Congestion in a Macroscopic Model of Selfdriven Particles Modeling Gregariousness
Abstract
We analyze a macroscopic model with a maximal density constraint which describes short range repulsion in biological systems. This system aims at modeling finitesize 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 onedimensional Riemann problem and introduce a perturbation problem which regularizes the compressibleincompressible transition. Specific difficulties related to the nonconservativity of the problem are discussed.
 Publication:

Journal of Statistical Physics
 Pub Date:
 February 2010
 DOI:
 10.1007/s109550099879x
 arXiv:
 arXiv:0908.1817
 Bibcode:
 2010JSP...138...85D
 Keywords:

 Congestion;
 Riemann problem;
 Incompressiblecompressible transition;
 Clusters dynamics;
 Gregariousness;
 Steric constraints;
 Mathematical Physics
 EPrint:
 J. Stat. Phys., 138 (2010), pp. 85125