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Pattern formation of a nonlocal, anisotropic interaction model
journal contribution
posted on 2023-06-09, 08:20 authored by Martin Burger, Bertram Duering, Lisa Maria Kreusser, Peter A Markowich, Carola-Bibiane SchönliebWe consider a class of interacting particle models with anisotropic, repulsive-attractive interaction forces whose orientations depend on an underlying tensor field. An example of this class of models is the so-called Kücken-Champod model describing the formation of fingerprint patterns. This class of models can be regarded as a generalization of a gradient flow of a nonlocal interaction potential which has a local repulsion and a longrange attraction structure. In contrast to isotropic interaction models the anisotropic forces in our class of models cannot be derived from a potential. The underlying tensor field introduces an anisotropy leading to complex patterns which do not occur in isotropic models. This anisotropy is characterized by one parameter in the model. We study the variation of this parameter, describing the transition between the isotropic and the anisotropic model, analytically and numerically. We analyze the equilibria of the corresponding mean-field partial differential equation and investigate pattern formation numerically in two dimensions by studying the dependence of the parameters in the model on the resulting patterns.
Funding
Novel discretisations of higher-order nonlinear PDE; G1603; LEVERHULME TRUST; RPG-2015-069
History
Publication status
- Published
File Version
- Accepted version
Journal
Mathematical Models and Methods in Applied SciencesISSN
0218-2025Publisher
World Scientific PublishingExternal DOI
Issue
3Volume
28Page range
409-451Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Numerical Analysis and Scientific Computing Research Group Publications
Notes
Electronic version of an article published as Mathematical Models and Methods in Applied Sciences, 28 (3), 2018, pp. 409-451 https://doi.org/10.1142/S0218202518500112 © [copyright World Scientific Publishing Company] https://www.worldscientific.com/worldscinet/m3asFull text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2017-10-18First Open Access (FOA) Date
2018-12-29First Compliant Deposit (FCD) Date
2017-10-18Usage metrics
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