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A Finite Volume Method for Continuum Limit Equations of Nonlocally Interacting Active Chiral Particles

Kruk, N. and Carrillo, J.A. and Koeppl, H. (2020):
A Finite Volume Method for Continuum Limit Equations of Nonlocally Interacting Active Chiral Particles.
In: Journal of Computational Physics, Elsevier, [Article]

Abstract

The continuum description of active particle systems is an efficient instrument to analyze a finite size particle dynamics in the limit of a large number of particles. However, it is often the case that such equations appear as nonlinear integro-differential equations and purely analytical treatment becomes quite limited. We propose a general framework of finite volume methods (FVMs) to numerically solve partial differential equations (PDEs) of the continuum limit of nonlocally interacting chiral active particle systems confined to two dimensions. We demonstrate the performance of the method on spatially homogeneous problems, where the comparison to analytical results is available, and on general spatially inhomogeneous equations, where pattern formation is predicted by kinetic theory. We numerically investigate phase transitions of particular problems in both spatially homogeneous and inhomogeneous regimes and report the existence of different first and second order transitions.

Item Type: Article
Erschienen: 2020
Creators: Kruk, N. and Carrillo, J.A. and Koeppl, H.
Title: A Finite Volume Method for Continuum Limit Equations of Nonlocally Interacting Active Chiral Particles
Language: English
Abstract:

The continuum description of active particle systems is an efficient instrument to analyze a finite size particle dynamics in the limit of a large number of particles. However, it is often the case that such equations appear as nonlinear integro-differential equations and purely analytical treatment becomes quite limited. We propose a general framework of finite volume methods (FVMs) to numerically solve partial differential equations (PDEs) of the continuum limit of nonlocally interacting chiral active particle systems confined to two dimensions. We demonstrate the performance of the method on spatially homogeneous problems, where the comparison to analytical results is available, and on general spatially inhomogeneous equations, where pattern formation is predicted by kinetic theory. We numerically investigate phase transitions of particular problems in both spatially homogeneous and inhomogeneous regimes and report the existence of different first and second order transitions.

Journal or Publication Title: Journal of Computational Physics
Publisher: Elsevier
Uncontrolled Keywords: Numerical Analysis (math.NA); Soft Condensed Matter (cond-mat.soft); Analysis of PDEs (math.AP)
Divisions: 18 Department of Electrical Engineering and Information Technology
18 Department of Electrical Engineering and Information Technology > Institute for Telecommunications > Bioinspired Communication Systems
18 Department of Electrical Engineering and Information Technology > Institute for Telecommunications
Date Deposited: 22 Sep 2020 09:42
Official URL: https://arxiv.org/abs/2008.08493
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