Numerical analysis on the traveling pulse in a kinetic chemotaxis model (Mathematical Analysis in Fluid and Gas Dynamics)

Abstract

A kinetic transport equation for chemotactic bacteria, i.e., a kinetic chemotaxis equation, coupled with reaction-diffusion equations for chemoattractants is considered. The Keller-Segel type equation for the population density of bacteria is derived by the asymptotic analysis of the kinetic chemotaxis equation in the continuum limit, where the ratio of the mean run length of bacteria to the characteristic length of the system, i.e., the Knudsen number, vanishes. Monte Carlo (MC) simulations of the kinetic chemotaxis model are performed for the traveling pulse problem with variation in the Knudsen number. The results of MC simulations are numerically compared with the Keller-Segel type equation. It is found that the results of MC simulations approach to that of the Keller-Segel type equation as decreasing the Knudsen number. However, a significant difference still remains for moderately small Knudsen numbers which correspond to the micro scale systems. This result demonstrates an importance of the kinetic chemotaxis model in the micro scale systems.