A one-dimensional model for chemotaxis with hard-core interactions

Abstract

In this paper we consider a biased velocity jump process with excluded-volume interactions for chemotaxis, where we account for the size of each particle. Starting with a system of N individual hard rod particles in one dimension, we derive a nonlinear kinetic model using two different approaches. The first approach is a systematic derivation for small occupied fraction of particles based the method of matched asymptotic expansions. The second approach, based on a compression method that exploits the single-file motion of hard core particles, does not have the limitation of a small occupied fraction but requires constant tumbling rates. We validate our nonlinear model with numerical simulations, comparing its solutions with the corresponding noninteracting linear model as well as stochastic simulations of the underlying particle system.

References in corpus (9)

• How to Simulate Billiards and Similar Systems
• Jamming and Attraction of Interacting Run-and-Tumble Random Walkers
• Excluded-volume effects in the diffusion of hard spheres
• Diffusion of multiple species with excluded-volume effects
• Enhanced propagation of motile bacteria on surfaces due to forward scattering
• Diffusion of finite-size particles in confined geometries
• Single-File Diffusion of Externally Driven Particles
• Hard-sphere interactions in velocity jump models
• Reactions, Diffusion and Volume Exclusion in a Heterogeneous System of Interacting Particles

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