Crossing the Mesoscale No-Man's Land via Parallel Kinetic Monte Carlo

The kinetic Monte Carlo method and its variants are powerful tools for modeling materials at the mesoscale, meaning at length and time scales in between the atomic and continuum. We have completed a 3 year LDRD project with the goal of developing a parallel kinetic Monte Carlo capability and applying it to materials modeling problems of interest to Sandia. In this report we give an overview of the methods and algorithms developed, and describe our new open-source code called SPPARKS, for Stochastic Parallel PARticle Kinetic Simulator. We also highlight the development of several Monte Carlo models in SPPARKS for specific materials modeling applications, including grain growth, bubble formation, diffusion in nanoporous materials, defect formation in erbium hydrides, and surface growth and evolution.

[1]  Michael Biehl,et al.  A Kinetic Monte Carlo method for the simulation of heteroepitaxial growth , 2002 .

[2]  David A. Bader,et al.  A Graph-Theoretic Analysis of the Human Protein-Interaction Network Using Multicore Parallel Algorithms , 2007, IPDPS.

[3]  William S. Hlavacek,et al.  Rule-based modeling of biochemical networks: Research Articles , 2005 .

[4]  Michael A. Gibson,et al.  Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels , 2000 .

[5]  Dietrich E. Wolf,et al.  Diffusion on strained surfaces , 1997 .

[6]  P. Markondeya Raj,et al.  Anisotropic shrinkage during sintering of particle-oriented systems—numerical simulation and experimental studies , 2002 .

[7]  Anand Jagota,et al.  Viscosities and sintering rates of a two-dimensional granular composite , 1993 .

[8]  Veena Tikare,et al.  Multi‐Scale Study of Sintering: A Review , 2006 .

[9]  V. Turk,et al.  Lysozyme-catalyzed reaction of the N-acetylglucosamine hexasaccharide. Dependence of rate on pH. , 1973, The Journal of biological chemistry.

[10]  Makoto Itoh,et al.  Atomic-scale homoepitaxial growth simulations of reconstructed III–V surfaces , 2001 .

[11]  Hong Li,et al.  Efficient formulation of the stochastic simulation algorithm for chemically reacting systems. , 2004, The Journal of chemical physics.

[12]  Kazunari Shinagawa,et al.  Finite element simulation of sintering process : Microscopic modelling of powder compacts and constitutive equation for sintering , 1996 .

[13]  Y. G. Yang,et al.  A Monte Carlo simulation of the physical vapor deposition of nickel , 1997 .

[14]  Veena Tikare,et al.  Numerical simulation of solid state sintering II :sintering of a powder compact. , 2002 .

[15]  William S. Hlavacek,et al.  Rule-based modeling of biochemical networks , 2005, Complex..

[16]  Jacques G. Amar,et al.  Hybrid asynchronous algorithm for parallel kinetic Monte Carlo simulations of thin film growth , 2006, J. Comput. Phys..

[17]  Alan Weiss,et al.  Synchronous relaxation for parallel Ising spin simulations , 2001, Proceedings 15th Workshop on Parallel and Distributed Simulation.

[18]  Thomas Wilhelm,et al.  Physical and Functional Modularity of the Protein Network in Yeast* , 2003, Molecular & Cellular Proteomics.

[19]  Jeffrey W. Smith,et al.  Stochastic Gene Expression in a Single Cell , .

[20]  Muruhan Rathinam,et al.  Stiffness in stochastic chemically reacting systems: The implicit tau-leaping method , 2003 .

[21]  Jean Lapujoulade,et al.  The roughening of metal surfaces , 1994 .

[22]  Yang Cao,et al.  Multiscale stochastic simulation algorithm with stochastic partial equilibrium assumption for chemically reacting systems , 2005 .

[23]  ICHAEL,et al.  Formation and consequences of misfit dislocations in heteroepitaxial growth , 2007 .

