# Persistent random walkers and the telegrapher's equation

#### Persistent random walkers and the telegrapher's equation

- Event time: 11:30am until 12:30pm
- Event date: 21st June 2017
- Speaker: Professor Martin Evans (School of Physics & Astronomy, University of Edinburgh)
- Location: Room 2511, James Clerk Maxwell Building (JCMB) James Clerk Maxwell Building Peter Guthrie Tait Road Edinburgh EH9 3FD GB

### Event details

Persistent random walkers (who remember the direction of their last step)

are currently commonly used to model run and tumble bacteria. However they have been studied for some time before this. I'll review some simple results on the

relaxation time for a single persistent random walker which show that it can be

faster than the usual diffusive scaling relaxation time i.e $ \tau \sim O(L)$

rather than $\tau \sim O(L^2)$. I'll also show how a continuum limit for the Master equation yields the telegrapher's equation which is an equation that interpolates between the diffusion equation and the wave equation. I'll discuss the solution of the telegraphers equation. If time permits I'll mention some results derived with Alex Slowman and Richard Blythe on two interacting persistent walkers.

References:

Some applications of persistent random walkers and the telegrapher's equation

G. H. Weiss Physica A 311 (2002) p381-410

Jamming and Attraction of Interacting Run-and-Tumble Random Walkers

A.B. Slowman, M.R. Evans, and R.A. Blythe

Phys. Rev. Lett. 116, 218101 (2016)

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