An overview of spatial microscopic and accelerated kinetic Monte Carlo methods
10.1007/s10820-006-9042-9
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Springer Science and Business Media LLC
Journal of Computer-Aided Materials Design (297)
Bibliography

Chatterjee, A., & Vlachos, D. G. (2007). An overview of spatial microscopic and accelerated kinetic Monte Carlo methods. Journal of Computer-Aided Materials Design, 14(2), 253–308.

Authors 2
  1. Abhijit Chatterjee (first)
  2. Dionisios G. Vlachos (additional)
References 150 Referenced 385
  1. Metropolis N., Rosenbluth A.W., Rosenbluth M.N., Teller A.H., Teller E. (1953). Equation of state calculations by fast computing machines. J. Chem. Phys 21: 1087–1092 (10.1063/1.1699114) / J. Chem. Phys by N. Metropolis (1953)
  2. Allen M.P., Tildesley D.J. (1989). Computer Simulation of Liquids. Oxford Science Publications, Oxford / Computer Simulation of Liquids by M.P. Allen (1989)
  3. Frenkel D., Smit B. (1996). Understanding Molecular Simulation: From Algorithms to Applications. Academic Press, New York / Understanding Molecular Simulation: From Algorithms to Applications by D. Frenkel (1996)
  4. Auerbach S.M. (2000). Theory and simulation of jump dynamics, diffusion and phase equilibrium in nanopores. Int. Rev. Phys. Chem. 19: 155–198 (10.1080/01442350050020879) / Int. Rev. Phys. Chem. by S.M. Auerbach (2000)
  5. Binder K. (1986). Monte Carlo Methods in Statistical Physics, vol. 7. Springer, Berlin Heidelberg New York (10.1007/978-3-642-82803-4) / Monte Carlo Methods in Statistical Physics, vol. 7 by K. Binder (1986)
  6. Binder K. (1992). Atomistic modeling of materials properties by Monte-Carlo simulation. Adv. Mater 4: 540–547 (10.1002/adma.19920040904) / Adv. Mater by K. Binder (1992)
  7. Landau D.P., Binder K. (2000). A Guide to Monte Carlo Simulations in Statistical Physics. Cambridge University Press, Cambridge / A Guide to Monte Carlo Simulations in Statistical Physics by D.P. Landau (2000)
  8. Ciccotti G., Frenkel D., McDonald I.R. (1987). Simulation of Liquids and Solids. Molecular Dynamics and Monte Carlo Methods in Statistical Mechanics. North-Holland, Amsterdam / Simulation of Liquids and Solids Molecular. Dynamics and Monte Carlo Methods in Statistical Mechanics by G. Ciccotti (1987)
  9. Dooling D.J., Broadbelt L.J. (2001). Generic Monte Carlo tool for kinetic modeling. Ind. Eng. Chem. Res 40: 522–529 (10.1021/ie000310q) / Ind. Eng. Chem. Res by D.J. Dooling (2001)
  10. Gilmer G.H., Huang H.C., de la Rubia T.D., Dalla Torre J., Baumann F. (2000). Lattice Monte Carlo models of thin film deposition. Thin Solid Films 365: 189–200 (10.1016/S0040-6090(99)01057-3) / Thin Solid Films by G.H. Gilmer (2000)
  11. Nieminen R., Jansen A. (1997). Monte Carlo simulations of surface reactions. Appl. Catal. A: Gen 160: 99–123 (10.1016/S0926-860X(97)00130-0) / Appl. Catal. A: Gen by R. Nieminen (1997)
  12. Hill T.L. (1986). An Introduction to Statistical Thermodynamics. Dover, New York / An Introduction to Statistical Thermodynamics by T.L. Hill (1986)
  13. Chakraborty A.K. (2001). Molecular Modeling and Theory in Chemical Engineering, vol. 28. Academic Press, New York / Molecular Modeling and Theory in Chemical Engineering, vol. 28 by A.K. Chakraborty (2001)
  14. Broadbelt L., Snurr R. (2000). Applications of molecular modeling in heterogeneous catalysis research. Appl. Catal. A: Gen 200: 23–46 (10.1016/S0926-860X(00)00648-7) / Appl. Catal. A: Gen by L. Broadbelt (2000)
  15. Sholl D.S., Tully J.C. (1998). A generalized surface hopping method. J. Chem. Phys 109: 7702–7710 (10.1063/1.477416) / J. Chem. Phys by D.S. Sholl (1998)
  16. Catlow C.R.A., Bell R.G., Gale J.D. (1994). Computer modeling as a technique in materials chemistry. J. Mat. Chem 4: 781–792 (10.1039/jm9940400781) / J. Mat. Chem by C.R.A. Catlow (1994)
  17. Evans J.W., Miesch M.S. (1991). Catalytic reaction kinetics near a first-order poisoning transition. Surf. Sci 245: 401–410 (10.1016/0039-6028(91)90042-Q) / Surf. Sci by J.W. Evans (1991)
  18. Hansen E.W., Neurock M. (2000). First-principles-based Monte Carlo simulation of ethylene hydrogenation kinetics on Pd. J. Catal 196: 241–252 (10.1006/jcat.2000.3018) / J. Catal by E.W. Hansen (2000)
