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Active Particles, Volume 2High-Resolution Positivity and Asymptotic Preserving Numerical Methods for Chemotaxis and Related Models

Active Particles, Volume 2: High-Resolution Positivity and Asymptotic Preserving Numerical... [Many microorganisms exhibit a special pattern formation at the presence of a chemoattractant, food, light, or areas with high oxygen concentration. Collective cell movement can be described by a system of nonlinear PDEs on both macroscopic and microscopic levels. The classical PDE chemotaxis model is the Patlak-Keller-Segel system, which consists of a convection-diffusion equation for the cell density and a reaction-diffusion equation for the chemoattractant concentration. At the cellular (microscopic) level, a multiscale chemotaxis models can be used. These models are based on a combination of the macroscopic evolution equation for chemoattractant and microscopic models for cell evolution. The latter is governed by a Boltzmann-type kinetic equation with a local turning kernel operator that describes the velocity change of the cells.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Active Particles, Volume 2High-Resolution Positivity and Asymptotic Preserving Numerical Methods for Chemotaxis and Related Models

Part of the Modeling and Simulation in Science, Engineering and Technology Book Series
Editors: Bellomo, Nicola; Degond, Pierre; Tadmor, Eitan
Chertock, Alina; Kurganov, Alexander
Active Particles, Volume 2 — Aug 23, 2019
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39 pages

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Publisher
Springer International Publishing
Copyright
© Springer Nature Switzerland AG 2019
ISBN
978-3-030-20296-5
Pages
109 –148
DOI
10.1007/978-3-030-20297-2_4
Publisher site
See Chapter on Publisher Site

Abstract

[Many microorganisms exhibit a special pattern formation at the presence of a chemoattractant, food, light, or areas with high oxygen concentration. Collective cell movement can be described by a system of nonlinear PDEs on both macroscopic and microscopic levels. The classical PDE chemotaxis model is the Patlak-Keller-Segel system, which consists of a convection-diffusion equation for the cell density and a reaction-diffusion equation for the chemoattractant concentration. At the cellular (microscopic) level, a multiscale chemotaxis models can be used. These models are based on a combination of the macroscopic evolution equation for chemoattractant and microscopic models for cell evolution. The latter is governed by a Boltzmann-type kinetic equation with a local turning kernel operator that describes the velocity change of the cells.]

Published: Aug 23, 2019

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