Atmospheric ScienceAtmospheric Science BioinformaticsBioinformatics Computational ChemistryComputational Chemistry Crash Analysis/SimulationCrash Analysis/Simulation

• Atmospheric Science Atmospheric Science • Bioinformatics Bioinformatics • Computational ChemistryComputational Chemistry• Crash Analysis/SimulationCrash Analysis/Simulation• Generalized Finite Element Method Generalized Finite Element Method • PhysicsPhysics

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instruction

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HardwareHardware

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32 CPUs, 8 GB RAM, 300 GB Disk

• SGI Origin 3800 (k2)

48 CPUs, 48 GB RAM, 1.2 TB Disk

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Amass/DataMgr HSM, 7 TB, 4 DLT Drives

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Professor Lee PanettaProfessor Lee Panetta

Department of Atmospheric SciencesDepartment of Atmospheric Sciences

Atmospheric Sciences, Panetta

OverviewOverview

The nature of cross-jet transport is of interest to the chemistry of the stratosphere and the biology of the upper extratropical oceans. Here I use a combination of pseudo-spectral and particle tracking methods to investigate the nature of transport across self-organized jets in rapidly rotating stratified flow. Simulations indicate the presence of an anomalous, subdiffusive scaling regime for single particle dispersion which is intermediate between the short-time “ballistic” and long-time “diffusive” regimes. The regime is seen over a range of forcing strengths, but a physically based scaling can be chosen which collapses results to a single dispersion curve.


Mathematical ModelMathematical ModelThe two-layer system consists of two horizontal fluid layers, bounded above and below by a rigid horizontal surface, and separated by an immiscible interface. The layers have slightly different densities, with the denser (cold) fluid beneath the lighter (warm) fluid.

Key variables in the theory are the layer "potential vorticities" variables Q i, defined in terms of the non-dimensional streamfunction i in layer i, by Qi = y + 2 i + (-1)i (1 - 2 / 2). The system we integrate numerically governs the evolution of deviations Qi from a specified state with an interface having a spatially uniform structure, a tilt upward to the north. This is effectively a spatially uniform thermal forcing. The evolution equations are

Results shown here use a 512 x 512 grid in each layer.


Cross-Jet Transport in Geophysical TurbulenceCross-Jet Transport in Geophysical TurbulenceAfter a spin-up period, the solution settles into a quasi-steady state with a sequence of turbulent jets oriented in the east-west direction. The mean latitude of each jet is surprisingly persistent, even though eddy-to-mean-flow kinetic energy ratios can be well in excess of unity. The figure below shows the evolution in time of the x-averaged eastward component of the wind in the upper layer for in one simulation. There are four steady jets in the north, and alternately one and two in the south. Adjustment of domain width can remove this transience, which is a "quantization" effect due to the presence of a dynamically determined jet scale.


Cross-Jet Transport in Geophysical TurbulenceCross-Jet Transport in Geophysical Turbulence

Instantaneous fields of potential vorticity show narrowly concentrated regions of tight gradient, corresponding to eastward jets, and compact vortices which arise from waves which form on the jets and break. Both spatial structures play important roles in transport.


Cross-Jet Transport in Geophysical TurbulenceCross-Jet Transport in Geophysical TurbulenceThe figure below shows an instantaneous potential vorticity field for the upper layer, and two groups of tracers whose positions are indicated by asterisks. The tracers were released a short time before on lines of constant latitude halfway between westerly (i.e. eastward) jets, in regions of relatively weak potential vorticity gradient (compare previous figure). Also indicated by arrows on the side are the average positions of the nearest westerly jets.



The figure below shows a selection of four tracer trajectories, with initial release points indicated by asterisks. The dotted lines indicate the narrow regions of (time averaged) high gradients of potential vorticity, which are the regions of strong eastward jets. Two of the tracers shown started in these regions, and were cast out, and two started outside these regions. One of the latter (green trajectory) actually crossed a nearby jet. The animation provided below shows how this jet crossing occurs, namely in a wave-breaking event that results in a vortex being formed. The tracer is initially carried along by the vortex.

The statistics of such "cross-jet transport" are of our principal interest. To study this, information from repeated releases of groups of tracers of the sort shown in Fig 3 was analyzed.



Results on single particle dispersion rates from five different choices of B are summarized in Fig 5 below. Smaller values of B correspond to flows more strongly driven. The sampling strategy was that for each value of B, 10 groups of 1024 tracers were released halfway between mean westerly jet positions. To account for the difference in energy levels in the flows, distances were rescaled by interjet spacing distance.