  19. Huang H.C., Gilmer G.H. (1999). Multi-lattice Monte Carlo model of thin films. J. Comput. Aided Mater. Des 6: 117–127 (10.1023/A:1008722515055) / J. Comput. Aided Mater. Des by H.C. Huang (1999)
  20. Jansen A.P.J. (1995). Monte Carlo simulations of chemical reactions on a surface with time-dependent reaction-rate constants. Comput. Phys. Commun 86: 1–12 (10.1016/0010-4655(94)00155-U) / Comput. Phys. Commun by A.P.J. Jansen (1995)
  21. Kang H.C., Weinberg W.H. (1988). Dynamic Monte Carlo with a proper energy barrier: Surface diffusion and two-dimensional domain ordering. J. Chem. Phys 90: 2824–2830 (10.1063/1.455932) / J. Chem. Phys by H.C. Kang (1988)
  22. Kew J., Wilby M.R., Vvedensky D.D. (1993). Continuous-space Monte Carlo simulations of epitaxial-growth, Journal of Crystal Growth. J. Crystal Growth 127: 508–512 (10.1016/0022-0248(93)90671-I) / J. Crystal Growth by J. Kew (1993)
  23. Khor K.E., Das Sarma S. (2002). Quantum dot self-assembly in growth of strained-layer thin films: A kinetic Monte Carlo study. Phys. Rev. B 62: 16657–16664 (10.1103/PhysRevB.62.16657) / Phys. Rev. B by K.E. Khor (2002)
  24. Macedonia M.D., Maginn E.J. (2000). Impact of confinement on zeolite cracking selectivity via Monte Carlo integration. AIChE J. 46: 2504–2517 (10.1002/aic.690461217) / AIChE J. by M.D. Macedonia (2000)
  25. Nikolakis V., Vlachos D.G., Tsapatsis M. (1999). Modeling of zeolite L crystallization using continuum time Monte Carlo simulations. J. Chem. Phys. 111: 2143–2150 (10.1063/1.479484) / J. Chem. Phys. by V. Nikolakis (1999)
  26. Novere N.L., Shimizu T.S. (2001). STOCHSIM: modelling of stochastic biomolecular processes. Bioinformatics 17: 575–576 (10.1093/bioinformatics/17.6.575) / Bioinformatics by N.L. Novere (2001)
  27. Schulze T.P. (2004). A hybrid scheme for simulating epitaxial growth. J. Crystal Growth 263: 605–615 (10.1016/j.jcrysgro.2003.11.108) / J. Crystal Growth by T.P. Schulze (2004)
  28. Zhdanov V.P., Kasemo B. (1997). Kinetics of rapid reactions on nanometer catalyst particles. Phys. Rev. B, 55, 4105–4108 (10.1103/PhysRevB.55.4105) / Phys. Rev. B, by V.P. Zhdanov (1997)
  29. Gilmer G. (1980). Computer models of crystal growth. Science 208: 355–363 (10.1126/science.208.4442.355) / Science by G. Gilmer (1980)
  30. Muller-Krumbhaar H. (1978). Kinetics of crystal growth. In: Kaldis E. (eds) Current Topics in Materials Science. North-Holland, Amsterdam, pp. 1–46 / Current Topics in Materials Science. by H. Muller-Krumbhaar (1978)
  31. Drews T.O., Ganley J.C., Alkire R.C. (2003). Evolution of surface roughness during copper electrodeposition in the presence of additives - Comparison of experiments and Monte Carlo simulations. J. Electrochem. Soc 150: C325–C334 (10.1149/1.1563653) / J. Electrochem. Soc by T.O. Drews (2003)
  32. Lou Y., Christofides P.D. (2004). Feedback control of surface roughness of GaAs (001) thin films using kinetic Monte Carlo models. Comput. Chem. Eng 29: 225–241 (10.1016/j.compchemeng.2004.07.006) / Comput. Chem. Eng by Y. Lou (2004)
  33. Gallivan M.A., Murray R.M. (2004). Reduction and identification methods for Markovian control systems, with application to thin film deposition. Int. J. Robust Nonlinear Control 14: 113–132 (10.1002/rnc.866) / Int. J. Robust Nonlinear Control by M.A. Gallivan (2004)
  34. Wicke E., Kunmann P., Keil W., Schiefler J. (1980). Unstable and oscillatory behavior in heterogeneous catalysis. Berichte der Bunsen-Gesellschaft-Phys. Chem. Chem. Phys 84: 315–323 (10.1002/bbpc.19800840405) / Berichte der Bunsen-Gesellschaft-Phys. Chem. Chem. Phys by E. Wicke (1980)
  35. Ziff R.M., Gulari E., Barshad Y. (1986). Kinetic phase transitions in an irreversible surface-reaction model. Phys. Rev. Lett. 56: 2553–2556 (10.1103/PhysRevLett.56.2553) / Phys. Rev. Lett. by R.M. Ziff (1986)
  36. Vlachos D.G. (2005). A review of multiscale analysis: Examples from systems biology, materials engineering, and other fluid-surface interacting systems. Adv. Chem. Eng 30: 1–61 (10.1016/S0065-2377(05)30001-9) / Adv. Chem. Eng by D.G. Vlachos (2005)
  37. Cuitino A.M., Stainier L., Wang G.F., Strachan A., Cagin T., Goddard W.A., Ortiz M. (2002). A multiscale approach for modeling crystalline solids. J. Comput. Aided Mater. Des 8: 127–149 (10.1023/A:1020012431230) / J. Comput. Aided Mater. Des by A.M. Cuitino (2002)
