Numerical Simulations of Kinetic Models for Chemotaxis

Numerical Simulations of Kinetic Models for Chemotaxis

We present a new algorithm based on a Cartesian mesh for the numerical approximation of kinetic models for chemosensitive movements set in an arbitrary geometry. We investigate the influence of the geometry on the collective behavior of bacteria described by a kinetic equation interacting with nutrients and chemoattractants. Numerical simulations are performed to verify accuracy and stability o...

Numerical simulation of a kinetic model for chemotaxis

Drift-diffusion Limits of Kinetic Models for Chemotaxis: a Generalization

We study a kinetic model for chemotaxis introduced by Othmer, Dunbar, and Alt [22], which was motivated by earlier results of Alt, presented in [1], [2]. In two papers by Chalub, Markowich, Perthame and Schmeiser, it was rigorously shown that, in three dimensions, this kinetic model leads to the classical KellerSegel model as its drift-diffusion limit when the equation of the chemo-attractant i...

Recent Developments in the Numerical Methods for the Chemotaxis Models

Here, ρ(x, y, t) is the cell density, c(x, y, t) is the chemoattractant concentration, χ is a chemotactic sensitivity constant, Ω is a bounded domain in R, ∂Ω is its boundary, and n is a unit normal vector. Chemotaxis refers to mechanisms by which cellular motion occurs in response to an external stimulus, usually a chemical one. Chemotaxis is an important process in many medical and biological...

Numerical simulations of stellar winds: polytropic models

We discuss steady-state transonic outflows obtained by direct numerical solution of the hydrodynamic and magnetohydrodynamic equations. We make use of the Versatile Advection Code, a software package for solving systems of (hyperbolic) partial differential equations. We proceed stepwise from a spherically symmetric, isothermal, unmagnetized, non-rotating Parker wind to arrive at axisymmetric, p...