Animation of ResultsAnimation of Results

• The labels on the side are nondimensional length units in the x (eastward) and y (northward) directions;

• Colors indicate potential vorticity, with high values indicated by red and low values by blue. The sharp gradation between yellow and red, and between yellow and blue, correspond to cores of two eastward jets;

• The dashed curves are lines of constant streamfunction values. Each jet is seen to be part of a street-like array; eddies of locally high streamfunction values are the south, and locally low values are to the north (see the "H" and "L");

• There are different symbols indicating positions (see arrow) of the three tracers released in the flow at nondimensional time "t=0". As time evolves these tracers quickly become widely separated, and the tracer marked by the asterisk is seen in the animation to actually cross the southern jet in a wave-breaking event.

The animation shows a number of features (see the first frame below):


QuickTime™ and aCinepak decompressorare needed to see this picture.

Professor David L. AdelsonProfessor David L. Adelson

Clare A. GillClare A. Gill

Bioinformatics, Adelson and Gill

Current projectsCurrent projects

• Our most pressing project at present is our contribution of bovine BAC clones to the Bovine Genome Project.

• We have sent 50,000 BACs to Marco Marra’s group for fingerprinting.

• We need to end sequence these clones as well (bidirectional).


For this we require laboratory automationFor this we require laboratory automation

Biorobotfor DNAisolations

HighthroughputPCR machine

96 capillaryDNA Sequencer


Automation consequencesAutomation consequences

• Sample tracking:– Labeling needs to be automated.– Sample sheets need to be automated.

• Results need to be collected and entered into a database.• With over 500 sequences collected every day, an analysis

pipeline needs to be in place and at least semi-automated.• Database needs to be integrated to manage not only DNA

preps and sequences, but phenotypes, genotypes and BLAST results.


Work flow for automated sequencingWork flow for automated sequencing

• Select 384 well plate for growth.• Automatically generate MegaBACE sample sheets (4x96)

and transfer over network to MegaBACE.• Inoculate 4x96 well grow boxes and bar code.• Grow clones.• Robotic DNA isolation (bar code DNA plates).• Robotic DNA sequencing reaction set up (bar code).• Cycle sequencing• Robotic sequencing clean up (bar code).• Load sequencer (bar code reader).• Auto file transfer to sequence analysis server.


Sequence data pipelineSequence data pipeline

Trace files(sequencer)

phred(LINUX box) HT-BLAST

SGI Origin 3800 48 cpu supercomputer

Tab delimitedparsed output(LINUX box)

MySQL table(LINUX box)

Web server(LINUX box)


SGI Origion 3800SGI Origion 3800

• High throughput BLAST1,2 requires a multiprocessor machine with large, shared memory for maximum speed of search.

• BLAST parallelizes and scales well, allowing the data pipeline to keep up with the new data generated and update search results for previously generated data.

1Altschul, Stephen F., Thomas L. Madden, Alejandro A. Schaffer, Jinghui Zhang, Zheng Zhang, Webb Miller, and David J.Lipman (1997), "Gapped BLAST and PSI-BLAST: a new generation of protein database search programs", Nucleic Acids Res. 25:3389-3402.

2Camp, N., Cofer, H., and Gomperts, R. 1998. High-Throughput BLAST. http://www.sgi.com/industries/sciences/chembio/resources/papers/HTBlast/HT_Whitepaper.html

Ref Type: Electronic Citation.

http://www.sgi.com/industries/sciences/chembio/resources/papers/HTBlast/HT_Whitepaper.html








Database structureDatabase structure

• Multiple databases at present, not a single integrated database.

• Angleton data in one database

• Sequence similarity in another db.

• Sensory panel data (meat science) in another db.


Family database Family database


Meat sensory dataMeat sensory data


Sequence similarity dbSequence similarity db


In silicoIn silico mapping mapping

• We get two kinds of information back from sequence similarity searches– Location of homolog in reference genome.– Functional properties of homolog.

• We would like to be able to represent both types of information simultaneously.

• For now we can only provide the physical location of the homolog in the reference genome (usually the human genome).


Overall db diagramOverall db diagram

Texas A&M UniversityDepartment of Chemistry

Director: Prof. Michael B. HallManager: Lisa M. Thomson

Contributors:M. B. Hall

L. M. ThomsonJ. D. Hoefelmeyer

F. GabbaïC. E. WebsterD. H. RussellH. A. SawyerG. F. Verbeck

http://www.chem.tamu.edu/LMS

Computational Chemistry, Hall et al.