  38. Miller R.E., Tadmor E.B. (2002). The quasicontinuum method: Overview, applications and current directions. J. Comput. Aided Mater. Des 9: 203–239 (10.1023/A:1026098010127) / J. Comput. Aided Mater. Des by R.E. Miller (2002)
  39. Maroudas D. (2003). Multiscale modeling. In: Challenges for the Chemical Sciences in the 21st Century: Information and Communications Report. National Academies, Washington, DC, pp. 133–136 / In: Challenges for the Chemical Sciences in the 21st Century: Information and Communications Report. by D. Maroudas (2003)
  40. Grujicic M., Lai S.G. (2001). Multi-length scale modeling of chemical vapor deposition of titanium nitride coatings. J. Mater. Sci 36: 2937–2953 (10.1023/A:1017958621586) / J. Mater. Sci by M. Grujicic (2001)
  41. Jaraiz M., Rubio E., Castrillo P., Pelaz L., Bailon L., Barbolla J., Gilmer G.H., Rafferty C.S. (2000). Kinetic Monte Carlo simulations: an accurate bridge between ab initio calculations and standard process experimental data. Mater. Sci. Semiconductor Process 3: 59–63 (10.1016/S1369-8001(00)00013-5) / Mater. Sci. Semiconductor Process by M. Jaraiz (2000)
  42. Kremer K., Muller-Plathe F. (2002). Multiscale simulation in polymer science. Mol. Simul 28: 729–750 (10.1080/0892702021000002458) / Mol. Simul by K. Kremer (2002)
  43. Duke T.A.J., Le Novere N., Bray D. (2001). Conformational spread in a ring of proteins: A stochastic approach to allostery. J. Mol. Biol 308: 541–553 (10.1006/jmbi.2001.4610) / J. Mol. Biol by T.A.J. Duke (2001)
  44. McAdams H.H., Arkin A. (1997). Stochastic mechanisms in gene expression. Proc. Natl. Acad. Sci 94: 814–819 (10.1073/pnas.94.3.814) / Proc. Natl. Acad. Sci by H.H. McAdams (1997)
  45. McAdams H.H., Arkin A. (1999). It’s a noisy business! Genetic regulation at the nanomolar scale. Trends in Genetics 15: 65–69 (10.1016/S0168-9525(98)01659-X) / Trends in Genetics by H.H. McAdams (1999)
  46. Woolf P.J., Linderman J.J. (2003). Self organization of membrane proteins via dimerization. Biophys. Chem 104: 217–227 (10.1016/S0301-4622(02)00369-1) / Biophys. Chem by P.J. Woolf (2003)
  47. Mayawala K., Vlachos D.G., Edwards J.S. (2006). Spatial modeling of dimerization reaction dynamics in the plasma membrane: Monte Carlo vs. continuum differential equations. Biophys. Chem 121: 194–208 (10.1016/j.bpc.2006.01.008) / Biophys. Chem by K. Mayawala (2006)
  48. National Research Council (NRC): Beyond the Molecular Frontier: Challenges for Chemistry and Chemical Engineering. National Research Council, The National Academy Press, BCST, www.nap.edu publication (2003)
  49. Partnership, C.I.V.T., Chemical Industry Vision2020 Technology Partnership, Chemical Industry R&D Roadmap for Nanomaterials by design. www.ChemicalVision2020.org (2003)
  50. Vlachos, D.G.: Molecular modeling for non-equilibrium chemical processes. In: Lee, S. (ed.) Encyclopedia of Chemical Processing, pp. 1717–1726. Taylor and Francis, New York.
  51. Voter, A.F.: Introduction to the Kinetic Monte Carlo Method. Radiation Effects in Solids. Springer, NATO Publishing unit, Dordrecht (2006) in press.
  52. Gardiner C.W. (1985). Handbook of Stochastic Methods, 2nd edn. Springer, Berlin Heidelberg New York / Handbook of Stochastic Methods by C.W. Gardiner (1985)
  53. Ghez R. (1988). A Primer of Diffusion Problems. John Wiley & Sons, New York (10.1002/3527602836) / A Primer of Diffusion Problems by R. Ghez (1988)
  54. Vlachos D.G., Schmidt L.D., Aris R. (1993). Kinetics of faceting of crystals in growth, etching, and equilibrium. Phys. Rev. B 47: 4896–4909 (10.1103/PhysRevB.47.4896) / Phys. Rev. B by D.G. Vlachos (1993)
  55. Magna A.L., Coffa S., Colomo L. (1999). Role of externded vacancy-vacancy interaction on the ripening of voids in silicon. Phys. Rev. Lett 82: 1720–1723 (10.1103/PhysRevLett.82.1720) / Phys. Rev. Lett by A.L. Magna (1999)
  56. Domain C., Becquart C.S., Malerba L. (2004). Simulation of radiation damage in Fe alloys: an object kinetic Monte Carlo approach. J. Nucl. Mater 335: 121–145 (10.1016/j.jnucmat.2004.07.037) / J. Nucl. Mater by C. Domain (2004)
  57. Sadigh B., Lenosky T.J., Theiss S.K., Caturla M.J., de la Rubia T.D., Foad M.A. (1999). Mechanism of boron diffusion in silicon: An ab initio and kinetic Monte Carlo study. Phys. Rev. Lett. 83: 4341–4344 (10.1103/PhysRevLett.83.4341) / Phys. Rev. Lett. by B. Sadigh (1999)
