Congestion in a macroscopic model of self-driven particles modeling gregariousness - Mathematical PhysicsReport as inadecuate




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Abstract: We analyze a macroscopic model with a maximal density constraint whichdescribes short range repulsion in biological systems. This system aims atmodeling finite-size particles which cannot overlap and repel each other whenthey are too close. The parts of the fluid where the maximal density is reachedbehave like incompressible fluids while lower density regions are compressible.This paper investigates the transition between the compressible andincompressible regions. To capture this transition, we study a one-dimensionalRiemann problem and introduce a perturbation problem which regularizes thecompressible-incompressible transition. Specific difficulties related to thenon-conservativity of the problem are discussed.



Author: Pierre Degond IMT, Laurent Navoret IMT, Richard Bon CRCA, David Sanchez IMT

Source: https://arxiv.org/



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