In this paper we consider a  velocity jump process with excluded-volume interactions in the context of cell chemotaxis, where  the size of each particle affects the motion . 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 , based on matched asymptotic expansions, is systematic and hence does not rely on a closure assumption. It is valid in the limit of small but finite particle occupied fraction and in the presence of external signals . The second method , 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 non-interacting linear model as well as stochastic simulations of the underlying particle system.
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.
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biased
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in the context of cell
for
A
we account for
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affects the motion
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, based on matched asymptotic expansions, is systematic and hence does not rely on a closure assumption. It is valid in the limit of small but finite particle occupied fraction and in the presence of external signals
is a systematic derivation for small occupied fraction of particles based the method of matched asymptotic expansions
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method
approach
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non-interacting
noninteracting