Run-and-tumble particles on a line with a fertile site

Pascal Grange*, Xueqi Yao

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We propose a model of run-and-tumble particles (RTPs) on a line with a fertile site at the origin. After going through the fertile site, a run-and-tumble particle gives rise to new particles until it flips direction. The process of creation of new particles is modelled by a fertility function (of the distance to the fertile site), multiplied by a fertility rate. If the initial conditions correspond to a single RTP with even probability density, the system is parity-invariant. The equations of motion can be solved in the Laplace domain, in terms of the density of right-movers at the origin. At large time, this density is shown to grow exponentially, at a rate that depends only on the fertility function and fertility rate. Moreover, the total density of RTPs (divided by the density of right-movers at the origin), reaches a stationary state that does not depend on the initial conditions, and presents a local minimum at the fertile site.

Original languageEnglish
Article number325007
JournalJournal of Physics A: Mathematical and Theoretical
Volume54
Issue number32
DOIs
Publication statusPublished - Aug 2021

Keywords

  • Out-of-equilibrium statistical physics
  • Run-and-tumble particles
  • Stochastic processes

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