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Title: Classical localization and percolation in random environments on trees
Authors: Bressloff, P.C.
Dwyer, Vincent M.
Kearney, Michael J.
Issue Date: 1997
Publisher: © American Physical Society
Citation: BRESSLOFF, P.C., DWYER, V.M. and KEARNEY, M.J., 1997. Classical localization and percolation in random environments on trees. Physical Review E, 55(6), pp. 6765–6775
Abstract: We consider a simple model of transport on a regular tree, whereby species evolve according to the drift-diffusion equation, and the drift velocity on each branch of the tree is a quenched random variable. The inverse of the steady-state amplitude at the origin is expressed in terms of a random geometric series whose convergence or otherwise determines whether the system is localized or delocalized. In a recent paper [P. C. Bressloff et al., Phys. Rev. Lett. 77, 5075 (1996)], exact criteria were presented that enable one to determine the critical phase boundary for the transition, valid for any distribution of the drift velocities. In this paper we present a detailed derivation of these criteria, consider a number of examples of interest, and establish a connection with conventional percolation theory. The latter suggests a wider application of the results to other models of statistical processes occurring on treelike structures. Generalizations to the case where the underlying tree is irregular in nature are also considered.
Description: This article was pubished in the journal, Physical Review E [© American Physical Society]. It is also available at: http://link.aps.org/abstract/PRE/v55/p6765.
URI: https://dspace.lboro.ac.uk/2134/1720
ISSN: 1063-651x
Appears in Collections:Published Articles (Maths)
Published Articles (Mechanical, Electrical and Manufacturing Engineering)

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