Hard-sphere interactions in velocity-jump models

Benjamin Franz, Jake P. Taylor-King, Christian Yates, and Radek Erban
Phys. Rev. E 94, 012129 – Published 20 July 2016

Abstract

Group-level behavior of particles undergoing a velocity-jump process with hard-sphere interactions is investigated. We derive N-particle transport equations that include the possibility of collisions between particles and apply different approximation techniques to get expressions for the dependence of the collective diffusion coefficient on the number of particles and their diameter. The derived approximations are compared with numerical results obtained from individual-based simulations. The theoretical results compare well with Monte Carlo simulations providing the excluded-volume fraction is small.

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  • Received 2 June 2016

DOI:https://doi.org/10.1103/PhysRevE.94.012129

©2016 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
  1. Physical Systems
Statistical Physics & Thermodynamics

Authors & Affiliations

Benjamin Franz1,*, Jake P. Taylor-King1, Christian Yates2, and Radek Erban1,†

  • 1Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, United Kingdom
  • 2Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, United Kingdom

  • *bfranz@google.com
  • erban@maths.ox.ac.uk

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Issue

Vol. 94, Iss. 1 — July 2016

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