Dynamics of Run and Tumble Particles

Lead Research Organisation: University of Edinburgh
Department Name: Sch of Physics and Astronomy


The Asymmetric Simple Exclusion Process (ASEP) is a paradigm of nonequilibrium statistical mechanics due to the flexibility of the model and its rich phenomenology. One variant of the model is "run and tumble" dynamics, which provides a qualitative model of bacterial movement: particles hop stochastically on a (1D) lattice, and may reverse their direction of hopping after a tumbling event. This is subject to the constraint that particles cannot move through one another. In a recent paper by Slowman, Evans, and Blythe, the steady state for a system of two run and tumble particles was found. The current project aims to further the analysis to the temporal dynamics.


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Mallmin E (2019) A comparison of dynamical fluctuations of biased diffusion and run-and-tumble dynamics in one dimension in Journal of Physics A: Mathematical and Theoretical

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Mallmin E (2019) Exact spectral solution of two interacting run-and-tumble particles on a ring lattice in Journal of Statistical Mechanics: Theory and Experiment

Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/N509644/1 01/10/2016 30/09/2021
1941659 Studentship EP/N509644/1 01/09/2017 31/08/2021 Emil Jonathan Mallmin
Description During this award (still active), several aspects of run-and-tumble particles---an idealized random walk model of actively moving particles, such as bacteria---has been studied from a mostly analytical point of view. Key findings include an exact solution of a two-particle version of the model; a characterization of fluctuations in velocity and time spent at a given position for one particle; and a prototype study for how probabilistic conditioning can induce new interactions between run-and-tumble particles in an energy-efficient way. Overall, these results add to a growing literature on how the persistent-motion property of this model generates novel nonequilibrium phenomena.
Exploitation Route The published papers registered with this award will be used by other researchers working on similar physical models.
Sectors Other