LMS ResourcesLMS Resources

• HARDWAREHARDWARE - All computationally intensive calculations are carried out on the Texas A&M Supercomputing Facility’s systems:

– 32-cpu IBM Regatta p690 – 32-cpu SGI Origin 2000– 48-cpu SGI Origin 3800

• SOFTWARESOFTWARE - The LMS uses a variety of molecular modeling software. This software includes the following:

– AMPAC – Cerius2– CHARMm – Dalton– Gaussian 98 (G98) – GaussView– Insight II– MacroModel

– Materials Studio – Molden– MOLPRO – Q-Chem – Quanta – Spock – TINKER


Molybdenum containing enzymes are a broad class of enzymes that are essential for the metabolism of carbon, nitrogen and sulfur in a wide variety of organisms. In humans, sulfite oxidase is the enzyme responsible for the metabolism of the toxin sulfite to sulfate. Analogue reaction systems have been developed to mimic the activity of the molybdoenzymes. These analogue systems can be used to verify experimental data on the structure and reaction mechanism of the complex enzyme systems. This study focuses on the elucidation of the reaction mechanism of an analogue system. Density functional calculations on MoO2(NHCHCH2SH)2 + P(CH3)3 MoO(NHCHCH2SH)2 + OP(CH3)3

were performed at the B3P86 level of theory as implemented in Gaussian 94/98, using a double- quality basis set for all atoms and the inclusion of a polarization function on the phosphorus. The DFT results indicate that this reaction proceeds through a two step mechanism via an associative intermediate shown in the Figure A. The substrate was found to attack one of the terminal oxo groups to form an unusual 3c-4e - O-P-C bond in the first transition state, TSI. The OP(CH3)3 group then rotates to almost lie in the MoO2 plane to form the intermediate,

INT. The second transition state, TSII, involves the weakening of the Mo-OP(CH3)3 bond and the concomitant

rearrangement of the ligands. Figure B shows an important anti-bonding interaction the help to eliminate the product, OP(CH3)3. The overall exothermicity of this reaction is 32.7 kcal/mol (-Ho) and Go = -27.1 kcal/mol, a

value consistent with the equilibrium lying far to the right. The H‡ for the first step (rate determining) was found to be 9.4 kcal/mol, and the second step had a H‡ = 3.3 kcal/mol. These results are within the uncertainty of the experimental system, for which the rate determining H‡ = 9.6(6).

A Theoretical Study of the Primary Oxo Transfer Reaction of a Dioxo Molybdenum(VI) Compound with Imine Thiolate Chelating Ligands: A

Molybdenum Oxotransferase Analogue (Thomson and Hall)


Figure A. The B3P86 results for the reaction of MoO2(NHCHCH2SH)2 +

P(CH3)3 MoO(NHCHCH2SH)2 + OP(CH3)3. These results indicate that this

reaction proceeds through a two step mechanism via an associative intermediate.


Figure B. 0.05 isodensity surface of a) REAC, b) TS1 and c) INT. (b) shows the important anti-bonding interaction the help to eliminate the product, OP(CH3)3


Owing to their isoelectronic relationship to neutral methyl radicals, the chemistry of stable boron-centered radical anions R3B

•- (R=aryl rings) has been investigated intensely. Although delocalization of the radical over the aryl rings

accounts for the stability of such systems, EPR studies show that, in some instances, the unpaired electron is mainly localized at boron. In organodiboranes, one-electron reduction leads to the formation of a one-electron s-bond formed by the overlap of the parallel pz boron orbitals. Interestingly, the isolation of boron radicals in which the unpaired

electron occupies a molecular orbital formed by the combination of overlapping colinear atomic orbitals is much more elusive. Motivated by the importance of stable radicals to the field of material science, we have set out to prepare a stable boron radical, of the general form (R3B)2

•-, and report on the formation of a radical that features a boron-boron

one electron -bond. A single-crystal X-ray analysis of 1,8-bis(diphenylboryl)-naphthalene revealed the existence of a sterically congested structure with a boron-boron distance of 3.002(2) Å (Figure A). A one-electron reduction of 1 affords the radical anion 2 (Figure A). While it has so far not been possible to obtain single crystals of 2, we have performed a series of DFT calculations on 1 and 2 with the B3LYP functional as implemented in Gaussian 98 ( Basis set: 6-31G on C, and H, and 6-31+G* basis set on B). Examination of the B3LYP orbitals (Figure B) reveals that, in 1, the pz

orbitals of the neighboring boron centers overlap substantially and contribute to the Lowest Unoccupied Molecular Orbital (LUMO). The calculated structure for 2 differs from that of 1 in several aspects, but most noteworthy is that the boron-boron distance decreases substantially (3.16 Å in 1 to 2.82 Å in 2) in agreement with the presence of a bonding interaction. Both boron atoms are the dominant contributors to the singly occupied Highest Occupied Molecular Orbital (HOMO), which has a strong boron-boron -bond character (Figure B). This one-electron -bond can be viewed as the occupation of the formerly vacant boron pz-orbitals upon one-electron reduction of 1. The minor

contributions of the ring carbon atoms substantiate the importance of the stabilizing effect provided by aryl substituents in stable radicals.