  58. Noda T. (2003). Modeling of Indium diffusion and end-of-range defects in Silicon using a kinetic Monte Carlo simulation. J. Appl. Phys 94: 6396–6400 (10.1063/1.1621087) / J. Appl. Phys by T. Noda (2003)
  59. Gordon S.M.J., Kenny S.D., Smith R. (2005). Diffusion dynamics of defects in Fe and Fe-P systems. Phys. Rev. B 72: 214104 (10.1103/PhysRevB.72.214104) / Phys. Rev. B by S.M.J. Gordon (2005)
  60. Soneda N., Rubia T.D. (1998). Defect production, annealing kinetics and damage evolution in a-Fe: an atomic-scale compuer simulation. Philos. Mag. A 78: 995–1019 (10.1080/01418619808239970) / Philos. Mag. A by N. Soneda (1998)
  61. Dai J., Kanter J.M., Kapur S.S., Seider W.D., Sinno T. (2005). On-lattice kinetic Monte Carlo simulations of point defect aggregation in entropically influenced crystalline systems. Phys. Rev. B 72: 134102 (10.1103/PhysRevB.72.134102) / Phys. Rev. B by J. Dai (2005)
  62. Fahey P.M., Griffin B.P., Plummer J.D. (1989). Point defects and dopant diffusion in silicon. Rev. Mod. Phys 61: 289 (10.1103/RevModPhys.61.289) / Rev. Mod. Phys by P.M. Fahey (1989)
  63. Flynn C.P. (1972). Point defects and diffusion. Calderon Press, Oxford / Point defects and diffusion by C.P. Flynn (1972)
  64. Vlachos D.G., Katsoulakis M.A. (2000). Derivation and validation of mesoscopic theories for diffusion of interacting molecules. Phys. Rev. Lett 85: 3898–3901 (10.1103/PhysRevLett.85.3898) / Phys. Rev. Lett by D.G. Vlachos (2000)
  65. Lam R., Basak T., Vlachos D.G., Katsoulakis M.A. (2001). Validation of mesoscopic theories and their application to computing effective diffusivities. J. Chem. Phys 115: 11278–11288 (10.1063/1.1415460) / J. Chem. Phys by R. Lam (2001)
  66. Gillespie D.T. (1976). A general method for numerically simulating the stochastic evolution of coupled chemical reactions. J. Comput. Phys 22: 403–434 (10.1016/0021-9991(76)90041-3) / J. Comput. Phys by D.T. Gillespie (1976)
  67. Gomer R. (1990). Diffusion of adsorbates on metal surfaces. Rep. Prog. Phys 53: 917–1002 (10.1088/0034-4885/53/7/002) / Rep. Prog. Phys by R. Gomer (1990)
  68. Kapur S.S., Prasad M., Crocker J.C., Sinno T. (2005). Role of configurational entropy in the thermodynamics of clusters of point defects in crystalline solids. Phys. Rev. B 72: 014119 (10.1103/PhysRevB.72.014119) / Phys. Rev. B by S.S. Kapur (2005)
  69. Henkelman G., Jonsson H. (2001). Long time scale kinetic Monte Carlo simulations without lattice approximation and predefined event table. J. Chem. Phys 115: 9657 (10.1063/1.1415500) / J. Chem. Phys by G. Henkelman (2001)
  70. Schulze T.P. (2002). Kinetic Monte Carlo simulations with minimal searching. Phys. Rev. E 65: 036704 (10.1103/PhysRevE.65.036704) / Phys. Rev. E by T.P. Schulze (2002)
  71. Lukkien J.J., Segers J.P.L., Hilbers P.A.J., Gelten R.J., Jansen A.P.J. (1998). Efficient Monte Carlo methods for the simulation of catalytic surface reactions. Phys. Rev. E 58: 2598–2610 (10.1103/PhysRevE.58.2598) / Phys. Rev. E by J.J. Lukkien (1998)
  72. Bortz A.B., Kalos M.H., Lebowitz J.L. (1975). A new algorithm for Monte Carlo simulations of Ising spin systems. J. Comput. Phys 17: 10–18 (10.1016/0021-9991(75)90060-1) / J. Comput. Phys by A.B. Bortz (1975)
  73. Snyder M.A., Chatterjee A., Vlachos D.G. (2004). Net-event kinetic Monte Carlo for overcoming stiffness in spatially homogeneous and distributed systems, invited. Comput. Chem. Eng 29: 701–712 (10.1016/j.compchemeng.2004.09.016) / Comput. Chem. Eng by M.A. Snyder (2004)
  74. Vlachos D.G. (1998). Stochastic modeling of chemical microreactors with detailed kinetics: induction times and ignitions of H2 in air. Chem. Eng. Sci 53: 157–168 (10.1016/S0009-2509(97)00275-3) / Chem. Eng. Sci by D.G. Vlachos (1998)
  75. Resat H., Wiley H.S., Dixon D.A. (2001). Probability-weighted dynamic Monte Carlo method for reaction kinetics simulations. J. Chem. Phys 105: 11026–11034 (10.1021/jp010753n) / J. Chem. Phys by H. Resat (2001)
  76. DeVita J.P., Sander L.M., Smereka P. (2005). Multiscale kinetic Monte Carlo algorithm for simulating epitaxial growth. Phys. Rev. B 72: 205421 (10.1103/PhysRevB.72.205421) / Phys. Rev. B by J.P. DeVita (2005)
  77. Haseltine E.L., Rawlings J.B. (2002). Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics. J. Chem. Phys 117: 6959–6969 (10.1063/1.1505860) / J. Chem. Phys by E.L. Haseltine (2002)
