MATHKNOW

MS&ASeries Editors:

Alfio Quarteroni (Editor-in-Chief ) • Tom Hou • Claude Le Bris • Anthony T. Patera • Enrique Zuazua

Michele Emmer, Alfio Quarteroni (Eds.)

MATHKNOW

Mathematics, Applied Sciences

and Real Life

Michele EmmerUniversità degli studi “La Sapienza”Dipartimento di Matematica “G. Castelnuovo”Roma, Italy

Alfio QuarteroniMOX, Dipartimento di Matematica “F. Brioschi”Politecnico di MilanoMilan, ItalyandCMCS-IACSEcole Polytechnique Fédérale de LausanneLausanne, Switzerland

On the cover:Anelli borromei. BibliotecaAmbrosiana,Milano.©SabrinaProvenzi

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Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII

The misuse of mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Ralph Abraham

Mathematics and literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Andrew Crumey

Applied partial differential equations: visualizationby photography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Peter Markowich

The spirit of algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Claudio Procesi

Theory and applications of Raptor codes . . . . . . . . . . . . . . . . . . . 59Amin Shokrollahi

Other geometries in architecture: bubbles, knots andminimal surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91Tobias Wallisser

Soft matter: mathematical models of smart materials . . . . . . . 113Paolo Biscari

Soap films and soap bubbles: from Plateau to the olympicswimming pool in Beijing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119Michele Emmer

Games suggest how to define rational behavior. Surprisingaspects of interactive decision theory . . . . . . . . . . . . . . . . . . . . . . . 131Roberto Lucchetti

VI Contents

Archaeoastronomy at Giza: the ancient Egyptians’mathematical astronomy in action . . . . . . . . . . . . . . . . . . . . . . . . . . 147Giulio Magli

Mathematics and food: a tasty binomium . . . . . . . . . . . . . . . . . . . 157Luca Paglieri and Alfio Quarteroni

Detecting structural complexity: from visiometrics togenomics and brain research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167Renzo L. Ricca

Recreative mathematics: soldiers, eggs and a pirate crew . . . 183Nadia Ambrosetti

Mathematical magic and society . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193Fernando Blasco

Little Tom Thumb among cells: seeking the cues of life . . . . . 201Giacomo Aletti, Paola Causin, Giovanni Naldi and Matteo Semplice

Adam’s Pears . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215Guido Chiesa

Mathematics enters the picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217Massimo Fornasier

Multi-physics models for bio-hybrid device simulation . . . . . . 229Riccardo Sacco

Stress detection: a sonic approach . . . . . . . . . . . . . . . . . . . . . . . . . . 241Laura Tedeschini Lalli

Vulnerability to climate change: mathematics as a languageto clarify concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253Sarah Wolf

Preface

Mathematics is the oldest of all sciences. Its foundations are visible in math-ematical texts originating in the ancient Egyptian, Mesopotamian, Indian,Chinese, Greek and Islamic worlds.Since the very beginning, when mathematics was conceived for fulfilling

very basic needs like numbering, counting and measuring simple-shaped ar-eas, this discipline has evolved in a boisterous way thus producing significantresults that have strongly marked the evolution of mankind.Through the centuries, mathematical ideas and achievements have been

organized and shaped into fundamental branches like arithmetic, numbertheory, algebra, geometry, and trigonometry, as well as related sciences likeastronomy, mechanics and physics.The development of the discipline then bloomed in the 16th century, when

mathematical innovations started to interact with new scientific discoveries;and its growth has never ceased thereafter.Nowadays, mathematics is the most influential and pervasive of all sciences

in our society, because of its exclusive potential of establishing connectionsamong virtually all possible manifestation of our knowledge. As a matter offact, it is used throughout the world as an essential tool in many fields. Inparticular, applied mathematics tranfers mathematical knowledge into otherfields, offering new possibilities to manage the growing complexity of our realworld.Beautiful though they may be, mathematical results are not merely

museum-pieces, but form a vital underpinning for every branch of quanti-tative knowledge, including all domains of science and engineering. Mathe-matics is in constant and vigorous development, driven both by its internaldynamics and by the demands of other disciplines, henceforth impacting thewhole of our daily life.By gathering different contributions from several world-famous scientists

from mathematics and related sciences, this book highlights the way mathe-matics deeply permeates and fertilizes our society.

