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
Permalink -

https://research.usq.edu.au/item/q2156/continuous-time-random-walks-on-networks-with-vertex-and-time-dependent-forcing

Download files


Published Version
Angstmann_etal_PRE_v88n2_PV.pdf
File access level: Anyone

  • 1847
    total views
  • 231
    total downloads
  • 1
    views this month
  • 0
    downloads this month

Export as

Related outputs

Numerical investigation of two models of nonlinear fractional reaction subdiffusion equations
Osman, Sheelan and Langlands, Trevor. 2022. "Numerical investigation of two models of nonlinear fractional reaction subdiffusion equations." Fractional Calculus and Applied Analysis. 25 (6), pp. 2166-2192. https://doi.org/10.1007/s13540-022-00096-2
Connecting community online and through partnership: A reflective piece
Pickstone, Leigh, Sharma, Ekta, King, Rachel, Galligan, Linda and Langlands, Trevor. 2022. "Connecting community online and through partnership: A reflective piece." International Journal for Students as Partners. 6 (2), pp. 114-120. https://doi.org/10.15173/ijsap.v6i2.4825
Modern artificial intelligence model development for undergraduate student performance prediction: an investigation on engineering mathematics courses
Deo, Ravinesh C., Yaseen, Zaher Mundher, Al-Ansari, Nadhir, Nguyen-Huy, Thong, Langlands, Trevor and Galligan, Linda. 2020. "Modern artificial intelligence model development for undergraduate student performance prediction: an investigation on engineering mathematics courses." IEEE Access. 8, pp. 136697-136724. https://doi.org/10.1109/ACCESS.2020.3010938
An implicit Keller Box numerical scheme for the solution of fractional subdiffusion equations
Osman, S. A and Langlands, T. A. M.. 2019. "An implicit Keller Box numerical scheme for the solution of fractional subdiffusion equations." Applied Mathematics and Computation. 348, pp. 609-626. https://doi.org/10.1016/j.amc.2018.12.015
From stochastic processes to numerical methods: a new scheme for solving reaction subdiffusion fractional partial differential equations
Angstmann, C. N., Donnelly, I. C., Henry, B. I., Jacobs, B. A., Langlands, T. A. M. and Nichols, J. A.. 2016. "From stochastic processes to numerical methods: a new scheme for solving reaction subdiffusion fractional partial differential equations." Journal of Computational Physics. 307, pp. 508-534. https://doi.org/10.1016/j.jcp.2015.11.053
Fractional cable equation models for anomalous electrodiffusion in nerve cells: infinite domain solutions
Langlands, Trevor, Henry, B. I. and Wearne, S. L.. 2009. "Fractional cable equation models for anomalous electrodiffusion in nerve cells: infinite domain solutions." Journal of Mathematical Biology. 59 (6), pp. 761-808. https://doi.org/10.1007/s00285-009-0251-1
A mathematical model for the proliferation, accumulation and spread of pathogenic proteins along neuronal pathways with locally anomalous trapping
Angstmann, C. N., Donnelly, I. C., Henry, B. I. and Langlands, T. A. M.. 2016. "A mathematical model for the proliferation, accumulation and spread of pathogenic proteins along neuronal pathways with locally anomalous trapping." Mathematical Modelling of Natural Phenomena (MMNP). 11 (3), pp. 142-156. https://doi.org/10.1051/mmnp/20161139
Generalized continuous time random walks, master equations, and fractional Fokker-Planck equations
Angstmann, C. N., Donnelly, I. C., Henry, B. I., Langlands, T. A. M. and Straka, P.. 2015. "Generalized continuous time random walks, master equations, and fractional Fokker-Planck equations." SIAM Journal on Applied Mathematics. 75 (4), pp. 1445-1468. https://doi.org/10.1137/15M1011299
