Two-species particle aggregation and stability of co-dimension one solutions

Alan Mackey; Theodore Kolokolnikov; Andrea L. Bertozzi

doi:10.3934/dcdsb.2014.19.1411

Article Contents

2014, Volume 19, Issue 5: 1411-1436. Doi: 10.3934/dcdsb.2014.19.1411 open access

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Two-species particle aggregation and stability of co-dimension one solutions

1.
University of California, Los Angeles, Department of Mathematics, Box 951555, Los Angeles, CA 90095-1555
2.
Dalhousie University, Department of Mathematics and Statistics, Halifax, Nova Scotia, B3H 3J5
3.
University of California Los Angeles, Department of Mathematics, 520 Portola Plaza Box 951555, Los Angeles, CA 90095-1555

Received: May 2013

Revised: January 2014

Published: July 2014

Abstract / Introduction Related Papers Cited by

Abstract

Systems of pairwise-interacting particles model a cornucopia of physical systems, from insect swarms and bacterial colonies to nanoparticle self-assembly. We study a continuum model with densities supported on co-dimension one curves for two-species particle interaction in $\mathbb{R}^2$, and apply linear stability analysis of concentric ring steady states to characterize the steady state patterns and instabilities which form. Conditions for linear well-posedness are determined and these results are compared to simulations of the discrete particle dynamics, showing predictive power of the linear theory. Some intriguing steady state patterns are shown through numerical examples.

Keywords:

Mathematics Subject Classification: Primary: 35B35, 25B20, 35B36; Secondary: 35D30, 41A60.

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