Angstmann, C. N. and Donnelly, I. C. and Henry, B. I. and Langlands, T. A. M. (2013) Continuoustime random walks on networks with vertex and timedependent forcing. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics , 88 (2). ISSN 15393755

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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 timedependent 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 timedependent 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 selfchemotactic attraction in a spatial continuum. Our algebraic and numerical studies of this system reveal an interesting pairaggregation 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 selfchemotacticlike 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; continuoustime 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 
SocioEconomic 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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