Turkish Journal of Physics

Simulation of Non-Equilibrium Diffusion on a Cellular Automaton in Three Dimensional Space




The aim of this study is to investigate the fractal structure and the scaling properties of the diffusion front in three dimensions on a Cellular Automaton for which the rule is as follows: The linear dimensions of the lattice is L\times L\times L^\prime where the particles diffuse in the L^\prime directions. The system is completely empty at time t=0, except at the source. The lattice which has at most one particle per site is devided into Margolus blocks [1] in L\times L^\prime planes. For each iteration step, five independent random numbers are generated, according to which each cube that is formed from the Margolus blocks in the L\times \L^\prime planes is rotated clockwise or counterclockwise about the directions forming the L\times L plane, or stay immobile with equal probabilities, and then it is shifted along a body diagonal by a lattice constant. The percolation threshold p_c, the critical exponent \beta, the fractal dimension of the diffusion front D_f and the related quantities are computed. They are in agreement with the other simulation results[2,3].

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