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A continuum model for nematic alignment of self-propelled particles
File | Description | Size | Format | |
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MyxoSOH_Deriv_v3.pdf | Accepted version | 621.48 kB | Adobe PDF | View/Open |
13658.pdf | Published version | 639.74 kB | Adobe PDF | View/Open |
Title: | A continuum model for nematic alignment of self-propelled particles |
Authors: | Degond, PAA Manhart, A Yu, H |
Item Type: | Journal Article |
Abstract: | A continuum model for a population of self-propelled particles interacting through nematic alignment is derived from an individual-based model. The methodology consists of introducing a hydrodynamic scaling of the corresponding mean field kinetic equation. The resulting perturbation problem is solved thanks to the concept of generalized collision invariants. It yields a hyperbolic but non-conservative system of equations for the nematic mean direction of the ow and the densities of particles owing parallel or anti-parallel to this mean direction. Diffusive terms are introduced under a weakly non-local interaction assumption and the diffusion coefficient is proven to be positive. An application to the modeling of myxobacteria is outlined. |
Issue Date: | 1-Feb-2017 |
Date of Acceptance: | 4-Oct-2016 |
URI: | http://hdl.handle.net/10044/1/41271 |
DOI: | https://dx.doi.org/10.3934/dcdsb.2017063 |
ISSN: | 1553-524X |
Publisher: | American Institute of Mathematical Sciences (AIMS) |
Start Page: | 1295 |
End Page: | 1327 |
Journal / Book Title: | Discrete and Continuous Dynamical Systems - Series B |
Volume: | 22 |
Issue: | 4 |
Sponsor/Funder: | Engineering & Physical Science Research Council (EPSRC) The Royal Society Engineering & Physical Science Research Council (EPSRC) |
Funder's Grant Number: | EP/I019111/1 WM130048 EP/M006883/1 |
Keywords: | Science & Technology Physical Sciences Mathematics, Applied Mathematics Self-propelled particles nematic alignment hydrodynamic limit generalized collision invariant diffusion correction weakly non-local interaction myxobacteria PHASE-TRANSITION COLLECTIVE MOTION DRIVEN PARTICLES BROWNIAN WALKER MYXOBACTERIA DIFFUSION SYSTEM HYDRODYNAMICS PATTERNS WAVES math.AP q-bio.CB 35L60, 35K55, 35Q80, 82C05, 82C22, 82C70, 92D50 0101 Pure Mathematics 0102 Applied Mathematics Applied Mathematics |
Publication Status: | Published |
Appears in Collections: | Applied Mathematics and Mathematical Physics Faculty of Natural Sciences Mathematics |