 40123 - Bologna Italy
The heat transfer problem is one of the simplest case of non-equilibriumthermodynamics, but in spite of its simplicity, several questions are stillopen both form the theoretical and from the experimental point of view. Inparticular, very few experimental data are available in the literature.In this talk we will consider a gas or a gas mixture confined in a boundeddomain under the assumption that the walls are kept at different temper-atures. Referring to the Extended Thermodynamics [1] approach we willstudy the non-linear effects, the role of the domain geometry and that ofthe gas rarefaction, the differences due to the materials (monoatomic orpolyatomic gases, gas mixtures) [2-4], the effects of a non inertial frame orof a rotating wall [5]. The results will be compared with experimental dataor with Monte Carlo simulations, when available. The features of the solu-tion behaviour will be analysed and the differences between Classical andExtended Thermodynamics predictions will be investigated.
1. Muller, I. and Ruggeri, T. 1998 Rational Extended Thermodynamics.Springer, New York.
2. Barbera, E. and Brini, F. 2010 On stationary heat conduction in3D symmetric domains: An application of extended thermodynamics.Acta Mechanica 215, 241-260.
3. Barbera, E. and Brini, F. 2011 Heat transfer in gas mixtures: Advan-tages of an extended thermodynamics approach. Phys. Lett. A 375(4)827-831.
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4. Barbera, E., Brini, F., Sugiyama, M. 2014 Heat transfer problem ina van der Waals gas. Acta Applicandae Mathematicae (to be pub-lished).
5. Barbera, E. and Brini, F. 2014 Frame dependence of stationary heattransfer in an inert mixture of ideal gases. To appear on Acta Me-chanica DOI: 10.1007/s00707-014-1118-0.
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Signal and image processingtechniques, and applications
225
MSP - Signal and image processing techniques, and applications
Linear and nonlinear models for electricalconduction in biological tissues
Micol Amar - Daniele Andreucci - Roberto GianniDipartimento di Scienze di Base e Applicate per l’Ingegneria - Universita di Roma
“La Sapienza”Via A. Scarpa 16, 00161 Roma, Italy
micol.amar - daniele.andreucci - [email protected]
We collect some results concerning electrical conduction problems in biolog-ical tissues. Indeed, it is well known that electric potentials can be used indiagnostic devices to investigate the properties of biological tissues. Besidesthe well-known diagnostic techniques such as magnetic resonance, X-raysand so on, it plays an important role a more recent, cheap and noninvasivetechnique known as electric impedance tomography (EIT). Such a techniqueis essentially based on the possibility of determining the physiological prop-erties of a living body by means of the knowledge of its electrical behavior([5], [6]).
The models we present here are described by means of a finely mixedperiodic medium, with a very small characteristic length, made by two differ-ent conductive regions (the intracellular and extracellular spaces), separatedby an interface (the cell membrane), which exhibits both a capacitive and aconductive behavior. Due to the biochemical structure of the cell membrane,its conductive properties can perform a linear or a nonlinear behavior. Wewill discuss these two different situations, producing in each case a “macro-scopic” or “homogenized” model, obtained letting the spatial period of themedium go to zero ([1], [3]). The asymptotic behavior of the macroscopicpotential for large times is investigated, too ([2], [4]).
1. Amar, M. and Andreucci, D. and Bisegna, P. and Gianni, R. 2004Evolution and memory effects in the homogenization limit for electricalconduction in biological tissues. Mathematical Models and Methodsin Applied Sciences 14(9), 1261–1295.
2. Amar, M. and Andreucci, D. and Bisegna, P. and Gianni, R. 2009Exponential asymptotic stability for an elliptic equation with memoryarising in electrical conduction in biological tissues. Euro. Jnl of Ap-plied Mathematics 20, 431–459.
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3. Amar, M. and Andreucci, D. and Bisegna, P. and Gianni, R. 2013A hierarchy of models for the electrical conduction in biological tissuesvia two-scale convergence: the nonlinear case. Differential and IntegralEquations (9-10) 26, 885–912.
4. Amar, M. and Andreucci, D. and Gianni, R. 2014 paper in preparation.
5. Borcea, L. 2002 Electrical impedance tomography. Inverse Problems18, R99–R136.
6. Dehghani, H. and Soni, N. K. 2005 Electrical impedance spectroscopy:theory. In Alternative breast imaging: Four model-based approaches,(ed. K.D. Paulsen, P.M. Meaney and L.C. Gilman). 85–105. Springer.
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MSP - Signal and image processing techniques, and applications
Image Contrast Enhancement by means of FuzzyTechniques
Mario VersaciUniversita degli Studi di Reggio Calabria
via Graziella Feo di Vito, 89122 - Reggio Calabria Italy
Within the image processing, the contrast enhancement represents one of themost important procedures because of the rst step of perceptible enhance-ment of the quality of an image. Technically, the procedures of contrastenhancement can be divided into two main categories. The rst, of indirecttype, modies the histogram of the image through the assignation of new val-ues of levels of grey in each pixel. Indirect approaches, already consolidatedin literature, are the histogram specication and/or equalization [1], [2]. Onthe contrary, the procedures of direct type act on the formulation of a crite-rion of measurement of the contrast: the enhancement of the quality of theimage occurs through the improving of such measure [3], [4]. The images,however, are not free from uncertainties and/or imprecision, so it appearsevident the necessity to formulate algorithms of contrast enhancement basedon fuzzy criteria. In such work, the author presents a new approach for thecontrast enhancement based on fuzzy formulations of statistical-geometricaltype exploiting synergies between statistics of growing order, entropy eval-uations and fuzzy similarities inside unitary hyper-cubes. The features, ex-tracted directly from the image under examination by means of a procedurewith a reduced computational complexity, let the procedure be automaticcharacterizing its adapteness. The results obtained are wholly comparableboth in qualitative and quantitative form with those got with consolidatedtechniques and encourage further studies in depth.
1. Rajal, J.S. 2013 An Approach for Image Enhancement Using FuzzyInference System for Noisy Image. Journal of Engiheering, Computers& Applied Sciences, 2.
2. Cheng, H.D. and Xu H. 2000 A Novel Fuzzy Logic Approach to Con-trast Enhancement. Pattern Recognition, 33, 809-819.
3. Magudeeswaran, V. and Ravichandran, C.G. 2013 Fuzzy Logic-BasedHistogram Equalization for Image Contrast Enhancement. HindawiPublishing Corporation, Mathematical Problems in Engineering, ID891864.
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4. Kannan, P., Deepa, S. and Ramakrishnan, R. 2012 Contrast Enhance-ment of Sports Images Using Two Comparative Approaches. AmericanJournal of Intelligent Systems, 2, 141-147.
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MSP - Signal and image processing techniques, and applications
Topology preservation of radial basis functions forimage registration
Roberto CavorettoUniversita degli Studi di Torino
via Carlo Alberto 10, 10123 Torino, Italy
Alessandra De RossiUniversita degli Studi di Torino
via Carlo Alberto 10, 10123 Torino, Italy
Hanli QiaoUniversita degli Studi di Torino
via Carlo Alberto 10, 10123 Torino, Italy
Bernhard QuatemberInnsbruck Medical University
Anichstr. 35, 6020 Innsbruck, Austria
Image registration consists mainly in finding a suitable transformation be-tween two images, called source and target images, taken either at differenttimes or from different sensors or viewpoints. The scope is to determinea transformation such that the transformed version of the source image issimilar to the target one. There is a large number of applications demand-ing image registration, for an overview see e.g. [2]. In this talk we focuson landmark-based image registration, in particular on the topology preser-vation of radial basis functions (RBFs) transformations. Many RBFs areused to model deformations. In [1] the performances of Gneiting’s and Wu’sfunctions are compared with the ones of other well known schemes in imageregistration, as thin plate spline and Wendland’s functions. Several numer-ical experiments and real-life cases with medical images show differences inaccuracy and smoothness of the considered interpolation methods, whichcan be explained taking into account their topology preservation properties.Here we analyze analytically and experimentally the topology preservationperformances of Gneiting’s and Matern functions, comparing results withthe ones obtained in [3], where Wendland’s and Wu’s functions are consid-ered.
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1. Cavoretto, R. and De Rossi, A. 2013 Analysis of compactly supportedtransformations for landmark-based image registration. Appl. Math.Inf. Sci. 7, 2113-2121.
2. Modersitzki, J. 2004 Numerical Methods for Image Registration. Ox-ford Univ. Press, Oxford.
3. Yang, X., Xue, Z., Lia, X. and Xiong D. 2011 Topology preservationevaluation of compact-support radial basis functions for image regis-tration. Pattern Recognition Lett. 32, 1162-1177.
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MSP - Signal and Image Processing Techniques, and Applications
A Semi-Analytic Bayesian Approach for MultipleStatic Dipoles Estimation from a Time Series of
MEG Data
Alberto SorrentinoDipartimento di Matematica, Universita degli Studi di Genova
via Dodecaneso, 35 16146 - Genova Italy
Sara SommarivaDipartimento di Matematica, Universita degli Studi di Genova
via Dodecaneso, 35 16146 - Genova Italy
Magnetoencephalography is a non-invasive functional neuroimaging tech-nique used to reconstruct neuronal currents from the weak magnetic fieldrecorded.In a dipolar model framework neuronal currents are approximated as point–like sources, difficult to estimate because of the ill-posedness of the inverseproblem and because the number of active regions is typically unknown andis usually estimated heuristically. Extending the work in [1] we present anovel Bayesian computational method that exploits the linear dependenceof the data over the dipole moment and is able to estimate the number ofactive dipoles, their location and strength, from both single topographiesand full MEG time-series under the assumption that the number of sourcesand their position are fixed over time.In particular we show that assuming a Gaussian distribution for the dipolemoment and for the noise model we can approximate the posterior distribu-tion for the number of dipoles and their location through Sequential MonteCarlo sampler and then we can compute analytically the conditional poste-rior distribution for the dipole moment.We test our method with both real and simulated data which show thatit produces good approximations with both correlated and uncorrelatedsources.
1. A. Sorrentino et al., 2014. Bayesian Multi-Dipole Modeling of a SingleTopography in MEG by Adaptive Sequential Monte Carlo Sampler.Inverse Problem 30 045010.