An Intramolecular Boron-Boron One-Electron s-Bond (Hoefelmeyer and Gabbaï)


An Intramolecular Boron-Boron One-Electron -Bond (Hoefelmeyer and Gabbaï)

Figure A. X-ray crystal structure of 1,8-bis(diphenylboryl)-naphthalene, 1, and B3P86 optimized structure of the reduced species, 2, 1,8-bis(diphenylboryl)-naphthalene anion.

Figure B. 0.05 isodensity surface for the Lowest Unoccupied Molecular Orbital (LUMO) of 1, and the Highest Occupied Molecular Orbital (HOMO) for 2, illustrating the overlap of pz orbitals of the neighboring

boron centers forming the strong boron-boron -bond character in 2.


The reactions of cyclopropane with the coordinately unsaturated species produced by mild thermal activation of [Cp*Ir(P(CH3)3)CH3]

+L (L = Cl2CH2, OSO2CF3-) (shown in the scheme below) have been

investigated with density functional calculations (B3LYP). The pathway for the production of endo or exo 3-allyl complexes from the reaction of cyclopropane with the Ir III model complex [CpIr(PH3)CH3]

+ proceeds

through C-H bond activated IrV intermediates and CH4 elimination, followed by ring opening of the iridium

cyclopropyl complexes through an iridium carbene vinyl intermediate to their respective 3-allyl products. This unexpected mechanism breaks two C-C bonds simultaneously and then re-forms one en route from the iridium cyclopropane complex to the iridium allyl products. The interconversion between endo and exo 3-allyl can be assisted by solvent through an 1-allyl intermediate. Thermal rearrangement of the cyclopropyl kinetic product proceeds back through the same s-agostic complex, producing the thermodynamically more stable metallocyclobutane complex.

Theoretical Studies of Carbon-Hydrogen and Carbon-Carbon Bond Activation of Cyclopropane by Cationic Ir(III) (Webster and Hall)

Ir(H3C)3PCH3Ir(H3C)3P++Ir(H3C)3PH+CH3Ir(H3C)3P+Ir(H3C)3PCH2+-CH4


Schematic representation of the potential energy surface for the reaction of C3H6 with (CpIrPH3CH3)+. Relative energies

are in kcal mol-1 and for structures 8 and 8' through 14 and 14' include the energy of CH4. Optimized structures can be

found on the following slides.




Optimized structures of the reactant, transition states, intermediates, and products for the reaction of C3H6 with (CpIrPH3CH3)

+.



Optimized structures of the reactant, transition states, intermediates, and products for the reaction of C3H6 with (CpIrPH3CH3)

+.



Reaction paths for the conversion of endo and exo-allyl


Theoretical Studies of Carbon-Hydrogen and Carbon-Carbon Bond Activation of Theoretical Studies of Carbon-Hydrogen and Carbon-Carbon Bond Activation of Cyclopropane by Cationic Ir(III) (Webster and Hall)Cyclopropane by Cationic Ir(III) (Webster and Hall)

0.04 isodensity surface of Highest Occupied Molecular Orbital (HOMO) for the interconversion of endo and exo-allyl via “rotating” . The energetic diagram illustrates that this is a high barrier mechanism due to an increase in the energy of the HOMO.


Molecular Modeling and Ion Mobility Time-of-Flight Mass Molecular Modeling and Ion Mobility Time-of-Flight Mass Spectroscopy (Russell, Sawyer, Thomson, and Verbeck)Spectroscopy (Russell, Sawyer, Thomson, and Verbeck)

Dr. Russell’s group of the Laboratory for Biological Mass Spectrometry uses the Supercomputing Facility in conjunction with the Laboratory for Molecular Simulation (LMS), for predictive modeling of molecular ions drifting through a bath gas, usually He, Ar, and N2. Experimental analysis is carried out using ion mobility time-of-flight mass spectrometry.

Our first focus is on the separation of proteins and peptides due to conformational differences in the drift tube (labeled A in the following figure). In order to accurately analyze the peak profiles of the mobility spectra we use molecular mechanics/dynamics to sample the conformational space of the peptides and then calculate the energies of the different conformations using MOPAC calculations at the semi-empirical (AM1) level of theory.

Our second focus is on the separation of of small organic molecules with the same mass, but differ by electronic structure (labeled B). High-level ab initio calculations are used to analyze the potential energy surface of small radical cation organic molecules such that we can predict which radical cation reacts longer with the bath gas.


