We derive general kinetic and hydrodynamic models of chemotactic aggregation that describe certain features of the morphogenesis of biological colonies (like bacteria, amoebae, endothelial cells or social insects). Starting from a stochastic model defined in terms of N coupled Langevin...

We point out a remarkable analogy between the limiting mass of relativistic white dwarf stars (Chandrasekhar’s limit) and the critical mass of bacterial populations in a generalized Keller–Segel model of chemotaxis [P.H. Chavanis, C. Sire, Phys. Rev. E 69 (2004) 016116]. This model is based...

We perform a linear dynamical stability analysis of a general hydrodynamic model of chemotactic aggregation [P.H. Chavanis, C. Sire, Physica A 384 (2007) 199]. Specifically, we study the stability of an infinite and homogeneous distribution of cells against “chemotactic collapse”. We discuss...

We show that the critical mass Mc=8π of bacterial populations in two dimensions in the chemotactic problem is the counterpart of the critical temperature Tc=GMm/4kB of self-gravitating Brownian particles in two-dimensional gravity. We obtain these critical values by using the Virial theorem or...

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...