Net-event kinetic Monte Carlo for overcoming stiffness in spatially homogeneous and distributed systems

Computers and Chemical Engineering

Volumn 29, Issue 4, 2005, Pages 701-712

  Snyder, M A ^a   Chatterjee, A ^a   Vlachos, D G ^a  

^a University of Delaware   (United States)

Author keywords

Coarse graining; Fast reversible processes; Kinetic Monte Carlo; Multiscale simulations; Stiffness

Indexed keywords

DIFFUSION; MATHEMATICAL MODELS; MEMBRANES; RANDOM PROCESSES; STIFFNESS;

KINETIC MONTE CARLO; REVERSIBLE PROCESSES; THICK MEMBRANES;

MONTE CARLO METHODS;

MONTE CARLO SIMULATION;

ANALYTIC METHOD; MATHEMATICAL MODEL; MONTE CARLO METHOD; RATING SCALE; REVIEW; SEPARATION TECHNIQUE; STOCHASTIC MODEL;

EID: 15944368965     PISSN: 00981354     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compchemeng.2004.09.016     Document Type: Article

References (46)

1. S.M. Auerbach Theory and simulation of jump dynamics, diffusion and phase equilibrium in nanopores International Reviews in Physical Chemistry 19 2000 155
2. Chatterjee, A., Katsoulakis, M.A., & Vlachos, D.G. (2004). Spatially adaptive grand canonical Monte Carlo simulations. Physical Review E, submitted for publication.
3. Chatterjee, A., Snyder, M.A., & Vlachos, D.G. (2004). Mesoscopic modeling of chemical reactivity. Chemical Engineering Science, in press.
4. Chatterjee, A., Vlachos, D.G., & Katsoulakis, M.A. (2004). Spatially adaptive lattice coarse-grained Monte Carlo simulations for diffusion. Journal of Chemical Physics, submitted for publication.
5. P.D. Christofides, and A.R. Teel Singular perturbations and input-to-state stability IEEE Transactions on Automatic Control 41 1996 1645
6. J. Crank The mathematics of diffusion 2nd ed. 1986 Oxford University Press Oxford
7. W.M. Deen Analysis of transport phenomena 1998 Oxford University Press New York
8. T.O. Drews, E.G. Webb, D.L. Ma, J. Alameda, R.D. Braatz, and R.C. Alkire Coupled mesoscale - continuum simulations of copper electrodeposition in a trench AIChE Journal 50 2004 226
9. C.W. Gear Numerical initial value problems in ordinary differential equations 1971 Prentice-Hall Englewood Cliffs, NJ
10. C.W. Gear, J. Li, and I.G. Kevrekidis The gap-tooth method in particle simulations Physics Letters A 316 2003 190
11. R. Ghez A primer of diffusion problems 1988 Wiley New York
12. G. Giacomin, and J.L. Lebowitz Phase segregation dynamics in particle systems with long range interactions. I. Macroscopic limits Journal of Statistical Physics 87 1997 37
13. D.T. Gillespie The chemical Langevin equation Journal of Chemical Physics 113 2000 297
14. D.T. Gillespie Approximate accelerated stochastic simulation of chemically reacting systems Journal of Chemical Physics 115 2001 1716
15. E.L. Haseltine, and J.B. Rawlings Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics Journal of Chemical Physics 117 2002 6959
16. J. He, H. Zhang, J. Chen, and Y. Yang Monte Carlo simulation of kinetics and chain length distributions in living free-radical polymerization Macromolecules 30 1997 8010
17. M. Hildebrand, and A.S. Mikhailov Mesoscopic modeling in the kinetic theory of adsorbates Journal of Physical Chemistry 100 1996 19089
18. A.C. Hindmarsh Odepack, a systematized collection of ODE solvers R.S. Stepleman Scientific computing 1983 North-Holland Publishing Company Amsterdam (p. 55)
19. A. Ishikawa, and T. Ogawa Dynamics of spinodal decomposition in finite-lifetime systems: nonlinear statistical theory based on a coarse-grained lattice-gas model Physical Review E 65 2002 026131
20. A.E. Ismail, G.C. Rutledge, and G. Stephanopoulos Multiresolution analysis in statistical mechanics. I. Using wavelets to calculate thermodynamic properties Journal of Chemical Physics 118 2003 4414
21. A.E. Ismail, G. Stephanopoulos, and G.C. Rutledge Multiresolution analysis in statistical mechanics. II. The wavelet transform as a basis for Monte Carlo simulations on lattices Journal of Chemical Physics 118 2003 4424
22. S. Kalamatianos, Y.K. Park, and D.G. Vlachos Two-parameter continuation algorithms for computing ignitions and extinctions: sensitivity analysis, parametric dependence, mechanism reduction, and stability criteria Combustion and Flame 112 1998 45
