Simulating Physical Processes by Cellular Automata
When simulating physical processes by cellular automata (CA) the question on corresponding physical values to their modal values arises twice. For the first time this question arises when a CA is constructed and for the second time it is arisen when interpreting the simulation results. In this paper we propose a systematic approach for solving these problems; in fact, we establish general rules for constructing a CA and based on these rules we develop scaling methods for three main types of CA-models in details, namely, for a diffusion CA, for a hydrodynamic CA, and for an asynchronous kinetic CA.
Keywords
asynchronous kinetic CA ,
hydrodynamic CA ,
diffusion CA ,
cellular automata (CA) ,
поверхностная химия ,
клеточно-автоматная гидродинамика ,
реакционно-диффузионные процессы ,
пространственная динамика ,
клеточно-автоматное моделирование Authors
Всего: 1
References
Neizvestny I.G., Shvarts N.L., and Yanovitskaya Z. Sh. Two-dimensional epitaxial nucleation with large critical-nucleus size // Russian Microelectronics. Science Business Media LLC. 2002. V. 31. № 2. P. 70 - 78.
Медведев Ю.Г. Трехмерная клеточно-автоматная модель вязкой жидкости // Автометрия. 2003. Т. 39. № 3. С. 43 - 48.
Sahimi M. Flow phenomena in rocks: from continuum models to fractals, percolation, cellular automata and simulated annealing // Rev. Modern Physics. 1993. V. 65. № 4. P. 1533 -1660.
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 in the reaction of carbon monoxide oxidation over platinum and palladium surfaces // Kinetics and Catalysis. 2003. V. 44. № 5. С. 672 - 700.
Achasova S., Bandman O., Markova V., Piskunov S. Parallel substitution algorithm. Theory and Application. Singapore: World Scientific, 1994. 180 р.
Neizvestny I.G., Shwartz N.L., Yanovitskaya Z.Sh., Zverev A.V. 3D-model of epitaxial growth on porous {111} and {100} Si Surface. // Comp. Phys. Comm. 2002. V. 147. P. 272 - 275.
Succi S. The Lattice Boltzmann Equation for Fluid Dynamics and Beyond. N.Y.: Oxford University Press, 2001. 240 p.
Frish U., d'Humieres D., Hasslacher B., Lallemand P., Pomeau Y., Rivet J.P. Lattice-Gas hydrodynamics in two and three dimensions // Complex Systems. 1987. № 1. Р. 649 - 707.
Rothman D.H., Zalesky S. Lattice-Gas Cellular Automata. Simple Model of Complex Hydrodynamics. UK: Cambridge University press, 1997. 297 р.
Малинецкий Г.Г., Степанцов М.Е. Моделирование диффузионных процессов клеточными автоматами с окрестностью Марголуса // Журнал вычислительной математики и математической физики. 1998. № 6. С. 1 - 17.
Бандман О.Л. Клеточно-автоматное моделирование пространственной динамики // Системы информатики. Новосибирск: Изд-во СО РАН. Вып. 10. С. 59 - 113.
Toffolli T. Cellular automata as an alternative to (rather than approximation of) differential equations in modeling physics // Physica D. 1984. V. 10. P. 117 - 127.
Wolfram S. A new kind of science. Champaign, III., USA: Wolfram Media Inc., 2002. 1200 p.