Construction of an Isotropic Cellular Automaton for a Reaction-diffusion Equation by Means of a Random Walk
نویسنده
چکیده
We propose a new method to construct an isotropic cellular automaton corresponding to a reaction-diffusion equation. The method consists of replacing the diffusion term and the reaction term of the reaction-diffusion equation with a random walk of microscopic particles and a discrete vector field which defines the time evolution of the particles. The cellular automaton thus obtained can retain isotropy and therefore reproduces the patterns found in the numerical solutions of the reaction-diffusion equation. As a specific example, we apply the method to the Belousov-Zhabotinsky reaction in excitable media.
منابع مشابه
Probabilistic cellular automata model for reaction diffusion systems
Class of cellular automata (CA) for modeling reaction diffusion systems has been presented. The construction of the CA is general enough to be applicable to large class of reaction diffusion equation s. Tne automata are based on running average procedure and on probabilistic table look up to implement diffusion reactions. The evolution of probabilistic CA simulates a spatially distributed proce...
متن کاملThree-dimensional Free Vibration Analysis of a Transversely Isotropic Thermoelastic Diffusive Cylindrical Panel
The present paper is aimed to study an exact analysis of the free vibrations of a simply supported, homogeneous, transversely isotropic, cylindrical panel based on three-dimensional generalized theories of thermoelastic diffusion. After applying the displacement potential functions in the basic governing equations of generalized thermoelastic diffusion, it is noticed that a purely transverse mo...
متن کاملA numerical investigation of a reaction-diffusion equation arises from an ecological phenomenon
This paper deals with the numerical solution of a class of reaction diffusion equations arises from ecological phenomena. When two species are introduced into unoccupied habitat, they can spread across the environment as two travelling waves with the wave of the faster reproducer moving ahead of the slower.The mathematical modelling of invasions of species in more complex settings that include ...
متن کاملRandom Walk and Diffusion on a Smash Line Algebra
Working withing the framework of Hopf algebras, a random walk and the associated diffusion equation are constructed on a space that is algebraically described as the merging of the real line algebra with the anyonic line algebra. Technically this merged structure is a smash algebra, namely an algebra resulting by a braided tensoring of real with anyonic line algebras. The motivation of introduc...
متن کاملDerivation of Non-isotropic Phase Equations from a General Reaction-Diffusion Equation
A non-isotropic version of phase equations such as the Burgers equation, the K-dV-Burgers equation, the Kuramoto-Sivashinsky equation and the Benney equation in the three-dimensional space is systematically derived from a general reaction-diffusion system by means of the renormalization group method. PACS codes: 47.20.Ky
متن کامل