CONTINUUM LIMIT OF SELF-DRIVEN PARTICLES WITH ORIENTATION INTERACTION

Pierre Degond

295 citations0/0 files storedMathematical Models and Methods in Applied Sciences

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Evacuation and Crowd Dynamics Gas Dynamics and Kinetic Theory Distributed Control Multi-Agent Systems

Abstract

The discrete Couzin–Vicsek algorithm (CVA), which describes the interactions of individuals among animal societies such as fish schools is considered. In this paper, a kinetic (mean-field) version of the CVA model is proposed and its formal macroscopic limit is provided. The final macroscopic model involves a conservation equation for the density of the individuals and a non-conservative equation for the director of the mean velocity and is proved to be hyperbolic. The derivation is based on the introduction of a non-conventional concept of a collisional invariant of a collision operator.

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2006A Model for the Dynamics of large Queuing Networks and Supply Chains

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2011On the Modeling of Traffic and Crowds: A Survey of Models, Speculations, and Perspectives 2019Vehicular traffic, crowds, and swarms: From kinetic theory and multiscale methods to applications and research perspectives 2013A Hierarchy of Heuristic-Based Models of Crowd Dynamics 2008FIRST-ORDER MACROSCOPIC MODELLING OF HUMAN CROWD DYNAMICS

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