Molecular Modeling and Ion Mobility Time-of-Flight Mass Spectroscopy (Russell, Sawyer, Thomson, and Verbeck)

A

B

Collaborators:Collaborators:Ping LinPing Lin

Eric StratmannEric StratmannAlexandra NatalenseAlexandra Natalense

Robert ZuralesRobert ZuralesShaleen BottingShaleen Botting

Funding:Funding: Welch FoundationWelch Foundation

National Science FoundationNational Science FoundationTexas A&M Supercomputer FacilityTexas A&M Supercomputer Facility

Professor Robert R. LuccheseProfessor Robert R. LuccheseDepartment of ChemistryDepartment of ChemistryTexas A&M UniversityTexas A&M University

Computational Chemistry, Lucchese et al.

• When light of sufficient energy interacts with a molecule, a photon can be absorbed leading to the ionization of the molecule:

• The probability for ionization is proportional to the square of the dipole matrix element which is an integral over the wave functions that represent the initial state, the final ion state, and the photoelectron:

Molecular PhotoionizationMolecular Photoionization

€

M + hν → M + + e−


• The initial state, i, and the final ion state are, f, are described using standard quantum chemistry techniques.

• The wave function for the photoelectron, , is the solution of a one-electron integral scattering equation:

• This equation is not solved directly, we instead use a variational method to compute the required dipole matrix elements.

Scattering EquationsScattering Equations


Schwinger Variational EquationsSchwinger Variational Equations

• The dipole matrix element can be reduced to an integral over the coordinates of a single electron which in the bracket notation is:

• By expanding the wave function in a basis set, the matrix elements can be approximated by the following Schwinger variational matrix expression:


Single-Center ExpansionsSingle-Center Expansions

• All integrals are evaluated using single-center expansions where each function is expanded as

Typical values: lmax = 60 for N2 and lmax = 120 for CS2

• With this expansion all three-dimensional integrals become a sum over a set of radial integrals which are computed on a radial grid:

R. E. Stratmann et al., J. Chem. Phys. 104, 8989 (1996), and references therein.


• The most expensive computational step is the evaluation of two-electron exchange operators:

• Repeated transformations between the partial-wave and grid representations are used:

Two-Electron IntegralsTwo-Electron Integrals


Molecular Frame Photoelectron Molecular Frame Photoelectron Angular Distributions (MFPADs)Angular Distributions (MFPADs)

• The most detailed information that can be measured and computed is the molecular frame photoelectron angular distribution (MFPAD).

• The MFPAD depends on the relative orientation of the molecule and the polarization of the light (e. g. parallel, perpendicular, or magic angle 54º)

• The MFPADs can be either represented as 3D plots or in terms of four functions F00(k), F20(k), F21(k), and F22(k), where k is the angle between the molecular axis and the direction of the photoelectron.

• Good agreement with experiment is only obtained when a convolution with the apparatus function is performed.

R. R. Lucchese et al., Phys. Rev. A 65, 020702 (2002).


3D MFPAD in NO Photoionization3D MFPAD in NO PhotoionizationLeading to the Leading to the cc 33 State of NO State of NO++


MFPAD in NO PhotoionizationMFPAD in NO PhotoionizationLeading to the Leading to the cc 33 State of NO State of NO++

Dr. Akram Abu-OdehCenter for Transportation Computational Mechanics

Texas Transportation Institute

Roadside Safety Applications, Abu Odeh

Research Activities at TTIResearch Activities at TTI

• Side Impact with Rigid Pole

• Side Impact with Slip-Base Luminaire Pole








Side ImpactSide Impact

QuickTime™ and aCinepak decompressorare needed to see this picture.QuickTime™ and aCinepak decompressorare needed to see this picture.


CrushingCrushing


Total Force on Rigid Pole (35 km/hr)

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rce

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)

DYNA3DTest


Total Force on Rigid Pole (50 km/hr )

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-110

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Slip-Away Base Luminaire PoleSlip-Away Base Luminaire Pole


Slip-Away BaseSlip-Away Base


Slip-Away Base PlateSlip-Away Base Plate

• Bolts are torqued to sustain certain clamping force.

• Upper base moves upon impact.

• Lower base fixed to the ground.

• Bolts and nuts move out of the base.


Slip-Base Impact DirectionSlip-Base Impact Direction









Clamping Load ModelingClamping Load Modeling

• Springs between the two base.– Bolts, washers and nuts are not modeled.

• Springs between nut and bolt head.– Make nut sliding on bolt shaft.

• Thermal loads.– Drop bolt shaft temperature.

• Stress initialization.– Apply initial stress in the bolt shaft.




Initial Load Magnitude?Initial Load Magnitude?

