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Congestion in a Macroscopic Model of Self-driven Particles Modeling Gregariousness

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Abstract

We analyze a macroscopic model with a maximal density constraint which describes short range repulsion in biological systems. This system aims at modeling finite-size particles which cannot overlap and repel each other when they are too close. The parts of the fluid where the maximal density is reached behave like incompressible fluids while lower density regions are compressible. This paper investigates the transition between the compressible and incompressible regions. To capture this transition, we study a one-dimensional Riemann problem and introduce a perturbation problem which regularizes the compressible-incompressible transition. Specific difficulties related to the non-conservativity of the problem are discussed.

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Authors and Affiliations

  1. Université de Toulouse, UPS, INSA, UT1, UTM, Institut de Mathématiques de Toulouse, 31062, Toulouse, France

    Pierre Degond, Laurent Navoret & David Sanchez

  2. CNRS, Institut de Mathématiques de Toulouse, UMR 5219, 31062, Toulouse, France

    Pierre Degond, Laurent Navoret & David Sanchez

  3. Université de Toulouse, UPS, INSA, UT1, UTM, Centre de Recherches sur la Cognition Animale, 31062, Toulouse, France

    Richard Bon

  4. CNRS, Centre de Recherches sur la Cognition Animale, UMR 5169, 31062, Toulouse, France

    Richard Bon

Authors
  1. Pierre Degond
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  2. Laurent Navoret
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  3. Richard Bon
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  4. David Sanchez
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Correspondence to Pierre Degond.

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Degond, P., Navoret, L., Bon, R. et al. Congestion in a Macroscopic Model of Self-driven Particles Modeling Gregariousness. J Stat Phys 138, 85–125 (2010). https://doi.org/10.1007/s10955-009-9879-x

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  • DOI: https://doi.org/10.1007/s10955-009-9879-x

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