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Zass, Alexander (2017) Collective motion of living organisms: the Vicsek model. [Magistrali biennali]

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Abstract

The purpose of this work is to study the Vicsek model for self-driven articles, in particular its time-continuous version. We will study its mean-field limit, as well as the large-scale behaviour of the model. In particular, we find that the equilibrium distributions change according to whether the density is above or below a given threshold. Below this value, the only equilibrium distribution is isotropic in velocity direction and is stable; moreover, the convergence to this equilibrium is exponentially fast. When the density is above the threshold, we have a second class of anisotropic equilibria, formed by Von-Mises-Fischer distributions of arbitrary orientation. In this case, the isotropic equilibria become unstable and there is exponentially fast convergence to the anisotropic ones.

Item Type:Magistrali biennali
Subjects:Area 01 - Scienze matematiche e informatiche > MAT/06 Probabilità e statistica matematica
Codice ID:56242
Relatore:Dai Pra, Paolo
Data della tesi:07 July 2017
Biblioteca:Polo di Scienze > Biblioteca di Matematica

Bibliografia

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