Phase transitions in stochastic models of flow

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this talk I will review some very simple models of nonequilibrium systems known as the 'Asymmetric Exclusion Process' and the 'Zero-Range Process'. These involve particles hopping stochastically on a lattice and thus form stochastic models of flow. Systems driven out of equilibrium can often exhibit behaviour not seen in systems in thermal equilibrium - for example phase transitions in one-dimensional systems. I shall show how examples of such transitions may be interpreted as jamming transitions in the context of traffic flow. More generally I shall discuss other instances of the condensation transition which is the phenomenon of a finite fraction of the driven conserved quantity condensing into a small spatial region. Criteria for the occurrence of condensation may be formulated and the detailed properties of the condensate such as its fluctuations have recently been elucidated.

Original languageEnglish
Title of host publicationTraffic and Granular Flow ' 05
EditorsA Schadschneider, T Poschel, R Kuhne, M Schreckenberg, DE Wolf
Place of PublicationBERLIN
PublisherSpringer-Verlag GmbH
Pages447-459
Number of pages13
ISBN (Print)978-3-540-47640-5
Publication statusPublished - 2007
Event6th International Conference on Traffic and Granular Flow - Berlin
Duration: 10 Oct 200512 Oct 2005

Conference

Conference6th International Conference on Traffic and Granular Flow
CityBerlin
Period10/10/0512/10/05

Keywords

  • ZERO-RANGE PROCESS
  • FACTORIZED STEADY-STATES
  • PARTICLE-SYSTEMS
  • CONDENSATION
  • DYNAMICS
  • STATIONARY
  • SIMULATION

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