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MSP - Signal and image processing techniques, and applications
Beyond the BEM Solution of the M/EEGForward Problem: a Meshfree Approach
Guido Ala, Salvatore GanciDEIM, Universita degli Studi di Palermo
viale delle Scienze, Edificio 9, 90128 Palermo, Italy
[email protected], [email protected]
Gregory E. FasshauerDepartment of Applied Mathematics, Illinois Institute of Technology
10 W 32nd Street, Chicago, IL 60616, USA
Elisa FrancomanoDICGIM, Universita degli Studi di Palermo
viale delle Scienze, Edificio 6, 90128 Palermo, Italy
Michael J. McCourtDepartment of Mathematical and Statistical Sciences, University of Colorado at
Denver1250 14th Street, Suite 600, Denver, CO 80202, USA
Nowadays, the brain activity can be investigated non-invasively by meansof electromagnetic techniques, namely electroencephalography (EEG) andmagnetoencephalography (MEG). Such techniques require a typical inverseproblem to be solved. Therefore, an accurate and fast forward solver has tobe employed. As an alternative to the Boundary Element Method (BEM),which involves both complex meshing algorithms in the pre-processing stageand costly numerical integration routines, we propose the application of atruly meshfree solver for the numerical solution of the M/EEG forward prob-lem, i.e., a set of coupled boundary value problems for the 3D Laplacianoperator. The proposed method is based on the Method of FundamentalSolutions (MFS) and the Method of Particular Solutions (MPS), so it haspotential for spectral accuracy and it is integration-free. Flexibility andremarkable simplifications in the pre-processing stage are also reached. Nu-merical experiments on spherical head geometries, for which analytical or
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semi-analytical solution of the potential problem are known, show the po-tentiality of the proposed method when it is compared to the state-of-the-artBEM by considering both numerical accuracy and computational cost. Re-sults of experiments conducted on real head geometries are also shown.
1. Ala G., Di Blasi G. and Francomano E. 2012 A numerical meshless par-ticle method in solving the magnetoencephalography forward problem,International Journal of Numerical Modelling: Electronic Networks,Devices and Fields, vol. 25, pp. 428440.
2. Fairweather G. and Karageorghis A. 1998 The method of fundamentalsolutions for elliptic boundary value problems, Advances in Computa-tional Mathematics, vol. 9, pp. 6995.
3. Hmlinen M., Hari R., Ilmoniemi R. J., Knuutila J. and Lounasmaa O.V. 1993 Magnetoencephalographytheory, instrumentation, and appli-cations to noninvasive studies of the working human brain, Reviews ofModern Physics, vol. 65, pp. 413497.
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MSP - Signal and image processing techniques, and applications
Backlund Charts: commutative versusnon-commutative Equation Hierarchies
Sandra CarilloDipartimento SBAI- SEZ. Matematica, Sapienza Universita di Roma,
via A. Scarpa 16, 00161 - Rome, Italy
Mauro Lo SchiavoDipartimento SBAI- SEZ. Matematica, Sapienza Universita di Roma,
via A. Scarpa 16, 00161 - Rome, Italy
Cornelia SchieboldDepartment of Natural Sciences, Engineering and Mathematics,
Mid Sweden University, Sundsvall, Sweden
Here different Backlund Charts are considered both in the case of Commu-tative Equation Hierarchies as well as in the case of their Non-Commutativeanalogues. The aim is to point out differences and analogies[1]. Specifically,the case of the Cole-Hopf link between Burgers and Heat Equations [2, 3]and its extension to the corresponding Hierarchies are considered [4]. Fur-thermore, links connecting third order nonlinear evolution equations, suchas KdV, mKdV are analyzed, again, in both the commutative [5] and non-commutative case [6]. Notably, the latter give rise to a wider variety ofequations. Correspondingly, various different hierarchies of non- commu-tative equations are generated while, in the commutative case, there wasonly one hierarchy. Furthermore, the related recursion operators are con-sidered pointing out their peculiar properties in the non-commutative case.These properties, already directly proved in previous works, can be, now,verified on use of a computer algebra program ad hoc devised [7] to verifythe algebraic requirements which characterize recursion operators.
1. S. Carillo, C. Schiebold, M. Lo Schiavo, in progress.
2. J. D. Cole, On a quasilinear parabolic equation occuring in aerody-namics, Quart.App. Math. 92, pp.25-236,1951.
3. E. Hopf, The partial differential equation ut + uux = muuxx Comm.Pure Appl. Math., 3, pp. 201-230, 1950.
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4. S. Carillo, C. Schiebold, On the recursion operator for the noncom-mutative Burgers hierarchy, J. Nonlinear Math. Phys., 19 n.ro 1(2012).
5. S. Carillo and B. Fuchssteiner, The abundant symmetry structureof hierarchies of nonlinear equations obtained by reciprocal links. J.Math. Phys. 30, 1606–1613 (1989).
6. S. Carillo and C. Schiebold, Noncommutative KdV and mKdV hier-archies via recursion methods. J. Math. Phys. 50, 073510 (2009).
7. M. Lo Schiavo, Algebraic properties of non-commutative recursionoperators. preprint.
SIMAI 2014 236
MSP - Signal and Image Processing Techniques, and Applications
An anisotropic multiple multiresolution analysisfor image data processing
Mariantonia CotroneiUniversita degli Studi Mediterranea di Reggio Calabria
via Graziella, loc. Feo di Vito, 89122 Reggio Calabria, Italy
Milvia RossiniUniversita degli Studi di Milano-Bicocca
via Cozzi 53, 20125 Milano, Italy
Tomas SauerUniversitat Passau
Innstr. 43, 94032 Passau, Germany
The concept of multiple multiresolution analysis in L2(Rs) has recentlybeen introduced [2] as an extension of the classical wavelet setting. In suchan approach, each step of the filterbank implementation can be controlled bydifferent scaling matrices and filters, chosen from a finite dictionary, allow-ing for a directionally adapted processing of the data, so that, for example,singularities along lines can be handled. In this talk, we restrict to thebidimensional case and present a strategy for multiple filterbank construc-tion based on expanding matrices presenting anisotropic properties and verysmall determinant. This implies a considerable reduction in terms of com-putational efforts for processing image data, compared with the well-knowndiscrete shearlet transform [1]. After discussing about the filter constructionstrategy and the slope resolution property of our scheme, we will present afew examples of applications.
1. Kutyniok, G. and Sauer, T. 2009 Adaptive directional subdivision schemesand shearlet multiresolution analysis. SIAM J. Math. Anal. 41, 1436–1471.
2. Sauer, T. 2012 Shearlet Multiresolution and Multiple Refinement. In:Shearlets: Multiscale Analysis for Multivariate Data (ed. G. Kutyniokand D. Labate), 199–237. Springer.
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MSP - Signal and Image Processing Techniques, and Applications
A BeamFormer for source localization inElectroCOrticoGraphy
Annalisa PascarellaIstituto per le Applicazioni del Calcolo (IAC) M. Picone - CNR
Via dei Taurini, 19 - Roma Italy
ElectroCOrticoGraphy (ECoG) is a neuroimaging technique measuring theelectrical potential distribution produced by the neural currents by meansof a sensors grid implanted onbrain surface. Recording from the inside thebrain electrical activity provides a signal with high signal-to-noise ratio,which can be used to validate other non-invasive neurophysiological tech-niques like magneto- and electroencephalography [1]. In the last few years,some papers on methods to solve the ECoG inverse problem [2] of recon-structing the spatio-temporal distribution of the neural currents responsibleof the recorded signal are presented in literature.
This study addresses the ECoG source modelling developing a beamformermethod. First,the lead-field matrix, mapping the neural currents onto thesensors space, is created by using a new function provided by the Open-MEEG software [3]. Then, a systematic study of the numerical stabilityassociated to the ECoG inverse problem is performed by analyzing the con-dition number of the lead-field matrix. Finally, the source localization isrealized by applying a spatial lter to both synthetic data and experimentalmeasurements recorded under visual stimulation.
1. Huiskamp, Proceedings of the Second Joint., IEEE. , 2002
2. Dumpelmann et al., Human brain mapping, 2012
3. Kybic et al., IEEE Transactions on Medical Imaging, 2005
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MSP - Signal and image processing techniques, and applications
On the problem of recovering non regular surfacesfrom gridded data
Milvia RossiniUniversita di Milano-Bicocca
via Cozzi, 55 20125 - Milano Italy
In this talk we discuss the problem of recovering a non regular surface froma set of gridded data. By non regular surface, we mean that the functionunderlying the data or its gradient are discontinuous along a curve: fault inthe first case and gradient fault in the second.
This topic is of great interest in many applied problems, in fact surfaceswith discontinuity curves appears in many scientific applications includingsignal and image processing, geology, geophysics, economics, medicine. Forinstance, in the analysis of medical images as the magnetic resonance (MRI)the fault lines may indicate the presence of some pathology. In many prob-lems of geophysical interest, one has to deal with data that exhibit faults andalso gradient faults. This occurs when describing the topography of seafloorsurfaces, mountains with drainage patterns and in general the shape of ge-ological entities. In any case, discretely defined surfaces that exhibit suchfeatures can not correctly recovered without the knowledge of the position ofthe discontinuity curves and the type of discontinuity. The typical problemthat occurs is over-smoothing near gradient faults and Gibb’s phenomenumnear the faults. In general the solution of the problem consists of two steps.First we need to detect the discontinuity curve, to know the kind of discon-tinuity and to approximate it faithfully. Secondly, with these informationwe can recover the surface.
We assume that the discontinuity curve is known, and we propose aninterpolatory strategy which provides a satisfactory and effective solutionto the problem. The method is based on the Generalized Whittle–Maternkernels. Starting from these generalized kernels we construct an interpola-tory subdivision scheme based on the lagrangian function associated withthis new kernels.
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MSP - Signal and Image Processing Techniques, and Applications
Magnetic Tomography by Random SpatialSampling
Francesca PitolliDept. SBAI - Universita degli Studi di Roma ”La Sapienza”
Via Antonio Scarpa 16, 00161 Roma, Italy
The Magnetic Tomography (MT) is an imaging technique that aims at recon-structing an unknown electric current distribution flowing within a volumeconductor from the measurements of its magnetic field in the outer space.Among the other imaging techniques, MT has the advantage to be nonin-vasive and to have a high temporal resolution. For these reasons MT hasapplications in several fields, from geophysics to archeology, from nonde-structive analysis of structures to medical tomography [1].
MT devices do not give immediately an image of the electric currentthat flows in the conductor under study. Actually, to reconstruct the un-known current distribution from the magnetic data an highly ill-posed andill-conditioned inverse problem has to be solved. We propose to solve theMT inverse problem by an inversion method based on the random samplingof the source space. The main advantage of the method is the dimension-ality reduction that makes the method fast and the storage requirementsvery low. Moreover, the method can be easily applied to conductors of anyshape.
Some numerical tests showing the performances of the method on bothsynthetic and real data will be shown.
1. Wikswo J.P. 2000 Applications of SQUID magnetometers to biomag-netism and nondestructive evaluation. In Applications of Superconduc-tivity (ed. H. Weinstock) pp. 139–228. Kluwer Academic Publishers,Netherlands.
