Logotropic distributions

Pierre-Henri Chavanis and Clément Sire

Physica A: Statistical Mechanics and its Applications, 2007, vol. 375, issue 1, 140-158

Abstract: In all spatial dimensions d, we study the static and dynamical properties of a generalized Smoluchowski equation which describes the evolution of a gas obeying a logotropic equation of state, p=Alnρ. A logotrope can be viewed as a limiting form of polytrope (p=Kργ, γ=1+1/n), with index γ=0 or n=-1. In the language of generalized thermodynamics, it corresponds to a Tsallis distribution with index q=0. We solve the dynamical logotropic Smoluchowski equation in the presence of a fixed external force deriving from a quadratic potential, and for a gas of particles subjected to their mutual gravitational force. In the latter case, the collapse dynamics is studied for any negative index n, and the density scaling function is found to decay as r-α, with α=2n/(n-1) for n<-d/2, and α=2d/(d+2) for -d/2⩽n<0.

Keywords: Nonlinear meanfield Fokker–Planck equations; Generalized thermodynamics; Polytropic equation of state; Self-gravitating systems; Chemotaxis (search for similar items in EconPapers)
Date: 2007
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:375:y:2007:i:1:p:140-158

DOI: 10.1016/j.physa.2006.08.076

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