Disordered driven lattice gases
- Event time: 3:00pm
- Event date: 16th October 2009
- Speaker: Philip Greulich (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
Defects (e.g. obstacles) in active transport systems can decrease the maximum flow that can be achieved by tuning boundary conditions (the transport capacity). Systems of this kind can be modelled by driven lattice gases with spatially varying transition rates. They are characterized by a parameter regime exhibiting phase separation, while the current is independent on variation of boundary rates there. Prior works suggest that in driven lattice gases with randomly distributed defects (binary disorder), the transport capacity appears to be, in leading order, determined by the longest bottleneck, i.e. a stretch of consecutive defects (single-bottleneck approximation, SBA). In this approximation, I relate the mean transport capacity of disordered driven lattice gases to systems with a single bottleneck applying extreme value statistics . The Validity of SBA is checked, and results are refined, by a pertubative expansion taking into account defects near the longest bottleneck. By neglecting correlations at the boundaries of a bottleneck we find an approximative analytical scheme to determine the transport capacity in the totally asymmetric simple exclusion process (TASEP) with a single bottleneck which hence can provide (semi-) analytical results for the disordered TASEP.
This is a roughly weekly series of didactical blackboard talks focussing on some theoretical aspect of Condensed Matter, Biological, and Statistical Physics..