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MSP - Signal and image processing techniques, and applications
Design of a portable (CW) fNIRS embeddedsystem
Diego Agro, Gabriele Adamo, Maurizio Pinto, Riccardo Canicattı,Alessandro Tomasino, Antonino Parisi, Salvatore Stivala, Luciano
Curcio, Antonio Giordano, Costantino Giaconia, Alessandro BusaccaDEIM, Universita degli Studi di Palermo
Viale delle Scienze, Ed.9, 90128 - Palermo Italy
Diego AgroDEIM, Universita degli Studi di Palermo
Viale delle Scienze, Ed.9, 90128 - Palermo Italy
This paper deals with the design of a portable Continuous Wave (CW) func-tional Near InfraRed Spectroscopy (fNIRS) system for monitoring haemo-dynamic signals during brain activity. It can only provide oxygenated anddeoxygenated haemoglobin changes [2]. The prototype is based on a scal-able architecture composed by 8 modular probes, built on flexible stand,each one containing 4 bi-color LEDs, 16 photo-detectors and a temperaturesensor. Hardware originality is obtained by adopting Silicon PhotoMulti-plier (SiPM) optical sensors which could also increase the spatial resolutionof the fNIRS system [1]. The hardware structure allows to easily configure,thanks to an ARM microcontroller, several parameters: the switching timeand the optical power radiated by each LED; the acquisition and the work-ing voltage of each SiPM. Moreover, it is possible to choose the portion ofcerebral cortex to be analysed, by choosing the LED-SiPM couples that willbe involved in the measurement [3]. Furthermore, in order to display thehaemoglobin changes induced by brain activity (or possible diseases), rawdata are elaborated by the modified Beer-Lambert’s law and then they arefiltered through a 300 mHz low-pass filter so to reject the unwanted cardiacpulses [4]. Several preliminary functional tests were successfully carried out,thus achieving very encouraging results.
1. Adamo, G., Agro, D., Stivala, S., Parisi, A., Giaconia, C., Busacca,A.C., Mazzillo, M. C., Sanfilippo, D. and Fallica, G. 2013 Measure-ments of Silicon Photomultipliers Responsivity in Continuous WaveRegime. IEEE Transactions on Electron Devices, vol. 60, n. 11, pp.3718-3725.
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2. Rolfe, P. 2000 In Vivo Near Infra-Red Spectrophotometry Annual Re-views in Biomedical Engineering, vol. 2, pp. 315-354.
3. Sanfilippo, D., Valvo, G., Mazzillo, M., Piana, A., Carbone, B., Renna,L., Fallica, P. G., Agro, D., Morsellino, G., Pinto, M., Canicattı, R.,Galioto, N., Adamo, G., Stivala, S., Parisi, A., Curcio, L., Giaconia,C., Busacca, A. C., Pagano, R., Libertino, S. and Lombardo, S. 2014Design and development of a fNIRS system prototype based on SiPMdetectors. Photonics West 2014, Silicon Photonics IX, paper no. 8990-40.
4. Vikrant S. 2005 Near Infrared Spectroscopy: a study of celebral hemo-dynamics during breathholding and development of a system for hot-flash measurement M.S.Thesis. University of Arlington Texas
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MSP - Signal and image processing techinques, and applications
Wavelet packet as diagnostic tool: an EEG study
Alessandro Calamuneri, Angelo QuartaroneUniversity of Messina, Department of Neurosciences
via Consolare Valeria, 1 98125 - Messina Italy
[email protected], [email protected]
Simona De Salvo, Placido Bramanti, Lilla BonannoIRCCS Centro Neurolesi ”Bonino-Pulejo”
via Provinciale Palermo Ctr.da Casazza, 98124 - Messina Italy
[email protected], [email protected],
The aim of the study is to investigate a feature extraction method of anElectroencephalogram (EEG) by means of wavelet packet for discriminationof two cognitive stages: Alzheimer disease (AD) and Mild Cognitive Impair-ment (MCI) [1]. MCI is a term used to describe subjects who experiencetemporary lack of memory, but in a less severe manner if compared to AD,clinically characterized by serious impairments of memory and other cogni-tive functions. Fifty-five subjects (n=17 AD, n=19 MCI, n=19 Control),age range 72.0 ± 9.0 years have been enrolled for this study. EEG signalswere recorded from 19 electrodes in resting state condition. The idea is toemploy wavelet packet to extract two features (mean and energy coefficients)for different frequency bands ([.5−20] Hz) and 8 most significative channelsfor each group. Firstly, original EEG signals are sub-sampled and filtered.Then, signals are decomposed to the sixth level of wavelet packet transform.Finally, qualitative (Cluster Analysis) and quantitative (Mixed Effect Gen-eral Linear Model) analysis are performed to different subbands focusing onextracted features. The results demonstrate that coefficients energy betterdiscriminate cognitive impairment compared to coefficients mean, leading toa disease marker potentially able to monitor diagnosis ongoing status.
1. Jack, C. R., Albert, M. S., Knopman, D. S., McKhann, G. M., Sper-ling, R. A. and Carrillo, M. C., Thies, B. and Phelps, C. H. 2011Introduction to the recommendations from the National Institute onAging-Alzheimer’s Association workgroups on diagnostic guidelines forAlzheimer’s disease. Alzheimers Dement. 7, 257–262.
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MSP - Signal and image processing techniques, and applications
Backlund Charts: commutative versusnon-commutative Equation Hierarchies
Sandra CarilloDipartimento SBAI- SEZ. Matematica, Sapienza Universita di Roma,
via A. Scarpa 16, 00161 - Rome, Italy
Mauro Lo SchiavoDipartimento SBAI- SEZ. Matematica, Sapienza Universita di Roma,
via A. Scarpa 16, 00161 - Rome, Italy
Cornelia SchieboldDepartment of Natural Sciences, Engineering and Mathematics,
Mid Sweden University, Sundsvall, Sweden
Here different Backlund Charts are considered both in the case of Commu-tative Equation Hierarchies as well as in the case of their Non-Commutativeanalogues. The aim is to point out differences and analogies[1]. Specifically,the case of the Cole-Hopf link between Burgers and Heat Equations [2, 3]and its extension to the corresponding Hierarchies are considered [4]. Fur-thermore, links connecting third order nonlinear evolution equations, suchas KdV, mKdV are analyzed, again, in both the commutative [5] and non-commutative case [6]. Notably, the latter give rise to a wider variety ofequations. Correspondingly, various different hierarchies of non- commu-tative equations are generated while, in the commutative case, there wasonly one hierarchy. Furthermore, the related recursion operators are con-sidered pointing out their peculiar properties in the non-commutative case.These properties, already directly proved in previous works, can be, now,verified on use of a computer algebra program ad hoc devised [7] to verifythe algebraic requirements which characterize recursion operators.
1. S. Carillo, C. Schiebold, M. Lo Schiavo, in progress.
2. J. D. Cole, On a quasilinear parabolic equation occuring in aerody-namics, Quart.App. Math. 92, pp.25-236,1951.
3. E. Hopf, The partial differential equation ut + uux = muuxx Comm.Pure Appl. Math., 3, pp. 201-230, 1950.
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4. S. Carillo, C. Schiebold, On the recursion operator for the noncom-mutative Burgers hierarchy, J. Nonlinear Math. Phys., 19 n.ro 1(2012).
5. S. Carillo and B. Fuchssteiner, The abundant symmetry structureof hierarchies of nonlinear equations obtained by reciprocal links. J.Math. Phys. 30, 1606–1613 (1989).
6. S. Carillo and C. Schiebold, Noncommutative KdV and mKdV hier-archies via recursion methods. J. Math. Phys. 50, 073510 (2009).
7. M. Lo Schiavo, Algebraic properties of non-commutative recursionoperators. preprint.
SIMAI 2014 245
MSP - Signal and image processing techniques, and applications
Applications of sampling Kantorovich operators toImage Processing
Danilo CostarelliDepartment of Mathematics and Physics
Universita degli Studi Roma Tre
Gianluca VintiDipartimento di Matematica e Informatica
Universita degli Studi di Perugiavia Vanvitelli 1, 06123 Perugia
In this talk, we present the theory of multivariate sampling Kantorovichoperators and their applications to image processing [1, 4, 5]. In particular,applications to thermographic images for civil engineering and to medicalimages will be shown, see e.g., [3]. The above discrete operators are definedby:
(Swf)(x) =∑k∈Zn
χ(wx−tk)
[wn
Ak
∫Rw
k
f(u) du
](x ∈ Rn, w > 0), (I)
where χ : Rn → R is a kernel function satisfying the usual assumptions of theapproximate identities, tk = (tk1 , ..., tkn), (tki)ki∈Z, i = 1, 2, ..., n, are strictly
increasing sequences of real numbers, Rwk :=[tk1w ,
tk1+1
w
]×[tk2w ,
tk2+1
w
]×
... ×[tknw ,
tkn+1
w
], and Ak := ∆k1 · ∆k2 · ... · ∆kn with ∆ki := tki+1 − tki ,
i = 1, 2, ..., n. The function f : Rn → R is a locally integrable functionsuch that the above series is convergent for every x ∈ Rn. First, the theo-retical approximation results involving bounded continuous and uniformlycontinuous functions are discussed, together with a modular approximationtheorem for functions belonging to Orlicz spaces (see e.g., [2]). The algo-rithm for image reconstruction based on sampling Kantorovich operators isdescribed and several numerical examples and applications are shown.
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Recent advances on thetheory and applications ofSemi-Lagrangian methods
247
MSP - Recent advances on the theory and applications of Semi-Lagrangian methods
A Semi-Lagrangian scheme for a degeneratesecond order Mean Field Game system
Elisabetta CarliniSapienza Universita di Roma
Piazzale Aldo Moro, 5 00185 Roma Italy
Francisco J. SilvaXLIM, Universite de Limoges
Avenue Albert Thomas, 123 87060 Limoges, France
We present a fully discrete Semi-Lagrangian approximation of a second orderMean Field Game system, which can be degenerate. We prove that theresulting scheme is well posed and, if the state dimension is equal to one,we prove a convergence result. Some numerical simulations are provided,evidencing the convergence and the difference between the nume-rical resultsfor the degenerate and non-degenerate cases.
1. E. Carlini and F. J. Silva, 2014 A Fully Discrete Semi-LagrangianScheme for a First Order Mean Field Game Problem, SIAM J. Numer.Anal. 52-1, 45–67.
2. E. Carlini and F. J. Silva, 2013 Semi-Lagrangian schemes for meanfield game models, 52nd IEEE Conference on Decision and ControlDecember, 3115–3120.
3. E. Carlini and F. J. Silva, 2014 A Fully Discrete Semi-LagrangianScheme for a Second Order Mean Field Game Problem, arXiv:1404.5932.
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MSP - Recent advances on the theory and applications of Semi-Lagrangian methods
Semi-Lagrangian methods for parabolic problemsin divergence form
Luca BonaventuraMOX - Politecnico di Milano
Via Bonardi 9, 20133 - Milano Italy
Roberto FerrettiUniversita degli Studi Roma Tre
L.go S. Leonardo Murialdo 1, 00146, Roma, Italy
Luca BonaventuraMOX - Politecnico di Milano
Via Bonardi 9, 20133 - Milano Italy
Semi-Lagrangian methods have traditionally been developed in the frame-work of hyperbolic equations, but several extensions of the SL approach todiffusion and advection–diffusion problems have been proposed recently, seee.g. [1],[2]. These extensions are mostly based on probabilistic argumentsand share the common feature of treating second-order operators in traceform, which makes them unsuitable for for classical formulations of turbulentdiffusion employed in computational fluid dynamics and for mass conserva-tive models. We propose here some basic ideas for treating second-orderoperators in divergence form. A general framework for constructing con-sistent schemes in one space dimension is presented, and a specific case ofnonconservative discretization is discussed in detail and analysed. Finally,an extension to problems in an arbitrary number of dimensions is proposed.Although the resulting discretization approach is only of first order in time,numerical results in a number of test cases highlight the advantages of thesemethods for applications to computational fluid dynamics and their superi-ority over to more standard low order time discretization approaches.
