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Mathematical Modelling and Data Analysis

Department 8.4

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Title: Front propagation in one-dimensional spatially periodic bistable media
Author(s): J. Löber, M. Bär and H. Engel
Journal: Phys. Rev. E
Year: 2012
Volume: 86
Issue: 6 Pt 2
Pages: 066210
DOI: 10.1103/PhysRevE.86.066210
ISSN: 1550-2376
Web URL: http://www.ncbi.nlm.nih.gov/pubmed/23368027
Tags: 8.41, exc-media
Abstract: Front propagation in heterogeneous bistable media is studied using the Schlögl model as a representative example. Spatially periodic modulations in the parameters of the bistable kinetics are taken into account perturbatively. Depending on the ratio L/l (L is the spatial period of the heterogeneity, l is the front width), appropriate singular perturbation techniques are applied to derive an ordinary differential equation for the position of the front in the presence of the heterogeneities. From this equation, the dependence of the average propagation speed on L/l as well as on the modulation amplitude is calculated. The analytical results obtained predict velocity overshoot, different cases of propagation failure, and the propagation speed for very large spatial periods in quantitative agreement with the results of direct numerical simulations of the underlying reaction-diffusion equation.

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