11:00 am Wednesday, February 23, 2011
Mathematical Physics: Analytical and numerical study of a model of self-organization by Sebastien Motsch (University of Maryland, College Park) in RLM 12.166
Abstract: In many biological systems, we observe the emergence of self-organized dynamics (flock of birds, school of fish, aggregation of bacteria...). To understand the phenomenon of flocking, a simple model has been proposed, the so-called Vicsek model. This model describes how particles interact in order to align with their neighbors. In this talk, we first briefly explain how we can derive a large-scale limit of this model when the number of particles becomes very large. This derivation leads to a non-conservative hyperbolic system referred to as the "macroscopic model". In contrast, the original Vicsek model is called the "microscopic model". In a second part, different numerical methods are proposed to solve the macroscopic model. Since the model is non-conservative, the different methods lead to different solutions. However, the comparison between the numerical simulations and the microscopic model reveals that only one numerical method, called the "splitting method", is able to reproduce the large scale dynamics of the Vicsek model. Understand this result analytically is still an open problem. Submitted by
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