  78. Cao Y., Gillespie D.T., Petzold L.R. (2005). The slow-scale stochastic simulation algorithm. J. Chem. Phys 122: 014116 (10.1063/1.1824902) / J. Chem. Phys by Y. Cao (2005)
  79. Chatterjee A., Vlachos D.G. (2006). Multiscale spatial Monte Carlo simulations: multigriding, computational singular perturbation, and hierarchical stochastic closures. J. Chem. Phys 124: 064110 (10.1063/1.2166380) / J. Chem. Phys by A. Chatterjee (2006)
  80. Liu W.E.D., Eijnden E.V. (2005). Nested stochastic simulation algorithm for chemical kinetic systems with disparate rates. J. Chem. Phys 123: 1941071–19410716 / J. Chem. Phys by W.E.D. Liu (2005)
  81. Samant A., Vlachos D.G. (2005). Overcoming stiffness in stochastic simulation stemming from partial equilibrium: a multiscale Monte Carlo algorithm. J. Chem. Phys 123: 144114 (10.1063/1.2046628) / J. Chem. Phys by A. Samant (2005)
  82. Salis H., Kaznessis Y.N. (2005). An equation-free probabilistic steady-state approxaimtion: Multigriding, computational singular perturbation, and hierarchical stochastic closures. J. Chem. Phys 123: 2141061–21410616 (10.1063/1.2131050) / J. Chem. Phys by H. Salis (2005)
  83. Katsoulakis M., Majda A.J., Vlachos D.G. (2003). Coarse-grained stochastic processes for microscopic lattice systems. Proc. Natl. Acad. Sci 100: 782–787 (10.1073/pnas.242741499) / Proc. Natl. Acad. Sci by M. Katsoulakis (2003)
  84. Katsoulakis M.A., Vlachos D.G. (2003). Coarse-grained stochastic processes and kinetic Monte Carlo simulators for the diffusion of interacting particles. J. Chem. Phys 119: 9412–9428 (10.1063/1.1616513) / J. Chem. Phys by M.A. Katsoulakis (2003)
  85. Katsoulakis M.A., Majda A.J., Vlachos D.G. (2003). Coarse-grained stochastic processes and Monte Carlo simulations in lattice systems. J. Comput. Phys 186: 250–278 (10.1016/S0021-9991(03)00051-2) / J. Comput. Phys by M.A. Katsoulakis (2003)
  86. Chatterjee A., Vlachos D.G., Katsoulakis M.A. (2004). Spatially adaptive lattice coarse-grained Monte Carlo simulations for diffusion of interacting molecules. J. Chem. Phys 121: 11420–11431 (10.1063/1.1811601) / J. Chem. Phys by A. Chatterjee (2004)
  87. Chatterjee A., Katsoulakis M.A., Vlachos D.G. (2005). Spatially adaptive grand canonical Monte Carlo simulations. Phys. Rev. E 71: 026702 (10.1103/PhysRevE.71.026702) / Phys. Rev. E by A. Chatterjee (2005)
  88. Chatterjee A., Vlachos D.G., Katsoulakis M. (2005). Numerical assessment of theoretical error estimates in coarse-grained kinetic Monte Carlo simulations: application to surface diffusion. Int. J. Multiscale Comput. Eng 3: 59–70 (10.1615/IntJMultCompEng.v3.i1.50) / Int. J. Multiscale Comput. Eng by A. Chatterjee (2005)
  89. Ismail A.E., Rutledge G.C., Stephanopoulos G. (2003). Multiresolution analysis in statistical mechanics. I. Using wavelets to calculate thermodynamic properties. J. Chem. Phys 118: 4414–4423 (10.1063/1.1543581) / J. Chem. Phys by A.E. Ismail (2003)
  90. Ismail A.E., Stephanopoulos G., Rutledge G.C. (2003). Multiresolution analysis in statistical mechanics. II. The wavelet transform as a basis for Monte Carlo simulations on lattices. J. Chem. Phys 118: 4424–4431 (10.1063/1.1543582) / J. Chem. Phys by A.E. Ismail (2003)
  91. Chatterjee A., Vlachos D.G. (2006). Temporal acceleration of spatially distributed kinetic Monte Carlo simulations. J. Comput. Phys 211: 596–615 (10.1016/j.jcp.2005.06.004) / J. Comput. Phys by A. Chatterjee (2006)
  92. Gillespie D.T. (2001). Approximate accelerated stochastic simulation of chemically reacting systems. J. Chem. Phys 115: 1716–1733 (10.1063/1.1378322) / J. Chem. Phys by D.T. Gillespie (2001)
  93. Rathinam M., Petzold L.R., Cao Y., Gillespie D.T. (2003). Stiffness in stochastically reacting systems: the implict tau-leaping method. J. Chem. Phys 119: 12784–12794 (10.1063/1.1627296) / J. Chem. Phys by M. Rathinam (2003)
  94. Tian T., Burrage K. (2004). Binomial leap methods for simulating stochastic chemical kinetics. J. Chem. Phys 121: 10356–10364 (10.1063/1.1810475) / J. Chem. Phys by T. Tian (2004)
  95. Chatterjee A., Vlachos D.G., Katsoulakis M. (2005). Binomial distribution based τ-leap accelerated stochastic simulation. J. Chem. Phys 122: 024112 (10.1063/1.1833357) / J. Chem. Phys by A. Chatterjee (2005)
