Continuous-time random walks on networks with vertex- and time-dependent forcing

Angstmann, C. N. and Donnelly, I. C. and Henry, B. I. and Langlands, T. A. M. (2013) Continuous-time random walks on networks with vertex- and time-dependent forcing. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics , 88 (2). ISSN 1539-3755

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Abstract

We have investigated the transport of particles moving as random walks on the vertices of a network, subject to vertex- and time-dependent forcing. We have derived the generalized master equations for this transport using continuous time random walks, characterized by jump and waiting time densities, as the underlying stochastic process. The forcing is incorporated through a vertex- and time-dependent bias in the jump densities governing the random walking particles. As a particular case, we consider particle forcing proportional to the concentration of particles on adjacent vertices, analogous to self-chemotactic attraction in a spatial continuum. Our algebraic and numerical studies of this system reveal an interesting pair-aggregation pattern formation in which the steady state is composed of a high concentration of particles on a small number of isolated pairs of adjacent vertices. The steady states do not exhibit this pair aggregation if the transport is random on the vertices, i.e., without forcing. The manifestation of pair aggregation on a transport network may thus be a signature of self-chemotactic-like forcing.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: © 2013 American Physical Society. Open access - Publisher copyright must be acknowledged.
Faculty / Department / School: Current - Faculty of Health, Engineering and Sciences - School of Agricultural, Computational and Environmental Sciences
Date Deposited: 01 Oct 2013 22:41
Last Modified: 15 Jul 2014 03:42
Uncontrolled Keywords: Adjacent vertices; Continuous time random walks; continuous-time random walk; generalized master equations; isolated pairs; pattern formation; transport networks; transport of particles
Fields of Research : 01 Mathematical Sciences > 0104 Statistics > 010406 Stochastic Analysis and Modelling
08 Information and Computing Sciences > 0802 Computation Theory and Mathematics > 080299 Computation Theory and Mathematics not elsewhere classified
02 Physical Sciences > 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics > 020203 Particle Physics
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: 10.1103/PhysRevE.88.022811
URI: http://eprints.usq.edu.au/id/eprint/24102

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