[24]  A. Arkin,et al.  Stochastic mechanisms in gene expression. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[25]  D. Gillespie.  Approximate accelerated stochastic simulation of chemically reacting systems , 2001 .

[26]  Miroslav Kotrla,et al.  Numerical simulations in the theory of crystal growth , 1996 .

[27]  W. H. Weinberg,et al.  Theoretical foundations of dynamical Monte Carlo simulations , 1991 .

[28]  A. Voter,et al.  Classically exact overlayer dynamics: Diffusion of rhodium clusters on Rh(100). , 1986, Physical review. B, Condensed matter.

[29]  Veena Tikare,et al.  An Experimental Validation of a 3D Kinetic, Monte Carlo Model for Microstructural Evolution during Sintering , 2006 .

[30]  M. Kotrla,et al.  Theory and simulation of crystal growth , 1997 .

[31]  Eric Vanden-Eijnden,et al.  Nested stochastic simulation algorithm for chemical kinetic systems with disparate rates. , 2005, The Journal of chemical physics.

[32]  Thomas Edward Buchheit,et al.  Microstructural and mechanical properties investigation of electrodeposited and annealed LIGA nickel structures , 2002 .

[33]  Eugene A. Olevsky,et al.  Theory of sintering: from discrete to continuum , 1998 .

[34]  Peter Jaeckel,et al.  Monte Carlo methods in finance , 2002 .

[35]  E. Olevsky,et al.  Numerical Simulation of Solid‐State Sintering: I, Sintering of Three Particles , 2003 .

[36]  R. Johnson,et al.  Mechanisms, models and methods of vapor deposition , 2001 .

[37]  Nadia Busi,et al.  Stochastic Simulation of Biological Systems with Dynamical Compartment Structure , 2007, CMSB.

[38]  R. J. Dodd,et al.  Monte-Carlo simulations of galaxy systems , 1982 .

[39]  Elizabeth A. Holm,et al.  A fast serial algorithm for the finite temperature quenched Potts model , 1993 .

[40]  James E. Butler,et al.  A kinetic Monte Carlo method for the atomic-scale simulation of chemical vapor deposition: Application to diamond , 1997 .

[41]  Jared E. Toettcher,et al.  Stochastic Gene Expression in a Lentiviral Positive-Feedback Loop: HIV-1 Tat Fluctuations Drive Phenotypic Diversity , 2005, Cell.

[42]  Grant Heffelfinger,et al.  A comparison between two massively parallel algorithms for Monte Carlo computer simulation: An investigation in the grand canonical ensemble , 1996, J. Comput. Chem..

[43]  W. Mullins.  Theory of Thermal Grooving , 1957 .

[44]  Veena Tikare,et al.  Numerical simulation of solid state sintering , 2005 .

[45]  D G Vlachos,et al.  Overcoming stiffness in stochastic simulation stemming from partial equilibrium: a multiscale Monte Carlo algorithm. , 2005, The Journal of chemical physics.

[46]  A. Arkin,et al.  Stochastic amplification and signaling in enzymatic futile cycles through noise-induced bistability with oscillations. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[47]  Daniel T Gillespie,et al.  Stochastic simulation of chemical kinetics. , 2007, Annual review of physical chemistry.

[48]  Ryan R. Wixom,et al.  First principles site occupation and migration of hydrogen, helium, and oxygen in β-phase erbium hydride , 2008 .

[49]  Bennett L. Fox,et al.  Generating Markov-Chain Transitions Quickly: I , 1990, INFORMS J. Comput..

[50]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[51]  A. Chernov,et al.  Computer model of crystallization of binary systems; Kinetic phase transitions , 1967 .

[52]  D. Gillespie.  A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions , 1976 .

[53]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[54]  P. Swain,et al.  Stochastic Gene Expression in a Single Cell , 2002, Science.

[55]  Gerard T. Barkema,et al.  Monte Carlo Methods in Statistical Physics , 1999 .

