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| Collective displacements such as a flock of birds or a school of fish are one of the most astonishing examples of emergent behavior in nature. To model these phenomena, we can either use "microscopic models" describing the motion of each individual or "macroscopic models" describing the evolution of the density of individuals. In this talk, we discuss how we can link the two approaches using "kinetic theory". The difficulty is that, in contrast with particle systems in physics, models of collective displacements do not conserve momentum or energy. This lack of conservation requires to introduce new tools to derive and analyze their macroscopic limits. |
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