Numerical modelling of the one-dimensional diffusion by random walkers
Keywords:diffusion, cellular automata, continuous macroscopic description
In this paper we describe a numerical method of cellular automaton type to study the diffusion processes. The macroscopic diffusive behavior of a set of microscopic particles is obtained by the numerical simulation of particles motion as random walkers. We derive the averaging space-time scale needed for a macroscopical description of the diffusion process with a given precision. As an application we estimate the evacuation time by diffusion of a given number of particles from a fluid layer.
R. Balescu, Equilibrium and Nonequilibrium Satistical Mechanics, Wiley, New York, 1975.
H.S. Carslaw and J.C. Jaeger, Conduction of Heat in Solids, Oxford University Press, 1959.
J. Crank, The Mathematics of Diffusion, Oxford University Press, 1975.
L. Dragoş, Principiile mecanicii mediilor continue, Ed. Tehnică, Bucharest, 1983.
D.J. Evans and G.P. Morriss, Statistical Mechanics of Nonequilibrium Liquids, Academic Press, London, 1990.
C. W. Gardiner, Handbook of Stochastic Methods (for Physics, Chemistry and Natural Science), Springer, Verlag, 1983.
J.G. Kirkwood, Selected Topics in Statistical Machanics, R. W. Zwanzig (Ed.), Gordon and Breach, New York, 1967.
A. Kolmogorov and S. Fomine, Éléments de la théorie des fonctions et de l'analyse fonctionnelle, Mir. Moscou, 1974.
J. Koplik and J.R. Banavar, Continuum deductions from molecular hydrodynamics, Annu. Rev. Fluid Mech. 27 (1995), 257-292.
L.D. Landau and E.M. Lifşiţ, Fizică statistică, Ed. Tehnică, Bucharest, 1988.
I. Müller, Thermodynamics, Pitman, Boston, 1985.
K. Nishidate, M. Baba and R.J. Gaylord, Cellular automaton model for random walkers, Phys. Rev. Lett 77(9) (1996), 1675-1678.
L.Z. Rumşiski, Prelucrarea matematică a datelor experimentale, Ed. Tehnică, Bucharest, 1974.
C. Vamoş, A. Georgescu, N. Suciu and I. Turcu, Balance equations for physical systems with corpuscular structure, Physica A. 227 (1996), 81-92.
C. Vamoş, A. Georgescu and N. Suciu, Balance equations for a finite number of particles. St. Cerc. Mat. 48(1996), 115-127.
N.G. van Kampen, Stochastic Processes in Physics and Chemistry, North-Holland, 1981.
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