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A local interaction simulation approach to the solution of diffusion problems

Authors
Journal
Mathematical and Computer Modelling
0895-7177
Publisher
Elsevier
Publication Date
Volume
17
Issue
10
Identifiers
DOI: 10.1016/0895-7177(93)90115-f
Disciplines
  • Biology
  • Chemistry
  • Mathematics

Abstract

Abstract A technique for the solution of the master equation and of the diffusion equation, via a random walk simulation, is proposed and applied to a variety of problems of interest in the fields of physics, biology, and chemistry. They include the kinetics of a single particle, which can diffuse along a one-dimensional lattice and eventually leave it from its end points, with a given probability, and the generalization to more complex two-dimensional geometries or more particles (the many-walkers problem). The technique is particularly suitable for parallel processing, which provides extreme efficiency and flexibility to the method.

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