• Higher Than the Sustained Clamping Force• Washers, Bases and Nuts Are Loaded As

Well• Some Sort of Relaxation Is Needed• Thermal Initial Load Leads to Undesired

Bolt Shaft Transverse Deformation• Higher Initial Spring Loads Lead to

Undesired Nut/bolt Head Deformation


Stress InitializationStress Initialization

• INITIAL_STRESS_SOLID Command

• Applied at Every Integration Point for All the Solid Elements in the Bolt Shaft

• Usually Reaches Sustained Clamping Force Level in 8 Milliseconds


Load Jump on ReleaseLoad Jump on Release

• Very detailed meshing of the nuts and slots is needed.

• Localized yielding might play a factor.

• The model will be computationally expensive.


Sensitivity to Nut ChamferingSensitivity to Nut Chamfering











Professor Strouboulis, Zhang and BabuskaProfessor Strouboulis, Zhang and BabuskaDepartment of Aerospace EngineeringDepartment of Aerospace Engineering

Generalized Finite Element Method: Strouboulis et al.

OverviewOverview

• Goal of the research• Description of PUM• Description of meshless idea• Features of GFEM

– Linear dependence– Solver– Integration– Special functions

• Performance of GFEM– Numerically generated handbook functions

• Handbook-based GFEM– Hierarchical handbooks

• Homogenization


GoalGoal• Use knowledge about the boundary value problem• Avoid meshing complicated geometries• Less degrees of freedom, more accuracy


Partition of Unity MethodPartition of Unity Method






Meshless TechniqueMeshless Technique

• Computational mesh is obtained without considering the geometry of the domain

Examples of GFEM mesh


Features of GFEM – Linear DependenceFeatures of GFEM – Linear Dependence


Features of GFEM – SolverFeatures of GFEM – Solver


Features of GFEM – Solver PerformanceFeatures of GFEM – Solver Performance


Features of GFEM – IntegrationFeatures of GFEM – Integration






GFEM with Numerically Generated GFEM with Numerically Generated Handbook FunctionsHandbook Functions


Solutions of Handbook ProblemsSolutions of Handbook Problems


Usage of the Handbook Solutions in the GFEMUsage of the Handbook Solutions in the GFEM


GFEM Solution Using Numerical GFEM Solution Using Numerical Handbook FunctionsHandbook Functions


Bifurcated Crack: Handbook problem meshBifurcated Crack: Handbook problem mesh


Bifurcated Crack: Handbook meshes on actual domainBifurcated Crack: Handbook meshes on actual domain


Bifurcated Crack: Handbook problem solutionBifurcated Crack: Handbook problem solution


GFEM using Handbook Solution of Bifurcated CrackGFEM using Handbook Solution of Bifurcated Crack


Handbook-based GFEMHandbook-based GFEM


Hierarchical handbooks for more Hierarchical handbooks for more complex problemscomplex problems


Illustration of hierarchical handbooksIllustration of hierarchical handbooks

(a) Mesh for the original

problem

(b) First level handbook

(c) Mesh for the first level

handbook

(d) Second level handbook


Overkill solution for ProblemOverkill solution for Problem

The overkill mesh is obtained by uniformly refining the domain six times. The overkill solution is obtained by using p = 5 and one level handbook functions with phb = 1, and the handbook functions are obtained by using p = 5 and pvoids = 1.The figure shows the overkill solution for = 1.125.


Results for ProblemResults for Problem

Professor Roland Allen, Dou, Dumitrica, Graves, TorralvaProfessor Roland Allen, Dou, Dumitrica, Graves, TorralvaDepartment of PhysicsDepartment of Physics

Physics, Allen et al.

OverviewOverview

• The response of matter to ultra-fast and ultra-intense laser pulses is a current frontier of science.

• New discoveries often result from the ability to explore a new regime. Here one is exploring both extremely short time scales (below one hundred femtoseconds) and extremely high intensities (above one terawatt per square centimeter).

• The usual approximations of theoretical physics and chemistry break down under these conditions, and both electrons and atoms exhibit new kinds of behavior.


Nonthermal phase transitionNonthermal phase transitionin Ge (experiment)in Ge (experiment)

• The above figure provides experimental evidence for an ultrafast and nonthermal solid-to-liquid phase transition in Ge, followed by recrystallization. These x-ray diffraction probe measurements employed 1.54 Angstrom photons, following 100 fs, 800 nm pump pulses. [After C. W. Siders et al., Science 286, 1340 (1999).]


Nonthermal phase transitionNonthermal phase transitionin GaAs (simulation)in GaAs (simulation)

• In this figure, the time-dependent dielectric function is shown for GaAs (the most important compound semiconductor) after it has been subjected to a very short and intense laser pulse.

• The behavior here signals a nonthermal phase transition, due to destabilization of the atomic bonding on a femtosecond time scale.[The work represented by this and all of the following figures was supported by the Texas A&M Supercomputing Facility, and was performed by the group R. E. Allen, B. Torralva, T. Dumitrica, J. S. Graves, R. Hamilton, Q. Gao, S. Khosravi, A. Burzo, and Y. Dou in the Physics Department.]


