Speaker
Description
Volume-exclusion interactions play a crucial role in the self-organisation observed in many biological systems. In particular, they are fundamental to explain the spontaneous emergence of nematic order in populations of anisotropic particles, as observed, for example, in dense suspensions of myxobacteria \cite{balagam2015mechanism}. More generally, they also play an important role in cell migration, where particle shape and crowding strongly affect the behaviour of the migrating population \cite{dyson2015importance}.
In this talk, we consider a stochastic model of hard-core anisotropic particles in two dimensions, represented as non-overlapping rectangular particles undergoing Brownian motion with drift. Starting from this particle model, we use matched asymptotic expansions in the dilute regime to derive a kinetic equation for the one-particle probability density in position and orientation space. The resulting kinetic model explicitly shows how excluded-volume effects are encoded in the interaction kernel, which depends on particle aspect ratio. In the limit of vanishing width, we recover the corresponding description for non-overlapping needles \cite{bruna2023derivation}. Finally, we discuss possible extensions to ellipsoidal or capsule-shaped particles, as well as to anisotropic particles in three dimensions.
Bibliography
@article{balagam2015mechanism,
title={Mechanism for collective cell alignment in Myxococcus xanthus bacteria},
author={Balagam, Rajesh and Igoshin, Oleg A},
journal={PLoS computational biology},
volume={11},
number={8},
pages={e1004474},
year={2015},
publisher={Public Library of Science San Francisco, CA USA}
}
@article{dyson2015importance,
title={The importance of volume exclusion in modelling cellular migration},
author={Dyson, Louise and Baker, Ruth E},
journal={Journal of mathematical biology},
volume={71},
number={3},
pages={691--711},
year={2015},
publisher={Springer}
}
@article{bruna2023derivation,
title={Derivation of a macroscopic model for Brownian hard needles},
author={Bruna, Maria and Chapman, Stephen J and Schmidtchen, Markus},
journal={Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
volume={479},
number={2274},
year={2023},
publisher={The Royal Society}
}
