HomeIssuesDISCRETE MODELS OF PHYSICAL-CHEMICAL PROCESSES

DISCRETE MODELS OF PHYSICAL-CHEMICAL PROCESSES | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2009. № 3(5).

The results of the investigation of discrete models of physical-chemical kinetic processes are presented in a systematic form. The models are extensions of the classical fon-Neumann Cellular Automaton (CA), differing from it in two points: 1) transition functions are allowed to be probabilistic, and 2) not only synchronous, but asynchronous and composed modes of functioning may be used. Mathematical background of the models is based on the formalisms of the "Parallel Substitution Algorithm". Validity conditions and parallel implementation efficiency for synchronous and asynchronous CA-models are studied. All models are illustrated by the results of computer simulation of physical-chemical kinetics on micro- and nano- levels.
Download file
Counter downloads: 138
  • Title DISCRETE MODELS OF PHYSICAL-CHEMICAL PROCESSES
  • Headline DISCRETE MODELS OF PHYSICAL-CHEMICAL PROCESSES
  • Publesher Tomask State UniversityTomsk State University
  • Issue Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics 3(5)
  • Date:
  • DOI
Keywords
параллельные вычисления , кинетика наносистем , поверхностная химия , метод Монте-Карло , асинхронный клеточный автомат , мелкозернистый параллелизм , дискретное моделирование
Authors
References
Ziff R.M., Gulari E., Bershad Y. Kinetic phase transitions in irreversible surface-reaction model // Phys. Rev. Lett. 1986. V. 56. P. 553-2558.
Бандман О. Л. Методы композиции клеточных автоматов для моделирования пространственной динамики // Вестник Томского госуниверситета. 2002. №9(1). С. 188-192.
Bandman O. Comparative Study of Cellular automata Diffusion Models // Lect. Not. Сотр. Sci. 1999. V. 1662. P. 395-399.
Toffolli Т., Margolus N. Cellular Automata Machine. USA: MIT Press. 1987, 284 p.
Vichniac G. Simulating Physics by Cellular Automata // Phys. D. 1984. V. 10. P. 86-112.
Wolfram S. A new kind of science Champaign, 111., USA: Wolfram Media Inc, 2002. 2000 p.
Бандман О. Л. Параллельная реализация клеточно-автоматных алгоритмов моделирования пространственной динамики // Сибирский журн. вычислительной математики. 2007.№4. С. 45-361.
Bandman O. Parallel Simulation of Asynchronous Cellular Automata Evolution // Lect. Not. Сотр. Sci. V.4173. 2006. P. 41-48.
Achasova S., Bandman O., Markova V., Piskunov S.. Parallel Substitution Algorithm. Theory and Application. Singapore: World Scientific, 1994. 198 p.
Alba E., Troya J. M. Cellular Evolutionary Algorithms: evaluating the influence of ratio // Lect. Not. Сотр. Sci. 2000. V. 197. P. 29-38.
Malvanets A., Kapral R. Microscopic model for Fitz-Nagumo dynamics // Phys. Rev. E. 1997. V. 55. No. 5. P. 5657-5670.
Kovalev E. V., Resnyanskii E. D., Elokhin V. I., et al. Novel statistical lattice model for the supported nanoparticle. Features of the reaction performance influenced by the dynamically changed shape and surfaces morphology of the supported active particle // Phys.Chem.Chem.Phys. 2003. V. 5. P. 784-790.
Betz G., Husinsky W. Surface erosion and film growth studied by a combined molecular dynamics and kinetic Monte Carlo code // Izvestia of Russian Academy of Sciences. Phys. Ser. 2002. V.66. No. 4. P. 585-587.
Neizvestny I. G., Shwartz N. L., Yanovitskaya Z. Sh., and Zverev A. V. 3D-model of epitaxial growth on porous {111} and {100} Si surfaces // Сотр. Phys. Commun. 2002. V. 147. P. 272-275.
Elokhin V. I., Latkin E. I., Matveev A. V., Gorodetskii V. V. Application of Statistical Lattice Models to the Analysis of Oscillatory and Autowave Processes on the Reaction of Carbon Monoxide Oxidation over Platinum and Palladium Surfaces // Kinet. Catal. 2003. V. 44. No. 5. P. 672-700.
Rothman В. H., Zaleski S. Lattice-Gas Cellular Automata. Simple Models of Complex Hydrodynamics. London: Cambridge Univ. Press, 1997. 320 p.
Makeev A. G. Coarse bifurcation analysis of kinetic Monte Carlo simulations: a lattice-gas model with lateral interactions // J. Chem. Phys. 2002. V. 117. No. 18. P. 8229-8240.
Bandman О. Synchronous versus asynchronous cellular automata for simulating nano-systems kinetics // Bulletin of the Novosibirsk Computer Center. Series: Computer Science. Issue 27. 2006.P. 1-12.
Бандман О. Л. Клеточно-автоматные модели пространственной динамики // Системная информатика: Сб. научн. тр. Новосибирск: Изд-во СО РАН. 2006. Вып. 10: Методы и модели современного программирования. С. 59-111.
Boon J. P., Dab D., Kapral R., Lawniczak A. Lattice-Gas Automata for Reactive Systems // Phys. Rep. 1996. V. 273. P. 55-147.
Бандман О. Л. Мелкозернистый параллелизм в вычислительной математике // Программирование. 2001. №4. С. 1-18.
Wolfram S. Statistical mechanics of Cellular automata // Rev. Mod. Phys. 1993. V. 55. P. 607-640.
Toffolli Т. Cellular Automata as an Alternative to (rather than Approximation of) Differential Equations in Modeling Physics // Physica D.1984. V. 10. P. 117-127.
DISCRETE MODELS OF PHYSICAL-CHEMICAL PROCESSES | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2009. № 3(5).
DISCRETE MODELS OF PHYSICAL-CHEMICAL PROCESSES | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2009. № 3(5).
Download full-text version
Counter downloads: 208
Download file