  96. Chatterjee A., Mayawala K., Edwards J.S., Vlachos D.G. (2005). Time accelerated Monte Carlo simulations using the binomial τ-leap method. Bioinformatics 21: 2136–2137 (10.1093/bioinformatics/bti308) / Bioinformatics by A. Chatterjee (2005)
  97. Auger A., Chatelain P., Koumoutsakos P. (2006). R-leaping: Accelerating the stochastic simulation algorithm by reaction leaps. J. Chem. Phys 125: 084103 (10.1063/1.2218339) / J. Chem. Phys by A. Auger (2006)
  98. Cao Y., Petzold L.R., Rathinam M., Gillespie D.T. (2004). The numerical stability of leaping methods for stochastic simulation of chemically reacting systems. J. Chem. Phys 121: 12169–12178 (10.1063/1.1823412) / J. Chem. Phys by Y. Cao (2004)
  99. Thostrup P., Christoffersen E., Lorensen H.T., Jacobsen K.W., Besenbacher F., Norskov J.K. (2001). Adsorption-induced step formation. Phys. Rev. Lett 87: 126102 (10.1103/PhysRevLett.87.126102) / Phys. Rev. Lett by P. Thostrup (2001)
  100. Kratzer P., Penev E., Scheffler M. (2003). Understanding the growth mechanisms of GaAs and InGaAs thin films by employing first-principles calculations. Appl. Surf. Sci 216: 436–446 (10.1016/S0169-4332(03)00392-1) / Appl. Surf. Sci by P. Kratzer (2003)
  101. Fichthorn K.A., Scheffler M. (2000). Island nucleation in thin-film epitaxy: a first-principles investigation. Phys. Rev. Lett. 84: 5371 (10.1103/PhysRevLett.84.5371) / Phys. Rev. Lett. by K.A. Fichthorn (2000)
  102. Neurock M., Hansen E.W. (1998). First-principles-based molecular simulations of heterogeneous catalytic surface chemistry. Comput. Chem. Eng 22: S1045–S1060 (10.1016/S0098-1354(98)00210-5) / Comput. Chem. Eng by M. Neurock (1998)
  103. Haug K., Raibeck G. (2003). Kinetic Monte Carlo study of competing hydrogen pathways into connected (100), (110) and (111) Ni surfaces. J. Phys. Chem. B 107: 11433–11440 (10.1021/jp030596n) / J. Phys. Chem. B by K. Haug (2003)
  104. Truhlar D.G., Garrett B.C., Klippenstein S.J. (1996). Current status of transition-state theory. J. Phys. Chem 100: 12771–12800 (10.1021/jp953748q) / J. Phys. Chem by D.G. Truhlar (1996)
  105. Car R., Parrinello M. (1985). Unified approach for molecular dynamics and density functional theory. Phys. Rev. Lett 55: 2471–2474 (10.1103/PhysRevLett.55.2471) / Phys. Rev. Lett by R. Car (1985)
  106. Voter A.F. (1986). Classically exact overlayer dynamics: diffusion of Rhodium clusters on Rh(100). Phys. Rev. B 34: 6819–6829 (10.1103/PhysRevB.34.6819) / Phys. Rev. B by A.F. Voter (1986)
  107. Vvedensky D.D. (2004). Multiscale modelling of nanostructures. J. Phys. Cond. Mater 16: R1537–R1576 (10.1088/0953-8984/16/50/R01) / J. Phys. Cond. Mater by D.D. Vvedensky (2004)
  108. Maroudas D. (2000). Multiscale modeling of hard materials: Challenges and opportunities for chemical engineering. AIChE J 46: 878–882 (10.1002/aic.690460502) / AIChE J by D. Maroudas (2000)
  109. Wadley H.N.G., Zhou X., Johnson R.A., Neurock M. (2001). Mechanisms, models and methods of vapor deposition. Prog. Mater. Sci 46: 329–377 (10.1016/S0079-6425(00)00009-8) / Prog. Mater. Sci by H.N.G. Wadley (2001)
  110. Raimondeau S., Vlachos D.G. (2002). Recent developments on multiscale, hierarchical modeling of chemical reactors. Chem. Eng. J 90: 3–23 (10.1016/S1385-8947(02)00065-7) / Chem. Eng. J by S. Raimondeau (2002)
  111. Daw M.S., Foiles S.M., Baskes M.I. (1993). The embedded-atom method: a review of theory and applications. Mater. Sci. Rept. 9: 251–310 (10.1016/0920-2307(93)90001-U) / Mater. Sci. Rept. by M.S. Daw (1993)
  112. Jacobsen K.W., Norskov J.K., Puska M.J. (1987). Interatomic interactions in the effective-medium theory. Phys. Rev. B 35: 7423–7442 (10.1103/PhysRevB.35.7423) / Phys. Rev. B by K.W. Jacobsen (1987)
  113. Wang Z., Li Y., Adams J.B. (2000). Kinetic lattice Monte Carlo simulation of facet growth rate. Surf. Sci 450: 51–63 (10.1016/S0039-6028(99)01250-9) / Surf. Sci by Z. Wang (2000)
  114. Abraham F.F., Broughton J.Q., Bernstein N., Kaxiras E. (1998). Spanning the continuum to quantum length scales in a dynamic simulation of brittle fracture. Europhys. Lett 44: 783–787 (10.1209/epl/i1998-00536-9) / Europhys. Lett by F.F. Abraham (1998)