VIII Preface

In particular, here will we face the role of mathematics in applied sciencesshowing results in different fields in industry, environment, life sciences andarchitecture.This book has the ambition to excite the readers interest showing how

mathematics is also hidden in the natural world around us, independentlyof mankind presence and interference: there are maths schemes in any prey-predator interaction, Boltzmanns equations hidden in clouds, Navier-StokesEquations concealed in a waterfall, free boundary problems to be solved in amelting iceberg.Though this work will face maths problems that are not always elemen-

tary, yet it is not intended for mathematicians only. The rigorous, nonethelessreadable, exposition, the intriguing examples, the stimulating demonstrationsof the deep connections among science, technology, architecture, human sci-ences and mathematics will fascinate even those who, not being scientists orexperts of this discipline, have always felt attracted by the noblest and mostfundamental of modern sciences.

The Editors, and the Publisher as well, would like to thank all the authors andthe people who actively contributed to the success of this project, in particularLuca Paglieri, for his accuracy and concern in supporting the MATHKNOWexperience since the very beginning.

List of Contributors

Ralph AbrahamUniversity of CaliforniaSanta Cruz, CA, USArha@ucsc.edu

Giacomo AlettiDipartimento di Matematica“F. Enriques”Universita degli Studi di MilanoMilano, Italyaletti@mat.unimi.it

Nadia AmbrosettiDipartimento di Informatica eComunicazioneFacolta di Scienze Matematiche,Fisiche e NaturaliUniversita degli Studi di MilanoMilano, Italynadia.ambrosetti@unimi.it

Paolo BiscariDipartimento di MatematicaPolitecnico di MilanoMilano, Italypaolo.biscari@polimi.it

Fernando BlascoDepartamento de MatematicaAplicada a los Recursos NaturalesETSI MontesUniversidad Politecnica de MadridMadrid, Spainfernando.blasco@upm.es

Paola CausinDipartimento di Matematica“F. Enriques”Universita degli Studi di MilanoMilano, Italycausin@mat.unimi.it

Andrew CrumeySchool of English Literature,Language and LinguisticsNewcastle UniversityNewcastle upon Tyne, UKAndrew.Crumey@ncl.ac.uk

Guido ChiesaMovie DirectorPadova, Italyguido.chiesa@fastwebnet.it

X List of Contributors

Michele EmmerUniversita degli studi “La Sapienza”Dipartimento di Matematica“G. Castelnuovo”Roma, Italyemmer@mat.uniroma1.it

Massimo FornasierJohann Radon Institute forComputational and AppliedMathematics (RICAM)Linz, Austriamassimo.fornasier@oeaw.ac.at

Roberto LucchettiDipartimento di MatematicaPolitecnico di MilanoMilano, Italy

Giulio MagliFacolta di Architettura CivilePolitecnico di MilanoMilano, Italy

Peter MarkowichDAMTPCentre for Mathematical SciencesCambridge, UK

Giovanni NaldiDipartimento di Matematica“F. Enriques”Universita degli Studi di MilanoMilano, Italynaldi@mat.unimi.it

Luca PaglieriMOX, Dipartimento di Matematica“F. Brioschi”Politecnico di MilanoMilano, Italy

Claudio ProcesiUniversita degli studi “La Sapienza”Istituto di Matematica“G. Castelnuovo”Roma, Italy

Alfio QuarteroniMOX, Dipartimento di Matematica“F. Brioschi”Politecnico di MilanoMilano, ItalyandCMCS-IACSEcole Polytechnique Federale deLausanneLausanne, Switzerland

Renzo L. RiccaDipartimento di MatematicaApplicataUniversita Milano-BicoccaMilano, ItalyandInstitute for Scientific InterchangeTorino, Italyrenzo.ricca@unimib.it

www.matapp.unimib.it/~ricca

Riccardo SaccoDipartimento di Matematica“F. Brioschi”Politecnico di MilanoMilano, Italyriccardo.sacco@polimi.it

Matteo SempliceDipartimento di Matematica“F. Enriques”Universita degli Studi di MilanoMilano, Italysemplice@mat.unimi.it

List of Contributors XI

Amin ShokrollahiEcole Polytechnique Federale deLausanneLausanne, Switzerlandamin.shokrollahi@epfl.ch

Laura Tedeschini LalliDipartimento di MatematicaUniversita Roma TreRoma, Italy

Tobias WallisserStaatliche Akademie der BildendenKunste StuttgartStuttgart, Germany

Sarah WolfPotsdam Institute for ClimateImpact Research (PIK)Potsdam, Germanysarah.wolf@pik-potsdam.de