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arXiv · 1308.2883

Explicit Flock Solutions for Quasi-Morse potentials

Jose Antonio Carrillo·Yanghong Huang·Stephan Martin
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Abstract

We consider interacting particle systems and their mean-field limits, which are frequently used to model collective aggregation and are known to demonstrate a rich variety of pattern formations. The interaction is based on a pairwise potential combining short-range repulsion and long-range attraction. We study particular solutions, that are referred to as flocks in the second-order models, for the specific choice of the Quasi-Morse interaction potential. Our main result is a rigorous analysis of continuous, compactly supported flock profiles for the biologically relevant parameter regime. Existence and uniqueness is proven for three space dimension, whilst existence is shown for the two-dimensional case. Furthermore, we numerically investigate additional Morse-like interactions to complete the understanding of this class of potentials.

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Jose Antonio Carrillo, Yanghong Huang, Stephan Martin. 2014-04-12. Explicit Flock Solutions for Quasi-Morse potentials. https://doi.org/10.1017/s0956792514000126

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