Dielectric function shows electronic Dielectric function shows electronic structurestructure

• Note three aspects in the behavior of the dielectric function:

– (1) There is a loss of the original structural features, signaling a loss of the original tetrahedral bonding in the semiconductor.

– (2) The imaginary part of the dielectric function, which measures absorption, becomes nonzero for photon energies below the original band gap energy of about 1.4 eV, In fact, one observes metallic behavior, which demonstrates a complete collapse of the band gap, beyond about 250 fs.

– (3) There is a "hump" which persists even after the band gap has collapsed, and which appears to indicate that there are still bonding-to-antibonding transitions, even after the long-range crystalline order has been lost.


Nonlinear susceptibility shows atomic Nonlinear susceptibility shows atomic structurestructure

• Time-dependent nonlinear susceptibility for GaAs just above the threshold laser intensity for a nonthermal phase transition.

• The nonlinear susceptibility probes the atomic structure of the material, and is thus complementary to the linear dielectric function, which probes the electronic structure.

• Notice that the nonlinear susceptibility falls to zero over the entire range of photon energies, signaling a loss of the original symmetry of the GaAs lattice.

All these results of the theoretical group at Texas A&M are in agreement with the measurements of the experimental groups at Harvard University, the University of Essen, Bell Labs, M. I. T., and the University of California at Berkeley.


Photoisomerization in chemistry and Photoisomerization in chemistry and biologybiology

• The primary process in vision is photoisomerization of retinal molecules in the eye.

• We have not yet performed a simulation for this molecule, but we have observed similar photoisomerization of the simpler butadiene molecule. [In our butadiene simulation, the photon energy was 2.0 eV, the

fluence 0.36 kJ per square meter, and the pulse duration 15 fs FWHM.]


Experimental results of the M.I.T./Florida Experimental results of the M.I.T./Florida groupgroup

• Excitation of the breathing mode in C60 buckyballs by an ultrafast laser pulse.

• This figure demonstrates coherent phonon oscillations in K3 C60 at 300 K. The pump-probe data were taken in reflectivity with a single wavelength pump-probe setup having a time resolution of about 20 fs. The larger inset shows the Fourier transform power spectrum with a sharp peak at 492.5 inverse centimeters.

After Fleischer, Pevzner, Dougherty, Zeiger, Dresselhaus, Dresselhaus, Ippen, and Hebard, Appl. Phys. Lett. 71, 2734 (1997).


Experimental results of the Lawrence Experimental results of the Lawrence Berkeley groupBerkeley group

• Excitation of the breathing mode in C60, and the pentagonal pinch mode at higher frequency, following an ultrafast laser pulse.

• The figure shows the light-induced negative differential transmittance of a C60 thin film detected at 580 nm as a function of time delay between 12 fs pump and probe pulses centered on 620 nm. The Fourier power spectrum of the oscillatory part of the response is shown in the inset.

After Dexheimer, Mittleman, Schoenlein, Vareka, Xiang, Zettl, and Shank, in "Ultrafast Phenomena VIII", edited by J. L. Martin, A. Migus, G. A. Mourou, and A. H. Zewail (Springer-Verlag, Berlin, 1993).


Simulation at the Texas A&M Simulation at the Texas A&M Supercomputer CenterSupercomputer Center

• Our calculations resolve what might appear to be a discrepancy between the results of the two experimental groups, by demonstrating that only the breathing mode is seen at high laser intensity, whereas both the breathing mode and the pentagonal-pinch mode are seen at lower intensity.

[After B. Torralva, T. A. Niehaus, M. Elstner, S. Suhai, Th. Frauenheim, and R. E. Allen, Physical Review B 64, 153105 (2001).]


Photofragmentation of a CPhotofragmentation of a C6060 molecule molecule

• Following a 35 fs, 2.0 eV laser pulse with a fluence of 1.17 kJ per square meter

• There are two particularly striking features:

– The first is the dramatic opening of both ends of the fullerene, accompanied by the breaking of many bonds.

– The second is the release of a dimer (at t = 952 fs) with a kinetic energy of 0.25 eV, which is slightly more than half the value reported for the experiments (Hohmann et al., Z. Phys. D. 33, 143 (1995)).

• Following emission of the dimer, the remaining 58 atoms tend to move back toward one another and reform bonds with both hexagons and pentagons. However, complete reformation of a closed structure is not observed, since there is still a large population of electrons in excited states at the end of the simulation.


Photofragmentation of a CPhotofragmentation of a C6060 molecule (higher molecule (higher

intensity laser pulse)intensity laser pulse)

• For a still higher fluence of 1.24 kJ per square meter, we observe that the cage begins to break apart at t = 299 fs, with the emission of both a dimer and a trimer.