1 Ferretti, R. 2010 A technique for high-order treatment of diffusionterms in semi-Lagrangian schemes. Comm. Comp. Phys. 8, 445–470.
2 Falcone, M. and Ferretti, R. 2013 Semi-Lagrangian ApproximationSchemes for Linear and Hamilton-Jacobi Equations. SIAM
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MSP - Recent advances on the theory and applications of Semi-Lagrangian methods
Semi-Lagrangian approximation schemes fornon-Lambertian Shape-from-Shading models
Silvia TozzaSapienza - Universita di Roma
P.le Aldo Moro, 5 00185 - Roma Italy
Shape-from-Shading (SfS) is a classical problem in computer vision. Ituses the brightness variation in a single image to compute the three dimen-sional shape of a surface and leads to a nonlinear partial differential equation(PDE) of the first order [3, 2]. Two tasks have to be accomplished in solvingthe SfS problem. The first is to formulate an imaging model that describesthe relation between the surface shape and the image brightness. This re-lation should consider the three components of the problem which are thecamera, the light source and the surface reflectance. After establishing theimaging model, a numerical algorithm has to be developed to reconstructthe shape from the given image. In this talk we focus our attention on thislast numerical issue, fixing orthographic projection of the scene, one lightsource located at infinity and choosing three reflectance models (the clas-sical Lambertian model and two of non-Lambertian type [1], namely thediffuse Oren–Nayar model [4] and the specular Phong model [5]). We con-struct a semi-Lagrangian scheme corresponding to each PDEs coming out,analyzing the properties of the operators involved. Then, a comparison oftheir performance will be given in terms of some error indicators on seriesof benchmarks images.
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Bibliography
[1] A.H. Ahmed and A.A. Farag, Shape from Shading Under Various Imag-ing Conditions, IEEE Conference on Computer Vision and PatternRecognition, pp. 1–8, 2007.
[2] J.D. Durou, M. Falcone and M. Sagona, Numerical Methods for Shapefrom Shading: a new survey with benchmarks Computer Vision andImage Understanding, Elsevier, 109(1), 22–43, 2008.
[3] B.K.P. Horn and M. J. Brooks, Shape from Shading, The MIT Press,1989.
[4] M. Oren and S.K. Nayar, Generalization of the Lambertian model andimplications for machine vision, International Journal of Computer Vi-sion, 14(3): 227–251, 1995.
[5] B.T. Phong, Illumination for computer generated pictures, Communi-cations of the ACM, 18(6): 311–317, 1975.
251
MSP - Recent Advances on the Theory and Applications of Semi-Lagrangian Methods
Fast Semi-Lagrangian Schemes forHamilton-Jacobi-Bellman Equations
Simone CacaceDipartimento di Matematica, Sapienza – Universita di Roma
P.le Aldo Moro, 5 00185 - Roma Italy
Emiliano CristianiIAC–CNR
Via dei Taurini, 19 00185 - Roma Italy
Maurizio FalconeDipartimento di Matematica, Sapienza – Universita di Roma
P.le Aldo Moro, 5 00185 - Roma Italy
Hamilton-Jacobi-Bellman (HJB) equations arise in several contexts, includ-ing optimal control problems for nonlinear ordinary differential equationswith state/control constraints. Unfortunately, when the state dimension islarger than three, both single-pass and iterative numerical methods for HJBequations are hardly usable since they require a huge computational effortand memory allocation.
In this talk we investigate the possibility to use the Fast Iterative Method(FIM) [3] for solving general HJB equations and we compare the resultswith a new accelerated version of the Fast Sweeping Method (FSM) [4]. Wefind that FIM can be indeed used to solve HJB equations with no relevantmodifications with respect to the original algorithm proposed for the eikonalequation, and that it overcomes FSM in many cases.
Observing the evolution of the active list of FIM, we recover anothernumerical validation of the arguments recently discussed in [2] about theimpossibility of creating local single-pass methods for HJB equations.
1. Cacace, S., Cristiani, E. and Falcone, M. 2014 Two semi-Lagrangianfast methods for Hamilton-Jacobi-Bellman equations, submitted to Proc.IFIP 2013.
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2. Cacace, S., Cristiani, E. and Falcone, M. 2014 Can local single-passmethods solve any stationary Hamilton-Jacobi-Bellman equation?, SIAMJ. Sci. Comput. 36, A570–A587.
3. Jeong, W.-K. and Whitaker, R.T. 2008 A fast iterative method foreikonal equations, SIAM J. Sci. Comput. 30, 2512–2534.
4. Tsai, Y., Cheng, L., Osher, S. and Zhao, H. 2004 Fast sweeping al-gorithms for a class of Hamilton-Jacobi equations, SIAM J. Numer.Anal. 41, 673–694.
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MSP - Recent advances on the theory and applications of Semi-Lagrangian methods
Experiments on adaptive semi-Lagrangianadvection
in a DG framework
Giovanni TumoloThe Abdus Salam ICTP
Strada Costiera 11, 34151 - Trieste Italy
Luca BonaventuraMOX - Politecnico di Milano
Via Bonardi 9, 20133 - Milano Italy
Advection experiments are shown in the context of a high-order Discon-tinuous Galerkin semi-Lagrangian technique, with a focus on atmosphericapplications.
Discontinuous Galerkin methods are high order schemes that allow highflexibility but their combination with standard explicit time integrators ischaracterized by strong stability restrictions, a significant limitation if nu-merical weather prediction or even climate applications are envisaged.
The combination of DG methods with the semi-Lagrangian techniqueprovides an unconditionally stable discretization for advection, which is rel-evant for such geophysical applications [1].
We present some numerical experiments on advection both in Cartesianand spherical geometry, where the efficiency of the semi-Lagrangian DGdiscretization is improved through the introduction of a p-adaptivity strat-egy to effectively adapt the number of degrees of freedom employed in eachelement, taking advantage of the locality typical of DG and of the use ofhierarchical bases [2], [3], [4].
1. Restelli M., Bonaventura L., Sacco R. 2006 A semi-Lagrangian discon-tinuous Galerkin method for scalar advection by incompressible flows.J. Comput. Phys. 216, 195–215.
2. Tumolo G., Bonaventura L., Restelli M. 2013 A semi-implicit, semi-Lagrangian, p-adaptive discontinuous Galerkin method for the shallowwater equations. J. Comput. Phys. 232, 46–67.
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3. Tumolo G., Bonaventura L. 2014 An accurate and efficient numericalframework for adaptive numerical weather prediction. Report MOX18/2014 (submitted to Quarterly J. Royal Met. Soc.).
4. Bonaventura L., Ferretti R. 2014 Semi-Lagrangian methods for parabolicproblems in divergence form. Report MOX 19/2014 (submitted toSIAM J. Sci. Comp.).
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High order schemes fornonlinear evolutionary
Partial Differential Equations
256
MSP - High order schemes for nonlinear evolutionary Partial Differential Equations
High order semi-implicit schemes for evolutionarynon linear partial differential equations and
applications
Sebastiano BoscarinoUniversita degli Studi di Cataniavia A. Doria, 95125 Catania, Italy
Giovanni RussoUniversita degli Studi di Cataniavia A. Doria, 95125 Catania, Italy
Several systems of evolutionary partial differential equations may con-tain stiff terms, which require an implicit treatment. Typical examples arehyperbolic systems with stiff hyperbolic or parabolic relaxation and kineticequations in regimes close to fluid dynamic limit. In many cases, the stiffterms are clearly identified. For example, in hyperbolic systems with hyper-bolic relaxation, the hyperbolic term is usually non stiff, while the relaxationterm is stiff. A natural way to treat such systems is to adopt implicit-explicitschemes, in which the relaxation is treated by an implicit scheme, while thehyperbolic part is treated explicitly. In several cases, however, such a dis-tinction is not so clear. For example, in the case of hyperbolic systems withdiffusive relaxation, a standard approach would lead to schemes, which inthe stiff limit suffer from classical parabolic CFL restriction. Such systemscan be treated by a penalization method, consisting in adding and subtract-ing the same term, so that the system appears as the limit relaxed systemplus a small perturbation. There are cases, however, in which stiff terms arenot just additive, and the penalization method is not particularly effective,since the limit system itself is not easily solvable by standard techniques.For many such systems, we present a new approach, which includes par-titioned and additive approach. It consists in identifying the linearly stiffdependence of the system on the unknown variable. Only this linear de-pendence will be treated implicitly, while the rest of the system is treatedexplicitly. This approach generalizes classical IMEX schemes based on ad-ditive or partitioned Runge-Kutta methods, and allows the construction ofhigh order linearly implicit schemes, which are much simpler to use thanfully implicit ones. Several examples will be presented.
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MSP - High order schemes for nonlinear evolutionary Partial Differential Equations
Time integration schemes for semidiscreteapproximation of multiscale hyperbolic systems
Giovanni NaldiUniversita degli Studi di Milano
via Saldini, 50 20133 - Milano Italy
Fausto CavalliUniversita degli Studi di Milano Bicocca
Piazza dell’Ateneo Nuovo, 1 20126 - Milano Italy
In this talk we compare and study several numerical approaches for timeintegration in order to obtain all-speed, asymptotic preserving and uncon-ditionally stable numerical schemes for hyperbolic systems containing stirelaxation source terms [1, 2, 3, 4]. Such models arise in many physicalproblems, as in the modelling of multiphase flows involving phase transi-tions, kinetic-type phenomena, semiconductor devices, and biological sys-tems. As an example, we can mention isentropic Euler equations, Eulerequations with linear friction, radiative transfert models, Euler-Poisson sys-tems. The presence of the sti relaxation term allows to describe distinctphysical time-scales terms, which can exhibit different behaviours, from hy-perbolic to diffusive regime. The study and the numerical approximation ofthese models is particularly challenging, as several aspects have to be han-dled. We present several numerical experiments and comparisons togetherwith some preliminary theoretical results and considerations.
1. Cavalli, F. and Naldi, G. and Puppo, G. and Semplice, M. 2007. High-order relaxation schemes for nonlinear degenerate diusion problems.SIAM Journal on Numerical Analysis, 45(5), 2098-2119.
2. Cordier, F. and Degond, P. and Kumbaro, A. 2012. An asymptotic-preserving all-speed scheme for the euler and navier-stokes equations.Journal of Computational Physics. 231(17), 5685-704.
3. Haack, J. and Jin, S. and Liu, J. 2012, An all-speed asymptotic-preserving method for the isentropic Euler and Navier-Stokes equa-tions. Communications in Computational Physics. 12(4), 955-980.
