Jeans type instability for a chemotactic model of cellular aggregation

Abstract

We consider an inertial model of chemotactic aggregation generalizing the Keller-Segel model and we study the linear dynamical stability of an infinite and homogeneous distribution of cells (bacteria, amoebae, endothelial cells,...) when inertial effects are accounted for. These inertial terms model cells directional persistance. We determine the condition of instability and the growth rate of the perturbation as a function of the cell density and the wavelength of the perturbation. We discuss the differences between overdamped (Keller-Segel) and inertial models. Finally, we show the analogy between the instability criterion for biological populations and the Jeans instability criterion in astrophysics.

References in corpus (9)

• Percolation, Morphogenesis, and Burgers Dynamics in Blood Vessels Formation
• Generalized thermodynamics and Fokker-Planck equations. Applications to stellar dynamics, two-dimensional turbulence and Jupiter's great red spot
• Thermodynamics of self-gravitating systems
• Thermodynamics and collapse of self-gravitating Brownian particles in D dimensions
• Anomalous diffusion and collapse of self-gravitating Langevin particles in D dimensions
• Post-collapse dynamics of self-gravitating Brownian particles in D dimensions
• Virial theorem and dynamical evolution of self-gravitating Brownian particles and bacterial populations in an unbounded domain
• Numerical renormalization group of vortex aggregation in 2D decaying turbulence: the role of three-body interactions
• Estimate of blow-up and relaxation time for self-gravitating Brownian particles and bacterial populations

Cited by in corpus (15)

• Nonlinear mean field Fokker-Planck equations. Application to the chemotaxis of biological populations
• Hamiltonian and Brownian systems with long-range interactions: V. Stochastic kinetic equations and theory of fluctuations
• Logotropic distributions
• Kinetic and hydrodynamic models of chemotactic aggregation
• Jeans type instability of a complex self-interacting scalar field in general relativity
• Instability of a uniformly collapsing cloud of classical and quantum self-gravitating Brownian particles
• Jeans type analysis of chemotactic collapse
• Exact diffusion coefficient of self-gravitating Brownian particles in two dimensions
• Phase transitions in self-gravitating systems and bacterial populations with a screened attractive potential
• Dynamical stability of infinite homogeneous self-gravitating systems: application of the Nyquist method
• Phase separation of bacterial colonies in a limit of high degradation. Analogy with Jupiter's great red spot
• Partial-moment minimum-entropy models for kinetic chemotaxis equations in one and two dimensions
• Well-balanced finite volume schemes for hydrodynamic equations with general free energy
• Aggregation of chemotactic organisms in a differential flow
• Nonlinear stability of phase transition steady states to a hyperbolic-parabolic system modelling vascular networks