Cellular automaton model for diffusive and dissipative systems

Abstract

We study a cellular automaton model which allows diffusion of energy (or equivalently any other physical quantities such as mass of a particular compound) at every lattice site after each time step. A unit amount of energy is randomly added onto a site. Whenever the local energy content of a site reaches a fixed threshold Ec1, energy will be dissipated. The dissipation of energy propagates to the neighboring sites provided that the energy contents of those sites are greater than or equal to another fixed threshold Ec2 (≤Ec1). Under such dynamics, the system evolves into three different types of states depending on the values of Ec1 and Ec2 as reflected in their dissipation size distributions, namely, localized peaks, power laws, or exponential laws. This model is able to describe the behaviors of various physical systems including the statistics of burst sizes and burst rates in type-I x-ray bursters. Comparisons between our model and the famous forest-fire model are made. © 1995 The American Physical Society.