Fractional cable equation models for anomalous electrodiffusion in nerve cells: finite domain solutions
Langlands, T. A. M., Henry, B. I. and Wearne, S. L.. 2011. "Fractional cable equation models for anomalous electrodiffusion in nerve cells: finite domain solutions." SIAM Journal on Applied Mathematics. 71 (4), pp. 1168-1203. https://doi.org/10.1137/090775920
Fractional diffusion in force fields, fractional electro-diffusion and fractional chemotaxis diffusion
Langlands, Trevor, Henry, Bruce and Straka, Peter. 2010. "Fractional diffusion in force fields, fractional electro-diffusion and fractional chemotaxis diffusion." Henry, Bruce and Roberts, John (ed.) Dynamics Days Asia Pacific 6 Conference (DDAP6). Sydney, Australia 12 - 14 Jul 2010 Sydney, Australia.
Anomalous subdiffusion with multispecies linear reaction dynamics
Langlands, Trevor, Henry, B. I. and Wearne, S. L.. 2008. "Anomalous subdiffusion with multispecies linear reaction dynamics." Physical Review B: Covering condensed matter and materials physics. 77, pp. 1-9. https://doi.org/10.1103/PhysRevE.77.021111
Fractional cable models for spiny neuronal dendrites
Henry, B. I., Langlands, Trevor and Wearne, S. L.. 2008. "Fractional cable models for spiny neuronal dendrites." Physical Review Letters. 100 (12), pp. 1-4. https://doi.org/10.1103/PhysRevLett.100.128103
Turing pattern formation with fractional diffusion and fractional reactions
Langlands, T. A. M., Henry, B. I. and Wearne, S. L.. 2006. "Turing pattern formation with fractional diffusion and fractional reactions." Journal of Physics: Condensed Matter. 19 (6), pp. 065115 -065134. https://doi.org/10.1088/0953-8984/19/6/065115
Anomalous diffusion with linear reaction dynamics: From continuous time random walks to fractional reaction-diffusion equations
Henry, B. I., Langlands, Trevor and Wearne, S. L.. 2006. "Anomalous diffusion with linear reaction dynamics: From continuous time random walks to fractional reaction-diffusion equations." Physical Review E. 74 (3), pp. 1-15. https://doi.org/10.1103/PhysRevE.74.031116
Solution of a modified fractional diffusion equation
Langlands, T. A. M.. 2006. "Solution of a modified fractional diffusion equation." Physica A: Statistical Mechanics and its Applications. 367, pp. 136-144. https://doi.org/10.1016/j.physa.2005.12.012
Fractional Fokker-Planck equations for subdiffusion with space-and time-dependent forces
Henry, B. I., Langlands, T. A. M. and Straka, P.. 2010. "Fractional Fokker-Planck equations for subdiffusion with space-and time-dependent forces." Physical Review Letters. 105 (17), pp. 17062-1-170602-4. https://doi.org/10.1103/PhysRevLett.105.170602
Fractional chemotaxis diffusion equations
Langlands, T. A. M. and Henry, B. I.. 2010. "Fractional chemotaxis diffusion equations." Physical Review E. 81 (5), pp. 1-12. https://doi.org/10.1103/PhysRevE.81.051102
Optimal targeting of hepatitis C virus treatment among injecting drug users to those not enrolled in methadone maintenance programs
Zeiler, Irmgard, Langlands, Trevor, Murray, John M. and Ritter, Alison. 2010. "Optimal targeting of hepatitis C virus treatment among injecting drug users to those not enrolled in methadone maintenance programs." Drug and Alcohol Dependence. 110 (3), pp. 228-233. https://doi.org/10.1016/j.drugalcdep.2010.03.006
An introduction to fractional diffusion
Henry, B. I., Langlands, Trevor and Straka, P.. 2010. "An introduction to fractional diffusion." Dewar, Robert L. and Detering, Frank (ed.) 22nd Canberra International Physics Summer School. Canberra, Australia 08 - 19 Dec 2008 Singapore. https://doi.org/10.1142/9789814277327_0002