Stochastic flows, reaction-diffusion processes, and morphogenesis
Recently, an exact procedure has been introduced (C. A. Walsh and J. J. Kozak, Phys. Rev. Lett.. 47: 1500 (1981)) for calculating the expected walk length for a walker undergoing random displacements on a finite or infinite (periodic) d-dimensional lattice with traps (reactive sites). The method (which is based on a classification of the symmetry of the sites surrounding the central deep trap and a coding of the fate of the random walker as it encounters a site of given symmetry) is applied here to several problems in lattice statistics for each of which exact results are presented. First, we assess the importance of lattice geometry in influencing the efficiency of reaction-diffusion processs in simple and multiple trap systems by reporting values of for square (cubic) versus hexagonal lattices in d = 2,3. We then show how the method may be applied to variable-step (distance-dependent) walks for a single walker on a given lattice and also demonstrate the calculation of the expected walk length for the case of multiple walkers. Finally, we make contact with recent discussions of ''mixing'' by showing that the degree of chaos associated with flows in certain lattice-systems can be calibrated by monitoring the lattice walks induced by the Poincare map of a certain parabolic function.
- Research Organization:
- Department of Chemistry and Radiation Laboratory, University of Notre Dame, Notre Dame, Indiana 46556
- OSTI ID:
- 6257555
- Journal Information:
- J. Stat. Phys.; (United States), Journal Name: J. Stat. Phys.; (United States) Vol. 30:2; ISSN JSTPB
- Country of Publication:
- United States
- Language:
- English
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