[56]  Michael Hucka,et al.  A Correction to the Review Titled "Rules for Modeling Signal-Transduction Systems" by W. S. Hlavacek et al. , 2006, Science's STKE.

[57]  Christopher Roland,et al.  Thin film deposition: fundamentals and modeling , 1998 .

[58]  George H. Gilmer,et al.  3 – Statistical Thermodynamics of Clean Surfaces , 1975 .

[59]  Michael Biehl,et al.  Kinetic Monte Carlo simulations of heteroepitaxial growth , 2003 .

[60]  A. Arkin,et al.  Stochastic kinetic analysis of developmental pathway bifurcation in phage lambda-infected Escherichia coli cells. , 1998, Genetics.

[61]  Eric Fournié,et al.  Monte Carlo Methods in Finance , 2002 .

[62]  Jacques G. Amar,et al.  Semirigorous synchronous sublattice algorithm for parallel kinetic Monte Carlo simulations of thin film growth , 2005 .

[63]  L. Devroye.  Non-Uniform Random Variate Generation , 1986 .

[64]  Abhijit Chatterjee,et al.  An overview of spatial microscopic and accelerated kinetic Monte Carlo methods , 2007 .

[65]  M. Biehl,et al.  Interplay of strain relaxation and chemically induced diffusion barriers: Nanostructure formation in 2D alloys , 2004, cond-mat/0411271.

[66]  C. Rao,et al.  Control motifs for intracellular regulatory networks. , 2001, Annual review of biomedical engineering.

[67]  Roger Brent,et al.  Automatic generation of cellular reaction networks with Moleculizer 1.0 , 2005, Nature Biotechnology.

[68]  T. Kawamura,et al.  Monte Carlo simulation of thin film growth on Si surfaces , 1993 .

[69]  S. Lindskog.  Structure and mechanism of carbonic anhydrase. , 1997, Pharmacology & therapeutics.

[70]  Sanguthevar Rajasekaran,et al.  Fast algorithms for generating discrete random variates with changing distributions , 1993, TOMC.

[71]  J. Raser,et al.  Control of Stochasticity in Eukaryotic Gene Expression , 2004, Science.

[72]  Kurt Mehlhorn,et al.  Maintaining Discrete Probability Distributions Optimally , 1993, ICALP.

[73]  Jane Hillston,et al.  Modelling Yeast Pre-rRNA Processing , 2007, CMSB.

[74]  F. Much,et al.  Simulation of wetting-layer and island formation in heteroepitaxial growth , 2003 .

[75]  Haydn N. G. Wadley,et al.  Atomic assembly of Cu/Ta multilayers: Surface roughness, grain structure, misfit dislocations, and amorphization , 2007 .

[76]  A. Rollett,et al.  The Monte Carlo Method , 2004 .

[77]  Corbett Chandler. Battaile,et al.  Monte Carlo Methods for Simulating Thin Film Deposition , 2005 .

[78]  D. Gillespie.  Exact Stochastic Simulation of Coupled Chemical Reactions , 1977 .

[79]  Mads Kærn,et al.  Noise in eukaryotic gene expression , 2003, Nature.

[80]  David A. Bader,et al.  A Graph-Theoretic Analysis of the Human Protein-Interaction Network Using Multicore Parallel Algorithms , 2007, 2007 IEEE International Parallel and Distributed Processing Symposium.

[81]  A. B. Bortz,et al.  A new algorithm for Monte Carlo simulation of Ising spin systems , 1975 .

[82]  Enge Wang,et al.  Three-dimensional Schwoebel–Ehrlich barrier , 2000 .

[83]  James R Faeder,et al.  Kinetic Monte Carlo method for rule-based modeling of biochemical networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[84]  Tim P. Schulze,et al.  Efficient kinetic Monte Carlo simulation , 2008, J. Comput. Phys..

[85]  Arthur F. Voter,et al.  Introduction to the Kinetic Monte Carlo Method , 2007 .