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Phase transitions and solitons in self-propelled particles: kinetic theory and diagrammatic approach

Thursday 27th June 2013 - 17:15 to 17:45
Center for Mathematical Sciences
In this talk, I will summarize our recent progress on the kinetic theory of collective motion. The theory starts with an exact Markov chain for the Vicsek model in phase space and is made tractable by the mean-field-like Molecular Chaos approximation. This leads to an Enskog-like equation which we solve numerically as well as analytically in certain limits. The kinetic equation was also used to rigorously derive the hydrodynamic equations from the microscopic collision rules. We show that our results on the phase diagram and the formation of soliton-like waves agree quantitatively with direct simulations for large particle velocities. We find that the solitons modify the character of the flocking transition from continuous to discontinuous. To understand the behavior in the small velocity limit where mean-field theory is invalid, we developed a diagrammatic approach to systematically include particle correlations and show how they shift the flocking transition.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons