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Fronts from complex two-dimensional dispersal kernels: theory and application to Reid’s paradox

Bimodal dispersal probability distributions with characteristic distances differing by several orders of magnitude have been derived and favorably compared to observations by Nathan [Nature (London) 418, 409 (2002)]. For such bimodal kernels, we show that two-dimensional molecular dynamics computer simulations are unable to yield accurate front speeds. Analytically, the usual continuous-space random walks (CSRWs) are applied to two dimensions. We also introduce discrete-space random walks and use them to check the CSRW results (because of the inefficiency of the numerical simulations). The physical results reported are shown to predict front speeds high enough to possibly explain Reid’s paradox of rapid tree migration. We also show that, for a time-ordered evolution equation, fronts are always slower in two dimensions than in one dimension and that this difference is important both for unimodal and for bimodal kernels

Funded by European Commission Grant No. NEST-28192-FEPRE, MEC-FEDER Grant No. FIS-2006-12296-C02-02, and Generalitat de Catalunya Grant No. SGR-2005-00087

American Institute of Physics

Author: Fort, Joaquim
Abstract: Bimodal dispersal probability distributions with characteristic distances differing by several orders of magnitude have been derived and favorably compared to observations by Nathan [Nature (London) 418, 409 (2002)]. For such bimodal kernels, we show that two-dimensional molecular dynamics computer simulations are unable to yield accurate front speeds. Analytically, the usual continuous-space random walks (CSRWs) are applied to two dimensions. We also introduce discrete-space random walks and use them to check the CSRW results (because of the inefficiency of the numerical simulations). The physical results reported are shown to predict front speeds high enough to possibly explain Reid’s paradox of rapid tree migration. We also show that, for a time-ordered evolution equation, fronts are always slower in two dimensions than in one dimension and that this difference is important both for unimodal and for bimodal kernels
Funded by European Commission Grant No. NEST-28192-FEPRE, MEC-FEDER Grant No. FIS-2006-12296-C02-02, and Generalitat de Catalunya Grant No. SGR-2005-00087
Document access: http://hdl.handle.net/2072/101665
Language: eng
Publisher: American Institute of Physics
Rights: Tots els drets reservats
Subject: Àlgebra
Arbres (Teoria de grafs)
Diferències finites
Dinàmica molecular -- Simulació per ordinador
Distribució (Teoria de la probabilitat)
Kernel, Funcions de
Reid, Paradoxa de
Distribution (Probability theory)
Finite differences
Kernel functions
Molecular dynamics -- Computer simulation
Reid’s paradox
Trees (Graph theory)
Title: Fronts from complex two-dimensional dispersal kernels: theory and application to Reid’s paradox
Type: info:eu-repo/semantics/article
Repository: Recercat

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