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2006.206: Continuous-time random walks and travelling fronts

2006.206: Sergei Fedotov and Vicenç Mèndez (2002) Continuous-time random walks and travelling fronts. Physical Review E, 66. 030102. ISSN 1539-3755

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DOI: 10.1103/PhysRevE.66.030102


We present a geometric approach to the problem of propagating fronts into an unstable state, valid for an arbitrary continuous-time random walk with a Fisher–Kolmogorov-Petrovski-Piskunov growth/reaction rate. We derive an integral Hamilton-Jacobi type equation for the action functional determining the position of reaction front and its speed. Our method does not rely on the explicit derivation of a differential equation for the density of particles. In particular, we obtain an explicit formula for the propagation speed for the case of anomalous transport involving non-Markovian random processes.

Item Type:Article
Subjects:MSC 2000 > 60 Probability theory and stochastic processes
MSC 2000 > 82 Statistical mechanics, structure of matter
MIMS number:2006.206
Deposited By:Miss Louise Stait
Deposited On:19 July 2006

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