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A hydrodynamic limit for chemotaxis in a given heterogeneous environment
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Grosskinsky, Stefan, Marahrens, Daniel and Stevens, Angela (2017) A hydrodynamic limit for chemotaxis in a given heterogeneous environment. Vietnam Journal of Mathematics, 45 (1-2). pp. 127-152. doi:10.1007/s10013-016-0209-8 ISSN 2305-221X.
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Official URL: http://dx.doi.org/10.1007/s10013-016-0209-8
Abstract
In this paper, the first equation within a class of well-known chemotaxis systems is derived as a hydrodynamic limit from a stochastic interacting many particle system on the lattice. The cells are assumed to interact with attractive chemical molecules on a finite number of lattice sites, but they only directly interact among themselves on the same lattice site. The chemical environment is assumed to be stationary with a slowly varying mean, which results in a non-trivial macroscopic chemotaxis equation for the cells. Methodologically, the limiting procedure and its proofs are based on results by Koukkous (Stoch. Process. Appl. 84, 297–312, cite.Kou99) and Kipnis and Landim (Scaling limits of interacting particle systems, cite.KL99). Numerical simulations extend and illustrate the theoretical findings.
| Item Type: | Journal Article | ||||||||||
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| Subjects: | Q Science > QA Mathematics Q Science > QR Microbiology |
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| Divisions: | Faculty of Science, Engineering and Medicine > Research Centres > Centre for Complexity Science Faculty of Science, Engineering and Medicine > Science > Mathematics |
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| Library of Congress Subject Headings (LCSH): | Chemotaxis, Equations -- Numerical solutions | ||||||||||
| Journal or Publication Title: | Vietnam Journal of Mathematics | ||||||||||
| Publisher: | Springer New York LLC | ||||||||||
| ISSN: | 2305-221X | ||||||||||
| Official Date: | March 2017 | ||||||||||
| Dates: |
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| Volume: | 45 | ||||||||||
| Number: | 1-2 | ||||||||||
| Page Range: | pp. 127-152 | ||||||||||
| DOI: | 10.1007/s10013-016-0209-8 | ||||||||||
| Status: | Peer Reviewed | ||||||||||
| Publication Status: | Published | ||||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||||
| Date of first compliant deposit: | 14 July 2016 | ||||||||||
| Date of first compliant Open Access: | 7 June 2017 | ||||||||||
| Funder: | Universität Heidelberg , Isaac Newton Institute for Mathematical Sciences |
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