  115. Jónsson H., Mills G. (1998). Nudged elastic band methods for finding minimum energy paths of transitions. In: Berne B., Ciccotti G., Coker D.F., (eds.) Classical and Quantum Dynamics in Condensed Phase Simulations. World Scientific, Singapore, pp. 385–404 (10.1142/9789812839664_0016) / Classical and Quantum Dynamics in Condensed Phase Simulations. by H. Jónsson (1998)
  116. Wales D.J. (2006). Energy landscapes: calculating pathways and rates. Int. Rev. Phys. Chem 25: 237–282 (10.1080/01442350600676921) / Int. Rev. Phys. Chem by D.J. Wales (2006)
  117. Olsen R.A., Kroes G.J., Henkelman G., Arnaldsson A., Jonsson H. (2004). Comparison of methods for finding saddle points without knowledge of final states. J. Chem. Phys 121: 9776 (10.1063/1.1809574) / J. Chem. Phys by R.A. Olsen (2004)
  118. Voter A.F., Montalenti F., Germann T.C. (2002). Extending the time scales in atomistic simulation of materials. Annu. Rev. Mater. Res 32: 321–346 (10.1146/annurev.matsci.32.112601.141541) / Annu. Rev. Mater. Res by A.F. Voter (2002)
  119. Lavrentiev M., Allan N., Harding J., Harris D., Purton J. (2006). Atomistic simulations of surface diffusion and segregartion in ceramics. Comput. Mater. Sci 36: 54–59 (10.1016/j.commatsci.2004.11.010) / Comput. Mater. Sci by M. Lavrentiev (2006)
  120. Trushin O., Karim A., Kara A., Rahman T.S. (2005). Self-learning kinetic Monte Carlo method: Application to Cu(111). Phys. Rev. B 72: 1154011–1154019 (10.1103/PhysRevB.72.115401) / Phys. Rev. B by O. Trushin (2005)
  121. Renisch S., Schuster R., Wintterlin J., Ertl G. (1999). Dynamics of adatom motion under the influence of mutual interactions: O/Ru(0001). Phys. Rev. Lett 82: 3839–3842 (10.1103/PhysRevLett.82.3839) / Phys. Rev. Lett by S. Renisch (1999)
  122. Maroudas D. (2001). Modeling of radical-surface interactions in the plasma-enhanced chemical vapor deposition of silicon thin films. In: Chakraborty A.K. (eds) Molecular Modeling and Theory in Chemical Engineering. Academic Press, New York, pp. 252–296 / Molecular Modeling and Theory in Chemical Engineering. by D. Maroudas (2001)
  123. Raimondeau, S., Aghalayam, P., Vlachos, D.G., Katsoulakis, M.: Bridging the gap of multiple scales: From microscopic, to mesoscopic, to macroscopic models. In: Proceedings of the Foundations of Molecular Modeling and Simulation, AIChE Symposium Series No. 325, 97, pp. 155–158. Keystone, Co, USA (2001)
  124. Gillespie D.T. (1977). Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem 81: 2340–2361 (10.1021/j100540a008) / J. Phys. Chem by D.T. Gillespie (1977)
  125. Gibson M.A., Bruck J. (2000). Efficient exact stochastic simulation of chemical systems with many species and many channels. J. Phys. Chem. A 104: 1876–1889 (10.1021/jp993732q) / J. Phys. Chem. A by M.A. Gibson (2000)
  126. Gilmer G.H., Bennema P. (1972). Simulation of crystal growth with surface diffusion. J. Appl. Phys 43: 1347–1360 (10.1063/1.1661325) / J. Appl. Phys by G.H. Gilmer (1972)
  127. Reese J.S., Raimondeau S., Vlachos D.G. (2001). Monte Carlo algorithms for complex surface reaction mechanisms: efficiency and accuracy. J. Comput. Phys 173: 302–321 (10.1006/jcph.2001.6877) / J. Comput. Phys by J.S. Reese (2001)
  128. Vlachos D.G., Schmidt L.D., Aris R. (1990). The effects of phase transitions, surface diffusion, and defects on surface catalyzed reactions: Oscillations and fluctuations. J. Chem. Phys 93: 8306–8313 (10.1063/1.459313) / J. Chem. Phys by D.G. Vlachos (1990)
  129. Vlachos D.G., Schmidt L.D., Aris R. (1991). The effect of phase transitions, surface diffusion, and defects on heterogeneous reactions: multiplicities and fluctuations. Surf. Sci 249: 248–264 (10.1016/0039-6028(91)90850-R) / Surf. Sci by D.G. Vlachos (1991)
  130. Fichthorn F.A., Weinberg W.H. (1991). Theoretical foundations of dynamical Monte Carlo simulations. J. Chem. Phys 95: 1090–1096 (10.1063/1.461138) / J. Chem. Phys by F.A. Fichthorn (1991)
  131. Mayawala K., Vlachos D.G., Edwards J.S. (2005). Computational modeling reveals molecular details of epidermal growth factor binding. BMC Cell Biol 6(41): 1–11 / BMC Cell Biol by K. Mayawala (2005)
  132. van der Eerden J.P., Bennema P., Cherepanova T.A. (1978). Survey of Monte Carlo simulations of crystal surfaces and crystal growth. Prog. Crystal Growth Characterization 1: 219–254 (10.1016/0146-3535(78)90002-3) / Prog. Crystal Growth Characterization by J.P. Eerden van der (1978)