• Experimentally, it is well established that C60 should normally fragment with the emission of even numbered clusters. In the present case, however, the cage continues to open up, and at t = 998 fs another dimer is emitted.

• It is apparent that the remaining cluster is structurally unstable, and the atoms continue to move apart. At t=2000 fs, two corannulene-like structures of 29 and 24 atoms are connected by only one bond. One therefore expects that that they will eventually separate rather than reform as a stable odd-numbered cluster with greater than 32 atoms.


Collision of atom withCollision of atom with C C6060

• Here the first panel shows a representative trajectory in a DFTED (density-functional-based, tight-binding, electron-ion dynamics) simulation: A 155 eV projectile carbon atom impinges on a buckyball.

• At t = 147 fs, we see that the backside of the cage has already reformed, and that two dimers have been released. (The release of dimers in collisional experiments with C60 has been widely observed in experiments.) The projectile atom is out of the picture at this point, since it requires only 23 fs to pass through the buckyball.

• At t = 1500 fs, the remaining 56 atoms have joined to form a new closed-cage structure, whose prominent features include the formation of a seven-membered ring accompanied by a extra pentagon.


Computer simulations show processes Computer simulations show processes in microscopic detailin microscopic detail

• This illustrates the power of computational science: Quantities that are experimentally inaccessible can be studied in the simulations and used to achieve further understanding. On the other hand, it is important to also calculate quantities that can be compared with experiment, like the dielectric function and second-order nonlinear susceptibility. [The full-width-at-half-maximum pulse duration is 70 fs, and the complete pulse extends from 0 to 140 fs. The field intensity is indicated on the upper left, with the amplitude measured in gauss cm.]

• Average displacement of GaAs atoms from their equilibrium positions for various intensities of the applied laser pulse. The nonthermal transition clearly occurs above A = 1.50 gauss cm.

• Many quantities like this can be monitored during a simulation.


Biological molecules are complicated Biological molecules are complicated but within reachbut within reach

• Our calculated spectrum for chlorophyll, which we also intend to treat in the future.

• Since chlorophyll absorbs strongly in the red, with a secondary absorption peak in the blue, it is green by reflected light.


Photodissociation of a moleculePhotodissociation of a molecule

• Photodissociation can be studied, as when cyclobutane dissociates to form two ethylene molecules in this simulation.


Photoisomerization Photoisomerization of a moleculeof a molecule

• One can observe the detailed dynamics during photoisomerization, as in this cis-to-tran conversion of butadiene.


Simulation of Simulation of symmetry-forbidden reactionsymmetry-forbidden reaction

• Snapshots of a simulation of two ethylene molecules approaching each other, with a kinetic energy of 0.2 eV. At t = 43 fs, the two ethylenes reach their closest point, with a separation of only 1.63 Angstroms. However, they bounce off each other rather than bonding, and are 7.46 Angstroms apart at t = 81 fs.


Toward laser control of chemical reactionsToward laser control of chemical reactions

• I.e., molecules in excited states react differently from molecules in the ground state, and electrons can be promoted to excited states in a selective way with the use of tailored laser pulses.

• In the bottom right panel, the structure has been equilibrated; all remaining electrons occupying excited states have been forced into the bonding states, and the excess kinetic energy has been removed. [The apparently missing bonds in earlier frames are artifacts of the graphics program.]

• Snapshots of a simulation of the approach of two ethylene molecules following the irradiation of the ethylene on the right by a 5 fs, 5.5 eV laser pulse with a fluence of 1.4 kJ per square meter.

• The laser-pulse interaction with the ethylene molecule was sufficient to change the symmetry-forbidden reaction to one that is symmetry-allowed.


Photoisomerization of butadienePhotoisomerization of butadieneEvolution of dihedral angles and bond length. This is another example of how processes can be studied in detail at the atomic level in computer simulations.


Depopulation of excited states stabilizes new Depopulation of excited states stabilizes new structurestructure

Evolution of highest occupied molecular orbital, lowest unoccupied molecular orbital, and other states, in photoisomerization of butadiene. At several avoided crossings, the electrons in excited states are observed to automatically undergo transitions to lower-energy states, reducing the electronic energy of the molecule and stabilizing its new structure.


How the simulations are performed: ion and How the simulations are performed: ion and electron dynamicselectron dynamics


How the simulations are performed: coupling of How the simulations are performed: coupling of electrons to laser pulseelectrons to laser pulse


Dr. Allen’s GroupDr. Allen’s Group

CCW from top right:John (Trey) GravesTraian Dumitrica

Ben TorralvaYusheng DouRoland Allen

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