An Anisotropic Interaction Model for Simulating Fingerprints

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• Lisa Maria Kreusser (University of Cambridge)
• Thursday 02 May 2019, 16:30-16:45
• Centre for Mathematical Sciences, MR2.

If you have a question about this talk, please contact Ferdia Sherry.

Motivated by the formation of fingerprint patterns we consider a class of interaction models with anisotropic interaction forces whose orientations depend on an underlying tensor field. 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 long-range 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 steady states and their stability by considering the particle model and the associated mean-field equations. Besides, we propose a bio-inspired model to simulate fingerprint patterns as stationary solutions by choosing the underlying tensor field appropriately.

This talk is part of the SIAM-IMA Cambridge Student Chapter series.

This talk is included in these lists:

• Centre for Mathematical Sciences, MR2
• SIAM-IMA Cambridge Student Chapter

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