  133. Masel R.I. (1996). Principles of Adsorption and Reaction on Solid Surfaces. Wiley, NY / Principles of Adsorption and Reaction on Solid Surfaces by R.I. Masel (1996)
  134. Schoeberl B., Eichler-Jonsson C., Gilles E.D., Müller G. (2002). Computational modeling of the dynamics of the MAP kinase cascade activated by surface and internalized receptors. Nat. Biotechnol 20: 370–375 (10.1038/nbt0402-370) / Nat. Biotechnol by B. Schoeberl (2002)
  135. Dumesic, I.A., Rud, D.F., Aparicio, L.M., Rekoske, J.E., Revino, A.A.: The Microkinetics of Heterogeneous Catalysis. American Chemical Society, Washington, DC (1993)
  136. Cormen T.H., Leiserson C.E., Rivest R.L. (2001). Introduction to Algorithms. MIT Press, Cambridge, MA / Introduction to Algorithms by T.H. Cormen (2001)
  137. Cao Y., Li H., Petzold L.R. (2004). Efficient formulation of the stochastic simulation algorithm. J. Chem. Phys 121: 4059–4067 (10.1063/1.1778376) / J. Chem. Phys by Y. Cao (2004)
  138. Press W.H., Flannery B.P., Teukolsky S.A., Vetterling W.T. (1986). Numerical Recipes. Cambridge University Press, Cambridge / Numerical Recipes by W.H. Press (1986)
  139. Goldenfeld, N.: Lectures on Phase Transitions and the Renormalization Group, chap. 9. New York (1992)
  140. Chatterjee, A., Vlachos, D.G.: Systems tasks in nanotechnology via hierarchical multiscale: formation of nanodisks arrays in heteroepitaxy. Chem. Eng. Sci. In press (2007). (10.1016/j.ces.2006.12.049)
  141. Chatterjee A., Snyder M.A., Vlachos D.G. (2004). Mesoscopic modeling of chemical reactivity. Chem. Eng. Sci. ISCRE 18: invited 59: 5559–5567
  142. Chatterjee, A., Vlachos, D.G.: Hierarchical coarse-grained models derived from Kinetic Monte Carlo models: Part II: Coarse-grained Monte Carlo method for multiple interacting species, sites and crystallographic surface types. J. Chem. Phys. In preparation (2007)
  143. Daw M.S., Baskes M.I. (1984). Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals. Phys. Rev. B 29: 6443–6453 (10.1103/PhysRevB.29.6443) / Phys. Rev. B by M.S. Daw (1984)
  144. Stillinger F.H., Weber T.A. (1985). Computer-simulation of local order in condensed phases of silicon. Phys. Rev. B 31: 5262–5271 (10.1103/PhysRevB.31.5262) / Phys. Rev. B by F.H. Stillinger (1985)
  145. Haken H.(1977). Synergetics. Springer, Berlin Heidelberg New York (10.1007/978-3-642-96363-6) / Synergetics by H. Haken (1977)
  146. Rao C.V., Arkin A.P. (2003). Stochastic chemical kinetics and the quasi-steady-state assumption: Application to the Gillespie algorithm. J. Chem. Phys 118: 4999–5010 (10.1063/1.1545446) / J. Chem. Phys by C.V. Rao (2003)
  147. Hill T.L. (1987). Statistical Mechanics Principles and Selected Applications. Dover, New York / Statistical Mechanics Principles and Selected Applications by T.L. Hill (1987)
  148. Stinchcombe K.H., White H. (1989). Multilayer feedforward networks are universal approximators. Neural Netw 2: 359–366 (10.1016/0893-6080(89)90020-8) / Neural Netw by K.H. Stinchcombe (1989)
  149. Katsoulakis M., Trashorras J. (2006). Information loss in coarse-graining of stochastic particle dynamics. J. Stat. Phys. 122: 115–135 (10.1007/s10955-005-8063-1) / J. Stat. Phys. by M. Katsoulakis (2006)
  150. Burrage K., Tian T.H., Burrage P. (2004). A multi-scaled approach for simulating chemical reaction systems. Prog. Biophys. Mol. Biol 85: 217–234 (10.1016/j.pbiomolbio.2004.01.014) / Prog. Biophys. Mol. Biol by K. Burrage (2004)
Dates
Type When
Created 18 years, 5 months ago (Feb. 27, 2007, 8:12 a.m.)
Deposited 6 years, 2 months ago (May 30, 2019, 9:22 p.m.)
Indexed 4 days, 23 hours ago (Aug. 19, 2025, 7:01 a.m.)
Issued 18 years, 5 months ago (Feb. 28, 2007)
Published 18 years, 5 months ago (Feb. 28, 2007)
Published Online 18 years, 5 months ago (Feb. 28, 2007)
Published Print 18 years, 5 months ago (March 14, 2007)
Funders 0

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@article{Chatterjee_2007, title={An overview of spatial microscopic and accelerated kinetic Monte Carlo methods}, volume={14}, ISSN={1573-4900}, url={http://dx.doi.org/10.1007/s10820-006-9042-9}, DOI={10.1007/s10820-006-9042-9}, number={2}, journal={Journal of Computer-Aided Materials Design}, publisher={Springer Science and Business Media LLC}, author={Chatterjee, Abhijit and Vlachos, Dionisios G.}, year={2007}, month=feb, pages={253–308} }