Numerical modelling of the one-dimensional diffusion by random walkers


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


C. Vamos
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

N. Suciu
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

M. Peculea




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C. Vamoş, N. Suciu, M. Peculea, Numerical modelling of the one-dimensional diffusion by random walkers, Rev. Anal. Numér. Théor. Approx., 26 (1997) nos. 1-2, 237-247

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[1] R. Balescu, Equilibrium and Nonequilibrium Satistical Mechanics, Wiley, New York, 1975.

[2] H.S. Carslaw and J.C. Jaeger, Conduction of Heat in Solids, Oxford University Press, 1959.

[3] J. Crank, The Mathematics of Diffusion, Oxford University Press, 1975.

[4] L. Dragoş, Principiile mecanicii mediilor continue, Ed. Tehnică, Bucharest, 1983.

[5] D.J. Evans and G.P. Morriss, Statistical Mechanics of Nonequilibrium Liquids, Academic Press, London, 1990.

[6] C. W. Gardiner, Handbook of Stochastic Methods (for Physics, Chemistry and Natural Science), Springer, Verlag, 1983.

[7] J.G. Kirkwood, Selected Topics in Statistical Machanics, R. W. Zwanzig (Ed.), Gordon and Breach, New York, 1967.

[8] A. Kolmogorov and S. Fomine, Éléments de la théorie des fonctions et de l’analyse fonctionnelle, Mir. Moscou, 1974.

[9] J. Koplik and J.R. Banavar, Continuum deductions from molecular hydrodynamics, Annu.Rev. Fluid Mech. 27 (1995), 257-292.

[10] L.D. Landau and E.M. Lifşiţ, Fizică statistică, Ed. Tehnică, Bucharest, 1988.

[11] I. Müller, Thermodznamics, Pitman, Boston, 1985.

[12] K. Nishidate, M. Baba and R.J. Gaylord, Cellular automaton model for random walkers, Phys. Rev. Lett 77(9) (1996), 1675-1678.

[13] L.Z. Rumşiski, Prelucrarea matematică a datelor experimentale, Ed. Tehnică, Bucharest, 1974.

[14] C. Vamoş, A. Georgescu, N. Suciu and I. Turcu, Balance equations for physical systems with corpuscular structure, Physica A. 227 (1996), 81-92.

[15] C. Vamoş, A. Georgescu and N. Suciu, Balance equations for a finite number of particles. St. Cerc. Mat. 48(1996), 115-127.

[16] N.G. van Kampen, Stochastic Processes in Physics and Chemistry, North-Holland, 1981.


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