A Non-Markovian Asymmetric Simple Exclusion Process
- Event time: 1:00pm
- Event date: 23rd May 2011
- Speaker: Robert Concannon (Formerly 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
In this presentation we explore a novel modification to the Asymmetric Simple Exclusion Process (ASEP) on a 1D ring. We made the ASEP non-Markovian by drawing the time of the next move of each motile element from a power law distribution. This has interesting consequences for the flow of particles around the ring as, for a correctly chosen decay parameter, traffic jams spontaneously form and break apart. This behaviour is qualitatively different from condensation effects seen in other modifications of the ASEP. We find that traffic jams containing all motile elements exist for a finite fraction of the time, the fraction depending on the exponent of the power-law waiting time distribution and the number of the elements. We call such jams full clumps. We investigate the conditions under which we expect full clumps to occur. Using basic arguments and extreme value theory we can explain some of the features of the distributions of the clump formation times, clump lifetime and the time between clumps that we see in simulations.
This is a weekly series of informal talks given primarily by members of the soft condensed matter and statistical mechanics groups, but is also open to members of other groups and external visitors. The aim of the series is to promote discussion and learning of various topics at a level suitable to the broad background of the group. Everyone is welcome to attend..