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4. Jin, S. and Pareschi, L. and Toscani, G. 2001 Uniformly accurate diu-sive relaxation scheme for multiscale transport equations. SIAM Jour-nal on Numerical Analysis. 38(3), 913-36.
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MSP - High order schemes for nonlinear evolutionary Partial Differential Equations
Implicit-Explicit Runge-Kutta schemes for optimalcontrol problems and applications to hyperbolic
system with relaxation
Giacomo AlbiTechnische Univirsitat Munchen,
BoltzmannStraße, 3 85748 - Garching, Germany
Implicit-explicit (IMEX) Runge-Kutta methods play a major rule in thenumerical treatment of differential systems governed by stiff and non-stiffterms. In this talk we discuss order conditions and symplecticity propertiesof a class of IMEX Runge-Kutta methods in the context of optimal controlproblems. Using suitable transformations of the adjoint equation, orderconditions up to order three are proven as well as the relation betweenadjoint schemes obtained through different transformations is investigated.Conditions for the IMEX Runge-Kutta methods to be symplectic are alsoderived. We finally present some applications of the developed schemes tohyperbolic systems of partial differential equations with relaxation.
Joint work with L. Pareschi (Universita di Ferrara), C. Jorres, M. Hertyand S. Steffensen (RTWH Aachen).
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MSP - High order schemes for nonlinear evolutionary Partial Differential Equations
High order exponential schemes for nonlinearFokker-Planck equations
Lorenzo PareschiUniversita di Ferrara, via Machiavelli, 35 44121, Ferrara
In this talk we present some recent results on the construction of high-orderexponential schemes for nonlinear Fokker-Planck equations. The schemesare able to avoid the parabolic stiffness and to achieve the asymptotic-preserving property at the cost of an explicit method. The main advantagecompared to IMEX methods is the possibility to achieve very high orderaccuracy without introducing additional order conditions. Applications tothe Landau equation of plasma physics are presented.
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Mathematical Problems frommicro and nano-electronics
industry
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MSP - Mathematical Problems from micro and nano-electronics industry
Analytical and numerical characterization of thespin-wave properties emitted in a spintronic
nano-waveguide
Giancarlo ConsoloUniversita degli Studi di Messina
Dipartimento di Matematica e InformaticaViale F. Stagno D’Alcontres, 31 98166 - Messina Italy
Spin-wave dynamics induced by the combined action of magnetic fields andelectric currents have been receiving a great deal of attention from the-oreticians and experimentalists for the intriguing properties exhibited bythe nano-sized devices where such magnetization dynamics are observed [2]as well as for their industrial applications [3]. In this work we consider aferromagnetic heterostructure in the form of a one-dimensional waveguide.In this geometry, a localized excitation via an electric current favors theemission of spin-waves which are conveyed along the axis of the guide. Thefunctional dependence of the main characteristic wave parameters (thresholdcurrent, frequency, wavenumber and decay length) is analyzed as a functionof the size of the nanocontact area through which the electric current is in-jected. From the analytical viewpoint, such a goal has required to solve theLandau-Lifshitz-Gilbert-Slonczewski equation [4] together with boundaryand matching conditions associated to the waveguide geometry [1]. Owingto the complexity of the resulting transcendent system, particular solutionshave been obtained in the cases of elongated and contracted nanocontacts.These results have been successfully compared with those arising from nu-merical integration of the abovementioned system and with micromagneticsimulations based on finite-differences methods.
1. Consolo, G et al. 2013 Excitation of spin waves by a current-drivenmagnetic nanocontact in a perpendicularly magnetized waveguide. Phys.Rev. B 88, 014417.
2. Madami, M et al. 2011 Direct observation of a propagating spin waveinduced by spin-transfer torque. Nature Nanotechnolology 6, 635–638.
3. Slavin, A and Tiberkevich, V 2009 Nonlinear Auto-Oscillator Theoryof Microwave Generation by Spin-Polarized Current. IEEE Trans.Magn. 45, 1875–1918.
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4. Slonczewski, J.C. 1996 Current-driven excitation of magnetic multi-layers. J. Magn. Magn. Mater. 159, L1–L7.
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Particle Laden TurbulentShear Layers
265
MSP - Particle Laden Turbulent Shear Layers
On the importance of modeling the fluidacceleration term in a particle laden, compressible
turbulent boundary layer
Jorn SesterhennTechnische Universitat Berlin
Muller-Breslau-Straße 12, 10623 Berlin, Germany
Flavia Cavalcanti MirandaTechnische Universitat Berlin
Muller-Breslau-Straße 12, 10623 Berlin, Germany
Arne HeinrichTechnische Universitat Berlin
Muller-Breslau-Straße 12, 10623 Berlin, Germany
Numerical computations of turbulent flows customary just use the most ob-vious term
dup,idt = −1/τp (up,i − uf,i) of the Maxey Riley equation to model
the fluid forces acting upon a particle. We found the fluid acceleration termρf
Duf,iDt is equally important or even dominant in shock particle interaction
[1,2]. Recently was reported that the basset history force is important inisotropic turbulence and in sedimentation processes in two dimensional con-vection flows [3]. It turns out that both terms are customarily neglectedeither on ground of mere convenience or difficulties in computing them.Here we present a study which aims at pointing out the importance of thefluid acceleration term in a turbulent boundary layer at Reδ99,in = 4700and Ma = 0.8 on a flat plate. The Reynolds number is based on the inletboundary layer thickness.
Our particle to fluid density ratio ρp/ρf is around 2000, the Stokes num-ber based on the inlet conditions is St ≈ 0.2 and we have a volume fractionof order O(10−4).
The turbulent compressible boundary layer is simulated with a characteristic-type formulation of [4], high order compact finite difference schemes and aRunge-Kutta of fourth order for time integration.
1. Guseva, K., Feudel, U., and Te’l, T. (2013). Influence of the historyforce on inertial particle advection: Gravitational effects and horizon-tal diffusion. Phys. Rev. E, 88:042909.
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2. Miranda, F. C., Heinrich, A., and Sesterhenn, J. (2013). The influenceof the fluid acceleration term on the simulation of a particle-laden com-pressible jet with shock waves. In European Turbulence Conference14.
3. Olivieri, S., Picano, F., Sardina, G., Iudicone, D., and Brandt, L.(2014). The effect of the basset history force on particle clustering inhomogeneous and isotropic turbulence. arXiv:1401.5309 [physics.flu-dyn].
4. Sesterhenn, J. (2001). A characteristic - type formulation of theNavier-Stokes equations for high order upwind schemes. Computers& Fluids, 30(1):37-67.
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MSP - Particle Laden Turbulent Shear Layers
Exact regularized point particle method forparticle-laden flows in the two-way coupling
regime: application to turbulent free shear flows
P. Gualtieri1, F. Battista1, F. Picano2, C.M. Casciola1
1Dipartimento di Ingegneria Meccanica e Aerospaziale, Universita di Roma LaSapienza Via Eudossiana 18, 00184 Roma Italy.
2Dipartimento di Ingegneria Industriale, Universita degli studi di Padova, Via
Venezia 1, 35131 Padova, Italy.
Abstract : In this paper we present a new methodology which captures themomentum exchange between a carrier turbulent flow and hundred thou-sands of small inertial particles. The velocity disturbance produced by thedisperse phase is described analytically in terms of an exact regularizedunsteady Stokes solution. Results for actual turbulent flows laden withsub-Kolmogorov particles are discussed and the turbulence modulation isaddressed in two typical free shear flow configurations, e.g. a homogeneousshear flow and a round jet.
The effect of turbulent transport on particle dynamics has been exten-sively studied in many flow configurations. Much less is known about theeffect of the disperse phase on the carrier flow demanding for a renewedeffort in this direction, see e.g. [1]. In the so-called two-way coupling regimethe particles volume fraction is still small to neglect particle/particle col-lisions and hydrodynamic interactions but the mass loading on the fluidmight result of order one due to large density ratios. In such conditions themomentum exchange between the two phases is not negligible and must beproperly accounted for.
Modeling the back reaction in numerical simulations is an issue. Thelocal distortion of the carrier flow due to the disperse phase can be capturedonly resolving the boundary of each particle on the computational grid. Inthe so-called resolved particle simulations several approaches have been pro-posed to enforce the non slip boundary conditions on the particle boundary,see e.g. [2]. Alternative approaches are possible once recognized that theflow close to a small particle can be locally approximated by a Stokes Flow,[6, 4].
The approaches discussed so far, are feasible only for a relatively smallnumber of large particles i.e. of particles whose diameter dp is larger thanthe smallest fluid scale, i.e. the Kolmogorov scale η. However in many
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applications hundred thousands of small particles are carried by the flow andsuch methods can not be pursued. Our new approach is intended to describethe inter-phase momentum coupling for particles whose size ranges from sub-Kolmogorov dimensions up to a few Kolmogorov scales where physicallysound and computational efficient approaches are still lacking.
The inter-phase momentum coupling is achieved in terms of an exact so-lution of the local unsteady Stokes flow around each particle. In a nutshell, itis possible to evaluate in a closed analytical form the vorticity that each par-ticle generate along its trajectory. Due to viscous diffusion the disturbancevorticity reaches length-scales comparable to the smallest hydrodynamicalscales where the disturbance field can be transfered and represented on thecomputational grid where the Navier-Stokes equations of the carrier fluid aresolved. The momentum coupling between the two phases is based on thisphysical mechanisms and does not require any “ad hoc” numerical artifacts.In fact, due to the small value of the particle Reynolds number, the distur-bance flow produced particle is well described by the incompressible Stokesequations, ∂tv−ν∇2v+∇p = F , where F(x, t) = −D(t) δ [x− xp(t)] is the(singular) force that the particle exerts back on the fluid. D(t) is the hydro-dynamic force, δ(x) is the Dirac delta function and xp(t) the actual positionof the pth particle. To regularize the effects of the singular back-reaction onthe fluid we exploit the localization operated by the intrinsic diffusion of thevorticity field generated by the particle motion ζ = ∇× v,
∂ζ
∂t− ν∇2ζ = ∇× F = D(t)×∇δ [x− xp(t)] . (3)
The regularization procedure is based on a temporal cut-off εR such thatthe vorticity is additively split into a regular and a singular component,ζ(x, t) = ζR(x, t, ε)+ζS(x, t, ε). It is easy to derive the differential equationsatisfied by ζR(x, t) namely
∂ζR∂t− ν∇2ζR = −∇×D(t− εR)g [x− xp(t− εR), εR] , (4)
with g(x, ξ, t, τ) =(2πσ2
)−3/2exp
(−|x− ξ|2/2σ2
)is the fundamental solu-
tion of the heat equation with time dependent variance σ(t−τ) =√
2ν(t− τ).The singular part of the vorticity field is not neglected but is accounted forat later times when the singular field had enough time to diffuse and reachlength-scales comparable with the grid size. Given its smoothness propertiesthe field ζR(x, t) can be represented on a discrete grid, provided the gridsize ∆ is comparable with the smallest scale of the field σR(εR) thus achiev-ing the coupling with the carrier phase. In fact, the vorticity field given by
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eq.(4) provides the regularized disturbance produced by a small sphericalparticle experiencing the drag force D(t).