23. M.A. Katsoulakis, A.J. Majda, and D.G. Vlachos Coarse-grained stochastic processes and Monte Carlo simulations in lattice systems Journal of Computational Physics 186 2003 250
24. M. Katsoulakis, A.J. Majda, and D.G. Vlachos Coarse-grained stochastic processes for microscopic lattice systems Proceedings of the National Academy of the Sciences 100 2003 782
25. M.A. Katsoulakis, and D.G. Vlachos From microscopic interactions to macroscopic laws of cluster evolution Physical Review Letters 84 2000 1511
26. M.A. Katsoulakis, and D.G. Vlachos Coarse-grained stochastic processes and kinetic Monte Carlo simulators for the diffusion of interacting particles Journal of Chemical Physics 119 2003 9412
27. A. Kumar, P.D. Christofides, and P. Daoutidis Singular perturbation modeling of nonlinear processes with nonexplicit time-scale multiplicity Chemical Engineering Science 53 1998 1491
28. R. Lam, T. Basak, D.G. Vlachos, and M.A. Katsoulakis Validation of mesoscopic theories and their application to computing effective diffusivities Journal of Chemical Physics 115 2001 11278
29. Y. Lou, and P.D. Christofides Estimation and control of surface roughness in thin film growth using kinetic Monte-Carlo models Chemical Engineering Science 58 2003 3115
30. Y. Lou, and P.D. Christofides Feedback control of growth rate and surface roughness in thin film growth AIChE Journal 49 2003 2099
31. L.R. Petzold Automatic selection of methods for solving stiff and nonstiff systems of ordinary differential equations SIAM Journal on Scientific and Statistical Computing 4 1983 136
32. S. Raimondeau, P. Aghalayam, D.G. Vlachos, and M. Katsoulakis Bridging the gap of multiple scales: from microscopic, to mesoscopic, to macroscopic models P.T. Cummings P.R. Westmoreland B. Carnahan Foundations of molecular modeling and simulation 2000 American Institute of Chemical Engineers and Computer Aids for Chemical Engineering Education Colorado
33. S. Raimondeau, and D.G. Vlachos Recent developments on multiscale, hierarchical modeling of chemical reactors Chemical Engineering Journal 90 2002 3
34. C.V. Rao, and A.P. Arkin Stochastic chemical kinetics and the quasi-steady-state assumption: application to the Gillespie algorithm Journal of Chemical Physics 118 2003 4999
35. M. Rathinam, L.R. Petzold, and D.T. Gillespie Stiffness in stochastically reacting systems: the implicit tau-leaping method Journal of Chemical Physics 119 2003 12784
36. J.S. Reese, S. Raimondeau, and D.G. Vlachos Monte Carlo algorithms for complex surface reaction mechanisms: efficiency and accuracy Journal of Computational Physics 173 2001 302
37. H. Resat, H.S. Wiley, and D.A. Dixon Probability-weighted dynamic Monte Carlo method for reaction kinetics simulations Journal of Chemical Physics 105 2001 11026
38. T.P. Schulze A hybrid scheme for simulating epitaxial growth Journal of Crystal Growth 263 2004 605
39. T.P. Schulze, P. Smereka, and E. Weinan Coupling kinetic Monte-Carlo and continuum models with application to epitaxial growth Journal of Computational Physics 189 2003 197
40. M.A. Snyder, D.G. Vlachos, and M.A. Katsoulakis Mesoscopic modeling of transport and reaction in microporous crystalline membranes Chemical Engineering Science 58 2003 895
41. M. Tammaro, M. Sabella, and J.W. Evans Hybrid treatment of spatio-temporal behavior in surface reactions with coexisting immobile and highly mobile reactants Journal of Chemical Physics 103 1995 10277
42. D.G. Vlachos Multiscale integration hybrid algorithms for homogeneous-heterogeneous reactors AIChE Journal 43 1997 3031
43. D.G. Vlachos Stochastic modeling of chemical microreactors with detailed kinetics: induction times and ignitions of H2 in air Chemical Engineering Science 53 1998 157
44. Vlachos, D. G. (2004). A review of multiscale analysis: examples from systems biology, materials engineering, and other fluid-surface interacting systems. Advancement in Chemical Engineering, submitted for publication.
45. D.G. Vlachos, and M.A. Katsoulakis Derivation and validation of mesoscopic theories for diffusion of interacting molecules Physical Review Letters 85 2000 3898
46. E. Weinan, B. Engquist, and Z.Y. Huang Heterogeneous multiscale method: A general methodology for multiscale modeling Physical Review B 67 2003 article 092101, pp. 092101-1-092101-4