2pm - 3pm
Wednesday 26 October 2016
Self-propelled particle systems and the steady states in continuum limit
This is a joint FMS/DSPDE seminar. Yanghong Huang (Manchester) will be speaking.
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Complex behaviours of animal swarming such as fish schools and bird flocks exhibit macroscopic patterns from interactions between individuals. These phenomena can be modelled both by agent-based particle systems and their continuum limiting PDEs, providing a mathematical framework frequently used in crowd dynamics, opinion formation and cell biology.
In this talk, I will first discuss how complicated behaviours could arise from a few simple rules, and then focus on a self-propelled particle systems for concurrent moving flocks and rotating mills, with simple attractive-repulsive interactions.
The continuum (or mean field) limit of the particle system is then studied, showing that the concept of H-stable potentials originated from statistical mechanics for discrete particles is equivalent to the existence of stationary patterns for the continuum integro-differential equation for a special Quasi-Morse potential. This is a joint work with José Carrillo and Stephan Martin.