In the left panel of figure (2) we exploit the potential of the ERPPin dealing with actual turbulent flows. Here we present the data of anhomogeneous shear flow at a Taylor Reynolds number of Reλ = 60. Thecarrier phase is resolved by using Nx ×Ny ×Nz = 256× 256× 128 Fouriermodes in a 4π×2π×2π periodic box. The flow is laden with Np = 2.200.000inertial particles with diameter dp = 0.1η. The particle to fluid density ratiois ρp/ρf = 1800 corresponding to a particle Stokes time τp = (ρp/ρf ) d2p/18νequal to the Kolmogorov time scale τη, i.e. Stη = τp/τη = 1. The mass loadof the disperse phase is Φ = 0.4 where Φ is the ratio between the mass ofthe disperse phase and the carrier fluid. In the right panel of figure (2) wepresent a snapshot of the particle position in a xy plane containing the meanflow. As expected particles with Stη = 1 are characterized by small scaleclusters. Note also the preferential alignment of the aggregates accordingto the principal strain direction of the mean flow which is the signatureof the small scale anisotropy of the clusters. In the context of the ERPPmethodology we are able to compute in a closed analytical form the forcingoperated by the particles on the fluid which is reported as a contour plot inthe figure.
In the right panel of (2) we present an snapshot of the particle config-uration in a turbulent round jet operated at a Reynolds number of 1500.The carrier flow is resolved in a cylindrical domain 2π × 17R × 30R in theazimuthal, radial and axial direction respectively by means of a standardstaggered finite difference scheme as appropriate for incompressible flows.The jet inlet is provided by a companion simulation of a turbulent pipe flowwhich allows for realistic inflow conditions. The particles are injected at theinlet with a velocity matching the local fluid velocity. The mass loading,now defined as the ratio of particle-to-fluid mass throughput, is 0.4.
In the present contribution we will provide a detailed analysis of theturbulence modulation in the limit of dp/η → 0 by comparing the resultsobtained with the ERPP against the particle-in-cell approach [3, 5].
References
1. S. Balachandar and J.K. Eaton. Turbulent dispersed multiphase flow.Ann. Rev. Fluid Mech, 42: 111-133, 2010.
2. T.M. Burton and J.K. Eaton. Fully resolved simulations of a particle-turbulence interaction. J. Fluid Mech., 545: 67-111, 2005.
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3. Z. Zhang and A. Prosperetti. A second order method for three dimen-sional particle simulation. J. Comp. Phys., 210: 292-324, 2005.
4. P. Gualtieri, F. Picano, G. Sardina and C.M. Casciola. Clustering andturbulence modulation in particle-laden shear flow. J. Fluid Mech.,715: 134-162, 2013.
5. M.R. Maxey and B.K. Patel. Localized force representations for par-ticles sedimenting in Stokes flow. Int. J. Mult. Flow, 27: 1603-1626,2001.
6. F. Picano, G. Sardina, P. Gualtieri, CM Casciola. Particle-laden jets:particle distribution and back-reaction on the flow. 318(5): 052018,2011.
7. Z. Zhang and A. Prosperetti. A second order method for three dimen-sional particle simulation. J. Comp. Phys., 210: 292-324, 2005.
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Figure 2: Left: Snapshot of the instantaneous particles position and corre-sponding intensity of the forcing on the fluid (contour plot) in a thin slicealong the xy plane. The mean flow S y is in the x direction from left to right.Right, snapshot of the particle configuration and instantaneous intensity ofthe fluid axial velocity (contour plot).
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MSP - Particle Laden Turbulent Shear Layers
Particle statistics in turbulent channel flows withwall-roughness.
Barbara MiliciUniversita degli Studi di Enna “Kore”via delle Olimpiadi, 94100 - Enna Italy
Mauro De MarchisUniversita degli Studi di Enna “Kore”via delle Olimpiadi, 94100 - Enna Italy
Gaetano SardinaUniversita degli Studi di Enna “Kore”via delle Olimpiadi, 94100 - Enna Italy
Enrico NapoliUniversita degli Studi di Palermo
via delle Scienze, 90128 - Palermo Italy
Particle dynamics results in turbulent channel flows characterized by flatand rough walls will be shown in our talk. The two different flat and roughchannel configurations laden with particles have been analyzed by means ofDirect Numerical Simulation (DNS) to fully resolve the complex and multi-scale three-dimensional turbulent flow. Particle deposition and resuspen-sion mechanisms at the wall turbulent flows are dominated by the coherentvortical structures arising in the inner region. These turbulent structures,which control the turbulent regeneration cycles, are strongly affected by theroughness of the wall. Particle dynamics in flat channels is characterizedby a classical phenomenology named turbophoresis consisting in the pref-erential particle accumulation at the wall. Turbophoresis is investigated ina quantitative way as a function of the particle inertia. We show that wallroughness inhibits particle turbophoresis at the wall resulting in an increaseof the particle mass flux through the channel section with respect to the flatconfiguration. Particle statistics, in term of mean particle concentration andprobability density function of wall-normal particle velocity, show that theroughness produces a completely different scenario compared to the classicalsmooth wall, see [1] for a more detailed description.
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1. Milici B., De Marchis M., Sardina G. and Napoli E. 2014 Effects ofroughness on particle dynamics in turbulent channel flows: a DNSanalysis. J. Fluid Mech. 739, 465478.
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MSP - Particle Laden Turbulent Shear Layers
High-performance computing for Volcanic ashplumes: turbulence, heat transfer and particle
dynamics.
Matteo CerminaraIstituto Nazionale di Geofisica e Vulcanologia, Sezione di Pisa
Via della Faggiola 32, 56126 Pisa
Tomaso Esposti OngaroIstituto Nazionale di Geofisica e Vulcanologia, Sezione di Pisa
Via della Faggiola 32, 56126 Pisa
Luigi BerselliUniversita di Pisa
V. F.Buonarroti 1/c, I-56127, PISA
We have developed a compressible multiphase flow model to simulate thethree-dimensional dynamics of turbulent volcanic ash plumes. The modeldescribes the eruptive mixture as a polydisperse fluid, composed of differenttypes of gases and particles, treated as interpenetrating Eulerian phases.Solid phases represent the discrete ash classes into which the total granulo-metric spectrum is discretized, and can differ by size and density. The modelis designed to quickly and accurately resolve important physical phenomenain the dynamics of volcanic ash plumes. In particular, it can simulate tur-bulent mixing (driving atmospheric entrainment and controlling the heattransfer), thermal expansion (controlling the plume buoyancy), the interac-tion between solid particles and volcanic gas (including kinetic non- equilib-rium effects) and the effects of compressibility (over-pressured eruptions andinfrasonic measurements). The model is based on the turbulent dispersedmultiphase flow theory for dilute flows (volume concentration ¡0.001, imply-ing that averaged inter-particle distance is larger than 10 diameters) whereparticle collisions are neglected. Moreover, in order to speed up the codewithout losing accuracy, we make the hypothesis of fine particles (Stokesnumber ¡0.2 , i.e., volcanic ash particles finer then a millimeter), so that weare able to consider non-equilibrium effects only at the first order. We adoptLES formalism (which is preferable in transient regimes) for compressible
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flows to model the non-linear coupling between turbulent scales and the ef-fect of sub-grid turbulence on the large-scale dynamics. A three-dimensionalnumerical code has been developed basing on the OpenFOAM computa-tional framework, a CFD open source parallel software package. The codehas been tested on a variety of different numerical benchmarks, stressingall the physical aspects we want to resolve. Benchmarks demonstrate thatthe model is able to capture important non-equilibrium phenomena in gas-particle mixtures, such as particle clustering and ejection from large-eddyturbulent structures, as well as compressibility and thermal effects. A quan-titative assessment of the reliability of Direct Numerical Simulation (DNS)and LES results with respect to modeling approximations and numericalerrors has been carried out by comparing numerical results to experimentaland computational studies of homogeneous, isotropic turbulence. In such asimplified geometry, the numerical solver is able to accurately reproduce theturbulent spectrum and the so-called energy cascade. The parallel efficiencyon high-performance computing platforms exceeds 80numerical simulations.Other numerical benchmarks have been performed, such as the 2D lid-drivencavity, the natural convection in a square enclosure, the stratified mixing fora dam-break problem and the forced plume in an experimental setting. Allthese tests have given excellent results, in agreement with the data com-monly found in the literature. Finally, the model is applied to simulate thethree-dimensional dynamics of volcanic plume dynamics and demonstratethat gas-particle non-equilibrium phenomena have a significant impact onturbulent structures and can affect the entrainment rate and the subsequentatmospheric dispersal of volcanic ash.
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MSP - Particle Laden Turbulent Shear Layers
Bubble dynamics and related acoustics
Enrico De BernardisCNR-INSEAN, Marine Technology Research Institute
via di Vallerano 139, 00128 Rome, Italy
Giorgio RiccardiDepartment of Industrial and Information Engineering, Second University of
Naplesvia Roma 29, 81031 Aversa (CE), Italy
andCNR-INSEAN, Marine Technology Research Institute
via di Vallerano 139, 00128 Rome, Italy
The motion of a bubble of gas and vapour in an isochoric, inviscid liquid isnumerically investigated in free space or in presence of a free surface and agravitational force. The corresponding acoustic emission is evaluated. Theliquid is at rest at the initial time, so that the subsequent flow is irrotational.The bubble motion is described in terms of the velocity potential, whichis evaluated by means of an integral representation and the solution of anintegral equation on the bubble boundary and the free surface. The pressureinside the bubble is assumed uniform and its value at time t is related tothe bubble volume V by the state equation pB(t) = pV + pG0V (0)/V (t),pV and pG0 being the vapour and gas pressure at t = 0, respectively. Thecorresponding pressure on the liquid face of the bubble boundary B followsas p(z; t) = pB(t) − 2S/Rm(z; t), S being the surface tension and Rm themean curvature radius at the point z ∈ B. Once the pressure on the bubbleboundary is known, the Bernoulli law is used to integrate the boundaryvalues of the potential.
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Discrete and continuousmodels for pedestrian
movements
278
MSP - Discrete and Continuous Models for Pedestrian Movements
Crowd Dynamics and Conservation Laws withNon–local Point Constraints and Capacity Drop.
Theory and Numerical Simulations.
Boris AndreianovUniversite de Franche–Comte
16 route de Gray, 25030 Besanon, France.
Carlotta DonadelloUniversite de Franche–Comte
16 route de Gray, 25030 Besanon, France.
Ulrich RazafisonUniversite de Franche–Comte
16 route de Gray, 25030 Besanon, France.
Massimiliano D. RosiniICM, University of Warsaw
ul. Prosta 69, P.O. Box 00-838, Warsaw, Poland
This talk concerns the macroscopic model introduced by Andreianov,Donadello and Rosini for pedestrian evacuating a narrow corridor througha single exit. Starting from the classical scalar LWR model, we reproducethe gradual fall in the efficiency of the exit due to congestion by imposingthat the flux at the exit satisfies a non–local constraint which depends onthe density of pedestrians on a left neighbourhood of the door. The con-straint function is exogenous and has to be determined together with thefundamental diagram from empirical data.
