We study a Cellular Automata model for a synchronous random walk of many particles subject to an exclusion principle. A diffusive behavior with an adjustable diffusion constant is obtained. The macroscopic and continuous limits of the model are discussed. Deviations from Fick's law partial deriv_t #rho# = D nabla~2 #rho# are observed for finite size systems and nonhydrodynamical regimes. The telegraphist equation appears to be the natural way of describing our model, as a result of the finite speed of the particles. For a stationary state, it is found that the parameters of the rule can be chosen in order to solve with a very good accuracy the Laplace equation, even for small size systems.
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机译：我们研究了一个细胞自动机模型，该模型针对许多遵循排除原理的粒子进行同步随机游动。获得具有可调扩散常数的扩散行为。讨论了模型的宏观和连续极限。对于有限尺寸系统和非流体动力系统，观察到了与菲克定律偏导_rho＃= D nabla〜2＃rho＃的偏差。由于粒子的有限速度，电报方程式似乎是描述我们模型的自然方法。对于静止状态，发现可以选择规则的参数，以便即使对于小型系统也可以非常精确地求解拉普拉斯方程。
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