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

Article

Angstmann, C. N., Donnelly, I. C., Henry, B. I. and Langlands, T. A. M.. 2013. "Continuous-time random walks on networks with vertex- and time-dependent forcing." Physical Review E. 88 (2). https://doi.org/10.1103/PhysRevE.88.022811
Article Title

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

ERA Journal ID1018
Article CategoryArticle
AuthorsAngstmann, C. N. (Author), Donnelly, I. C. (Author), Henry, B. I. (Author) and Langlands, T. A. M. (Author)
Journal TitlePhysical Review E
Journal Citation88 (2)
Number of Pages9
Year2013
PublisherAmerican Physical Society
Place of PublicationUnited States
ISSN1539-3755
1550-2376
2470-0045
2470-0053
Digital Object Identifier (DOI)https://doi.org/10.1103/PhysRevE.88.022811
Web Address (URL)https://journals.aps.org/pre/abstract/10.1103/PhysRevE.88.022811
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.

KeywordsAdjacent vertices; Continuous time random walks; continuous-time random walk; generalized master equations; isolated pairs; pattern formation; transport networks; transport of particles
Contains Sensitive ContentDoes not contain sensitive content
ANZSRC Field of Research 2020490510. Stochastic analysis and modelling
461399. Theory of computation not elsewhere classified
510703. Particle physics
Public Notes

File reproduced in accordance with the copyright policy of the publisher/author.

Byline AffiliationsUniversity of New South Wales
Department of Mathematics and Computing
Institution of OriginUniversity of Southern Queensland
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