In [1] we prove the well–posedness of the Cauchy problem with Lipschitznon–local constraint by a procedure that combines the wave–front trackingalgorithm with the operator splitting method. In [2], also in collaborationwith Razafison, we study the Riemann problem in the case when the con-straint function is merely piecewise constant. In the recent work, [3], weadapt to our framework the finite volumes scheme in [4] and [5], we validateit against explicit solutions, then we show that our model can reproducephenomena as Faster is Slower and Braess’ paradox.
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1. Andreianov B., Donadello C. and Rosini M. D., 2013, Crowd dynamicsand conservation laws with non–local constraints and capacity drop,accepted for publication in MMMAS.
2. Andreianov B., Donadello C., Razafison U. and Rosini M. D., 2014,Riemann problems with non–local point constraints and capacity drop,
http://hal.archives-ouvertes.fr/hal-00959974.
3. Andreianov B., Donadello C., Razafison U. and Rosini M. D., 2014Numerical simulations in crowd dynamics for conservation laws withnon-local point constraints, in preparation.
4. Andreianov B., Goatin P. and Seguin N., 2010, Finite volume schemesfor locally constrained conservation laws, Numerische Mathematik,Springer Berlin / Heidelberg, 115,4, 609-645.
5. Chalons C., Goatin P. and Seguin N., 2013, General constrained con-servation laws. Application to pedestrian flow modeling, Networks andHeterogeneous Media, 8, 2, 433-463.
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MSP - Discrete and continuous models for pedestrian movements
Macroscopic modelling and simulations of crowddynamics
Monika TwarogowskaConsiglio Nazionale delle Ricerche, Istituto per le Applicazioni del Calcolo ”M.
Picone”Via della Ricerca Scientifica, 1; I-00133 Roma (Italy)
We consider two macroscopic models of crowd dynamics describing theevolution of the density of pedestrians in two space dimensions. The firstone, introduced by Hughes [1], consists of a scalar conservation law closedwith a speed-density relation. The second, proposed by Jiang et.al. [2], is ahigher-order model given by the Euler equations for isentropic gas dynamicswith relaxation source term and closed with a phenomenological law for theacceleration of pedestrians. Both systems take into account that pedestri-ans seek to minimize the path length towards their destination but tempertheir estimated travel time by avoiding high densities. This is obtained bycoupling the above equations with the eikonal equation with a density de-pendent running cost function. The gradient of its solutions indicates thedesired direction of motion of pedestrians.
We first provide a comparison between the two models regarding theirability of reproducing complex dynamics of crowd motion such as formationof stop-and-go waves and clogging at bottlenecks. Then we consider onlythe second order model and analyze the dependence of the behaviour of itssolutions on some of the parameters of the system. In particular, we focuson the effect of the strength of the internal repealing forces. Finally, westudy the optimization of the evacuation from a room through a narrowexit. Adapting the hypothesis of the inverse Braess paradox [3], we presentsome cases in which placing obstacles in front of the door prevents fromblocking and decreases the evacuation time.
[1 ] R. L. Hughes, A continuum theory for the flow of pedestrians, Trans-portation Research Part B: Methodological, 36(6) (2002), pp. 507-535
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[2 ] Y.Q. Jiang, P. Zhang, S.C. Wong, R.X. Liu, A higher-order macro-scopic model for pedestrian flow, Physica A: Statistical Mechanics andits Applications, 38(21) (2010), pp. 4623-4635
[3 ] D. Braess, A. Nagurney, T. Wakolbinger, On a Paradox of TrafficPlanning, Transportation Science, 4(39) (2005), pp. 446-450
[4 ] M. Twarogowska, P. Goatin, R. Duvigneau, Macroscopic modelingand simulations of room evacuation, to appear in Applied Mathemat-ical Modelling
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MSP - Discrete and continuous models for pedestrian movements
On the Hughes model for pedestrian flows:including local effects
Jose CarrilloImperial College London
United Kingdom
Stephan MartinImperial College London
United Kingdom
Marie-Therese WolframRadon Institute for Computational and Applied Mathematics
Austria
The Hughes model for pedestrian flow is based on the assumption that peoplewant to minimize their travel time but try to avoid regions of high density.Local effects such as limited vision are not included in the model; the overalldensity of the crowd is known to every agent. We present a modification ofthe Hughes model to include local effects. We discuss modeling aspects onthe micro- and macroscopic level as well as the efficient numerical simulationof the proposed models. Finally we illustrate the behavior of the modifiedmodel with various numerical experiments.
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MSP - Discrete and continuous models for pedestrian movements
On the CR model and its applications at thebottlenecks
Massimiliano D. RosiniICM, University of Warsaw
ul. Prosta 69, 00-838 Warsaw, Poland
The CR macroscopic model was introduced in [2] and its assumptions werelater qualitatively validated in [4]. We start from the basic assumptions forits construction and show that Laxian shocks can not describe the raise ofpanic among pedestrians.
We show then how to apply the model to reproduce phenomena typicalin crowd dynamics, namely the capacity drop at the bottlenecks [1], thefaster is slower effect [3] and the Braess paradox [5].
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Bibliography
[1] E. M. Cepolina. Phased evacuation: An optimisation model which takesinto account the capacity drop phenomenon in pedestrian flows. FireSafety Journal, 44(4):532–544, 2009.
[2] R. Colombo and M. Rosini. Pedestrian flows and non-classical shocks.Math. Methods Appl. Sci., 28(13):1553–1567, 2005.
[3] D. Helbing, I. Farkas, and T. Vicsek. Simulating dynamical features ofescape panic. Nature, 407(6803):487–490, 2000.
[4] D. Helbing, A. Johansson, and H. Z. Al-Abideen. Dynamics of crowddisasters: An empirical study. Phys. Rev. E, 75:046109, Apr 2007.
[5] R. Hughes. The flow of human crowds. In Annual review of fluid me-chanics, Vol. 35, pages 169–182. Annual Reviews, Palo Alto, CA, 2003.
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MSP - Discrete and continuous models for pedestrian movements
Mean field games with nonlinear mobilities inpedestrian dynamics
Martin BurgerInstitute for Computational and Applied Mathematics
University of MunsterEinsteinstrasse 62, D-48149 Munster
Marco Di FrancescoDepartment of Mathematical Sciences
University of Bath & University of L’Aquila4W, 1.14, University of Bath, Claverton Down, Bath (UK), BA2 7AY.
Peter A. MarkowichDepartment of Applied Mathematics and Theoretical Physics (DAMTP),
University of CambridgeWilberforce Road, Cambridge CB3 0WA, UK
Marie-Therese WolframUniversity of Vienna
Altenbergerstr. 69, 4040 Linz, Austria
We present an optimal control approach modeling fast exit scenarios inpedestrian crowds. In particular we consider the case of a large human crowdtrying to exit a room as fast as possible. The motion of every pedestrian isdetermined by minimizing a cost functional, which depends on his/her posi-tion, velocity, exit time and the overall density of people. This microscopicsetup leads in the mean-field limit to a parabolic optimal control problem.We discuss the modeling of the macroscopic optimal control approach andshow how the optimal conditions relate to the Hughes model for pedestrianflow. Furthermore we provide results on the existence and uniqueness ofminimizers and illustrate the behavior of the model with various numericalresults.
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MSP - Discrete and continuous models for pedestrian movements
Existence of weak solutions for Hughes model ofpedestrian flows
Debora AmadoriDISIM, University of L’Aquila
Paola GoatinINRIA Sophia Antipolis - Mediterranee, Sophia Antipolis Cedex, France
Massimiliano D. RosiniICM, University of Warsaw, Poland
This communication refers to the modeling of crowd dynamics presented in[3]. The model consists in a scalar conservation law coupled with an eikonalequation, meant to describe the motion of pedestrians in a densely crowdedregion. We consider this model on a bounded one-dimensional domain, withzero-density boundary conditions. Therefore, the ending points representthe exits of the domain. The discontinuity locus of the gradient of thesolution to the eikonal equation depends nonlocally on the solution to theconservation law, leading to a interesting mathematical problem. We showhow to deal successfully with this situation under suitable assumptions onthe initial data, leading to an existence result of discontinuous solutions forthe model above.
[1 ] D. Amadori, P. Goatin and M.D. Rosini. Existence results for Hughesmodel for pedestrian ows. Preprint 2014
[2 ] D. Amadori and M. Di Francesco. The one-dimensional Hughesmodel for pedestrian ow: Riemann-type solutions. Acta Math. Sci.Ser. B Engl. Ed. 32 (2012), 259280
[3 ] R.L. Hughes. A continuum theory for the ow of pedestrians. Transp.Research Part B 36 (2002), 507-535
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MSP - Discrete and Continuous Models for Pedestrian Movements
Modeling Crowd Dynamics within the Frameworkof FPT7 Projects
Nicola BellomoPolitecnico di Torino
This communication refers to the modeling of crowd dynamics by ki-netic theory methods where interactions are modeled by theoretical tools ofstochastic games. The theoretical approach and some applications [1],[2],[3]are referred to specific requirements of projects of the European Union,where the main one consists in developing approaches suitable to capturethe complexity features, including social behaviors, of the crowd viewed asa living system.
International Projects: EVAQUATE Dynamics of crowds in panic con-ditions, Started April 2013. SAFECITI Simulation Platform for the Anal-ysis of Crowds Behaviour in Urban Environments with Training and Predic-tive Capabilities, (Started March 1, 2014)
[1 ] N. Bellomo, and A. Bellouquid, On The Modeling of Crowd Dynam-ics: Looking at the Beautiful Shapes of Swarms, Netw. Heter. Media,6 (2011), 383–399.
[2 ] N. Bellomo and J. Soler, On the mathematical theory of the dynamicsof swarms viewed as complex systems, Math. Models Methods Appl.Sci., 22 (2012), 1140006 (29 pages).
[3 ] N. Bellomo and A. Bellouquid, From the micro-scale to collectivecrowd dynamics, SIAM Multiscale, 11, (2013), 943–963.
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MSP - Discrete and continuous models for pedestrian movements
Modeling rationality to control self-organization ofcrowds
Emiliano CristianiIstituto per le Applicazioni del Calcolo “M. Picone” - CNR, Roma
via dei Taurini, 19 00185 - Roma Italy
Fabio S. PriuliIstituto per le Applicazioni del Calcolo “M. Picone” - CNR, Roma
via dei Taurini, 19 00185 - Roma Italy
Andrea TosinIstituto per le Applicazioni del Calcolo “M. Picone” - CNR, Roma
via dei Taurini, 19 00185 - Roma Italy
In this talk we present some mathematical models for pedestrian crowds,in which different degrees of rationality can be used by individuals whenplanning their path [2].From the mathematical point of view, the pedestrian flow is described by a2D continuity equation with nonlocal flux, in the spirit of multiscale modelapproach presented in [1]. On the other hand, rationality is included intothe model by means of a suitable control problem that each walker has tosolve to decide how to move. In particular, when each individual is capableto forecast the long term effects of their choices (highly rational behavior),the two problems are fully coupled and we end up with a first order meanfield game [3].
