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Abstract
We study a model of selfpropelled particles exhibiting runandtumble dynamics on a lattice. This nonBrownian diffusion is characterized by a random walk with a finite persistence length between changes of direction and is inspired by the motion of bacteria such as E. coli. By defining a class of models with multiple species of particles and transmutation between species we can recreate such dynamics. These models admit exact analytical results whilst also forming a counterpart to previous continuum models of runandtumble dynamics. We solve the externally driven noninteracting and zerorange versions of the model exactly and utilize a fieldtheoretic approach to derive the continuum fluctuating hydrodynamics for more general interactions. We make contact with prior approaches to runandtumble dynamics off lattice and determine the steady state and linear stability for a class of crowding interactions, where the jump rate decreases as density increases. In addition to its interest from the perspective of nonequilibrium statistical mechanics, this lattice model constitutes an efficient tool to simulate a class of interacting runandtumble models relevant to bacterial motion, so long as certain conditions (that we derive) are met.
Original language  English 

Article number  P02029 
Pages (fromto)   
Number of pages  34 
Journal  Journal of Statistical Mechanics: Theory and Experiment 
DOIs  
Publication status  Published  Feb 2011 
Keywords
 solvable lattice models
 stochastic particle dynamics (theory)
 selfpropelled particles
 PATHINTEGRAL APPROACH
 ZERORANGE PROCESS
 FLAGELLAR FILAMENTS
 ESCHERICHIACOLI
 CHEMOTAXIS
 SYSTEMS
 STATES
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 1 Finished

Edinbugrh Soft Matter and Statistical Physics Programme Grant Renewal
Cates, M., Poon, W., Ackland, G., Clegg, P., Evans, M., MacPhee, C. & Marenduzzo, D.
1/10/07 → 31/03/12
Project: Research