From a microscopic solution to a continuum description of active particles with a recoil interaction in one dimension

M.J. Metson*, M.R. Evans, R.A. Blythe

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

We consider a model system of persistent random walkers that can jam, pass through each other or jump apart (recoil) on contact. In a continuum limit, where particle motion between stochastic changes in direction becomes deterministic, we find that the stationary inter-particle distribution functions are governed by an inhomogeneous fourth-order differential equation. Our main focus is on determining the boundary conditions that these distribution functions should satisfy. We find that these do not arise naturally from physical considerations, but need to be carefully matched to functional forms that arise from the analysis of an underlying discrete process. The inter-particle distribution functions, or their first derivatives, are generically found to be discontinuous at the boundaries.
Original languageEnglish
Article number044134
Pages (from-to)1-14
Number of pages14
JournalPhysical Review E
Volume107
Issue number4
DOIs
Publication statusPublished - 28 Apr 2023

Keywords / Materials (for Non-textual outputs)

  • cond-mat.stat-mech

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