Theoretical and numerical results will be presented to highlight the dif-ferent behaviors of pedestrians, depending on the amount of informationthey can use, and to suggest that environment design could be exploitedto get a “good” behavior even in the case of incomplete information andlimited predictive capabilities.
1. E. Cristiani, B. Piccoli, A. Tosin, Multiscale modeling of granularflows with application to crowd dynamics, Multiscale Model. Simul.,9 (1),155–182, 2011
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2. E. Cristiani, F. S. Priuli, A. Tosin, Modeling rationality to controlself-organization of crowds: An environmental approach, submitted.
3. F. S. Priuli, First order Mean-Field Games in crowd dynamics, sub-mitted, arXiv preprint: http://arxiv.org/abs/1402.7296
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Models and applications ofconservation laws
291
MSP - Models and applications of the theory of conservation laws
Initial-boundary value problems for transportequations with rough coefficients
Gianluca CrippaDepartement Mathematik und Informatik, Universitat Basel,
Rheinsprung 21, CH-4051 Basel, Switzerland.
Carlotta DonadelloLaboratoire de Mathematiques, Universite de Franche-Comte,
16 route de Gray, F-25030 Besancon Cedex, France
Laura V. SpinoloIMATI-CNR
via Ferrata 1, I-27100 Pavia, Italy
I will be concerned with existence and uniqueness results for transport equa-tions with weakly differentiable coefficients. The fundamental papers by DiPerna and Lions [4] and by Ambrosio [1] establish well-posedness of theCauchy problem for transport equations with Sobolev and BV (boundedtotal variation) coefficients, respectively. This analysis has relevant applica-tions to the study of several nonlinear partial differential equations, like forinstance hyperbolic systems of conservation laws in several space dimensions[2].My talk will aim at discussing existence and uniqueness results concerningsolutions of initial-boundary value problems for transport equations with BV(bounded total variation) coefficients. I will also exhibit counter-examplesshowing that, as soon as the BV regularity deteriorates at the domain bound-ary, uniqueness is in general violated.
1. Ambrosio, L. 2004 Transport equation and Cauchy problem for BVvector elds. Invent. Math., 158(2), 227-260.
2. Ambrosio, L., Bouchut, F. and De Lellis, C. 2004 Well-posedness for aclass of hyperbolic systems of conservation laws in several space dimen-sions. Comm. Partial Dierential Equations 29, no. 9-10,1635-1651.
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3. Crippa, G., Donadello, C. and Spinolo, L. V. Initial-boundary valueproblems for continuity equations with BV coecients, J. Math. PuresAppl. In press.
4. DiPerna, R. J. and Lions, P.-L. 1989 Ordinary dierential equations,transport theory and Sobolev spaces. Invent. Math., 98(3), 511-547.
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MSP - Models and applications of the theory of conservation laws
Rigorous derivation of theLighthill-Whitham-Richards model from the
follow-the-leader model as many particle limit
Marco Di FrancescoDepartment of Mathematical Sciences
University of Bath & University of L’Aquila4W, 1.14, University of Bath, Claverton Down, Bath (UK), BA2 7AY.
Massimiliano D. RosiniICM, University of Warsaw
ul. Prosta 69, P.O. Box 00-838, Warsaw, Poland
We prove that the unique entropy solution to the macroscopic Lighthill-Witham-Richards model for traffic flow can be rigorously obtained as thelarge particle limit of the microscopic follow-the-leader model, which is in-terpreted as the discrete Lagrangian approximation of the former. Moreprecisely, we prove that the empirical measure (respectively the discretiseddensity) obtained from the follow-the-leader system converges in the 1-Wasserstein topology (respectively in L1loc) to the unique entropy solutionof the Lighthill-Witham-Richards equation in the Kruzkov sense. The initialdata are taken in L infinity with compact support, hence we are able to han-dle densities with vacuum. Our result holds for a reasonably general class ofvelocity maps (including all the relevant examples in the applications) withpossible degenerate slope near the vacuum state. The proof of the result isbased on discrete BV estimates and on a discrete version of the one-sidedOleinik-type condition. In particular, we prove that the regularizing effect“L infinity to BV” is intrinsic of the discrete model.
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MSP - Models and applications of the theory of conservation laws
NAVIER-STOKES EQUATIONS WITHINCOMPATIBLE DATA IN THE ZERO
VISCOSITY LIMIT
Maria Carmela LombardoDepartment of Mathematic, University of Palermo
Marco SammartinoDepartment of Mathematic, University of Palermo
In this talk we shall consider an incompressible flow interacting with aboundary without assuming that the initial datum satisfies the no-slip con-dition at the boundary. A typical case when this situation occurs is theimpulsively started disk. Other instances widely studied in the literatureare when a vortical configuration, which is a steady solution of the Eulerequations (like the thick core vortex or the vortex array), is assumed tointeract instantaneously with a solid boundary.
Focusing our analysis on the Navier-Stokes equations on a half-space, weshall construct the initial-boundary layer corrector in the form of a Prandtlsolution with incompatible data. This corrector is the first term of an asymp-totic series that we shall prove to approximate, in the zero viscosity limitand for a short time, the Navier-Stokes solutions. Assuming analytic reg-ularity in the tangential direction, we shall prove that this time does notdepend on the viscosity.
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From computer aidedgeometric design to
industrial CAD modelingand simulations
296
MSP - From computer aided geometric design to industrial CAD modeling and
simulations
Compatible discretizations based on hierarchicalsplines
John A. EvansAerospace Engineering Sciences, University of Colorado at Boulder
Michael A. ScottDepartment of Civil and Environmental Engineering, Brigham Young University,
Provo, Utah
Derek C. ThomasDepartment of Physics and Astronomy, Brigham Young University, Provo, Utah
Rafael VazquezIstituto di Matematica Applicata e Tecnologie Informatiche Enrico Magenes”
via Ferrata 1, 27100 - Pavia Italy
Isogeometric analysis is an emerging technology that intends to advance to-wards the integration of CAD and CAE technologies. The idea is, invokingthe isoparametric concept, to use the same kind of basis functions for thegeometry description given by CAD and the test and trial spaces in the dis-crete problem to be solved by CAE. The functions most commonly used upto now are (rational) B-splines and their non-tensor-product generalizations,such as T-splines and hierarchical splines.
By abandoning the isoparametric concept, it is possible to extend isogeo-metric analysis to the definition of discrete differential forms based on splinespaces. This kind of discrete spaces are useful for compatible discretizationin computational electromagnetics and fluid mechanics, for instance, andthey can be seen as a generalization of edge and face elements. In this talk Iwill present the definition of differential forms based on hierarchical splines,extending the result of previous papers to the non-tensor-product setting.
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MSP - From computer aided geometric design to industrial CAD modeling and
simulations
3D interaction and sketch-based surface modeling
Flavio Bertini,Bojan Milosevic,Serena MorigiUniversita degli Studi di Bologna
flavio.bertini,bojan.milosevic,[email protected]
Elisabetta FarellaFBK Trento Italy
Serena MorigiUniversita degli Studi di Bologna
P.zza Porta San Donato, 5 40126 - Bologna Italy
We propose a new sketch-based modeling paradigm where the creation of 3Dmodels is automatically inferred from a 3D irregular curve network directlydrawn by the user into a virtual 3D space. The user traces the 3D curvenetwork using a natural user interface that mimics the free-hands drawing,which most users are familiar with. At this aim, we introduce a low cost,low power, wireless pen-like device, the SmartPen. The SmartPen is usedto draw the style lines of the object to be modeled in the virtual space.Starting from the traced 3D curves, the system automatically reconstructsthe sketched surface through an interactive optimization approach, findingthe smooth subdivision surface which best fits the traced 3D curve network.The SmartPen also provides interactive capabilities to support the modelingprocess, introducing facilities for navigation and editing of the virtual scene.Moreover, real-time visual feedback is provided to the user to ease the overallexperience. Various case tests are presented to demonstrate the effectivenessof the system in enabling the concurrent acquisition of the 3D curve networkand the modeling of the underlying surface.
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MSP - From computer aided geometric design to industrial CAD modeling and
simulations
Algebraic-Geometric Structures for RationalCamera Motions
Maria Lucia SampoliUniversita degli Studi di Siena
San Niccolo, Via Roma 56 53100 - Siena Italy
A spatial rigid body motion can be described in terms of the trajectoryof a distinguished point of the body and the variation of an orthonormalframe, specifying the orientation of the body along this trajectory. Sucha description essentially decomposes the spatial motion into translationaland orientational components. Typically, the first component is straight-forward, while the second one can pose difficulty. It is then important tobe able to accurately associate a suitable frame to each point of the curvedtrajectory. Typical operations in this context may involve curvilinear ab-scissa identification, offsets computation, and also moving frame construc-tion. Using classical polynomial/rational representations, these quantitiescan be non-rational and, consequently in commercial design applicationsthey are usually approximated. In order to facilitate the construction of(constrained) interpolation/application algorithms, certain classes of poly-nomial/rational curves with a specific algebraic-geometric structure havebeen widely investigated. By focusing on the description of a camera mov-ing along a spatial path while imaging a stationary object, a special familyof frames (called directed) have been recently introduced. In particular, therotation-minimizing property has been investigated.
In this talk, interpolation methods for constructing rational curves withrational directed rotation–minimizing frames are discussed.
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MSP - From Computer Aided Geometric Design to Industrial CAD Modeling and
Simulation
Geometric Modeling for Turbine Engine Design
David GroßmannMTU Aero Engines AG
Dachauer Strasse 665, 80995 Munich, Germany
The overall design of modern turbine engines is one of the most challengingtasks in todays engineering world comprising newest technologies in engi-neering design and simulation, material science and complex manufacturingprocesses. Within the design process, the capability of fast and robust ge-ometric algorithms for an automatic 3D shape optimization of turbine andcompressor blades is a key technology for creating highly efficient enginesminimizing flow losses.
The mini-symposium talk will introduce MTUs geometric modeling andprocessing software COBRA and the Marie Curie research project EXAM-PLE, both focusing on bridging the gap between advanced techniques incomputer aided geometric design and innovative industrial applications.COBRA combines geometric algorithms with a modern software architec-ture providing visualization, data management and user interfaces for a realindustrial software. Currently, it is deployed for the aerodynamic shapedesign of engines like the PW1100G for the Airbus A320neo. EXAMPLEfocuses on the scientific field of geometric techniques, especially on devel-oping hierarchical spline spaces, and their application within the industrialenvironment at MTU. Therefore, we will present first results for the adap-tive CAD model (re-)construction with the so-called truncated hierarchicalsplines and the integration of the adaptive modeling tool into CAD systemsthat comply with the current NURBS standard.
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Redazione file PDF a cura di:Dott. Leonardo Scandurra [email protected]
Universita di CataniaDipartimento di Matematica e Informatica
Viale A. Doria n6 - 95125 Catania
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