Fractional chemotaxis diffusion equations

Article

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
Article Title

Fractional chemotaxis diffusion equations

ERA Journal ID1018
Article CategoryArticle
AuthorsLanglands, T. A. M. (Author) and Henry, B. I. (Author)
Journal TitlePhysical Review E
Journal Citation81 (5), pp. 1-12
Number of Pages12
Year2010
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.81.051102
Web Address (URL)http://link.aps.org/doi/10.1103/PhysRevE.81.051102
Abstract

We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modeling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macromolecular crowding. The mesoscopic models are formulated using continuous time random walk equations and the macroscopic models are formulated with fractional order differential equations. Different models are proposed depending on the timing of the chemotactic forcing. Generalizations of the models to include linear reaction dynamics are also derived. Finally a Monte Carlo method for simulating anomalous subdiffusion with chemotaxis is introduced and simulation results are compared with numerical solutions of the model equations. The model equations developed here could be used to replace Keller-Segel type equations in biological systems with transport hindered by traps, macromolecular crowding or other obstacles.

Keywordsfractional calculus; anomalous subdiffusion; chemotaxis; reaction diffusion equations
Contains Sensitive ContentDoes not contain sensitive content
ANZSRC Field of Research 2020490510. Stochastic analysis and modelling
490410. Partial differential equations
490102. Biological mathematics
Public Notes

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

Byline AffiliationsDepartment of Mathematics and Computing
University of New South Wales
Permalink -

https://research.usq.edu.au/item/9zxqz/fractional-chemotaxis-diffusion-equations

Log in to edit

Download files

Accepted Version
Langlands_Henry_PhysRevE_2010_AV.pdf
File access level: Anyone

  • 1945
    total views
  • 326
    total downloads
  • 3
    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
Continuous-time random walks on networks with vertex- and time-dependent forcing
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
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
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