Non-markovian random processes and travelling fronts in a reaction-transport system with memory and long-range interactions

Fedotov, Sergei and Okuda, Yuki (2002) Non-markovian random processes and travelling fronts in a reaction-transport system with memory and long-range interactions. Physical Review E, 66. 021113. ISSN 1539-3755

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Abstract

The problem of finding the propagation rate for traveling waves in reaction-transport systems with memory and long-range interactions has been considered. Our approach makes use of the generalized master equation with logistic growth, hyperbolic scaling, and Hamilton-Jacobi theory. We consider the case when the waiting-time distribution for the underlying microscopic random walk is modeled by the family of gamma distributions, which in turn leads to non-Markovian random processes and corresponding memory effects on mesoscopic scales. We derive formulas that enable us to determine the front propagation rate and understand how the memory and long-range interactions influence the propagation rate for traveling fronts. Several examples involving the Gaussian and discrete distributions for jump densities are presented.

Item Type: Article
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes
MSC 2010, the AMS's Mathematics Subject Classification > 82 Statistical mechanics, structure of matter
Depositing User: Ms Lucy van Russelt
Date Deposited: 19 Jul 2006
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/396

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