Langlands, T. A. M. and Henry, B. I. (2010) Fractional chemotaxis diffusion equations. Physical Review E: Statistical Nonlinear and Soft Matter Physics, 81 (5). pp. 1-12. ISSN 1539-3755
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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.
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| Item Type: | Article (Commonwealth Reporting Category C) |
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| Refereed: | Yes |
| Item Status: | Live Archive |
| Additional Information: | Author's version of paper deposited in accordance with the copyright policy of the publisher |
| Faculty/School / Institute/Centre: | Historic - Faculty of Sciences - Department of Maths and Computing (Up to 30 Jun 2013) |
| Faculty/School / Institute/Centre: | Historic - Faculty of Sciences - Department of Maths and Computing (Up to 30 Jun 2013) |
| Date Deposited: | 04 Sep 2010 10:43 |
| Last Modified: | 02 Jul 2013 23:53 |
| Uncontrolled Keywords: | fractional calculus; anomalous subdiffusion; chemotaxis; reaction diffusion equations |
| Fields of Research (2008): | 01 Mathematical Sciences > 0104 Statistics > 010406 Stochastic Analysis and Modelling 01 Mathematical Sciences > 0101 Pure Mathematics > 010110 Partial Differential Equations 01 Mathematical Sciences > 0102 Applied Mathematics > 010202 Biological Mathematics |
| Fields of Research (2020): | 49 MATHEMATICAL SCIENCES > 4905 Statistics > 490510 Stochastic analysis and modelling 49 MATHEMATICAL SCIENCES > 4904 Pure mathematics > 490410 Partial differential equations 49 MATHEMATICAL SCIENCES > 4901 Applied mathematics > 490102 Biological mathematics |
| Socio-Economic Objectives (2008): | E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences |
| Identification Number or DOI: | https://doi.org/10.1103/PhysRevE.81.051102 |
| URI: | http://eprints.usq.edu.au/id/eprint/8029 |
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