# Dynamics of the asymmetric exclusion process in the reverse bias regime (Caley) --- Square-Triangle-Rhombus Tiling Model (Maria)

Tuesday Seminar
2 Shorter Talks

#### by Caley Finn / Maria Tsarenko

Institution:
Date: Tue 16th August 2011
Time: 1:00 PM
Location: Room 215, Richard Berry Building

Abstract: (Caley)
The asymmetric simple exclusion process (ASEP) is a model describing
the diffusion of hard-core particles along a one-dimensional chain.
With open boundaries, the ASEP is a non-equilibrium system with late
time behaviour described by a unique stationary distribution. The
relaxation rate to this distribution can be found by solving the Bethe
ansatz equations for the system. Earlier work found the asymptotic
behaviour of the relaxation rate in the forward bias regime. We
extend these results to the reverse bias regime and describe how fine
structure in the Bethe ansatz solutions changes the asymptotic
behaviour.

(Maria)
In this talk we introduce a new integrable tiling model,
Square-triangle-rhombus tiling. It is an extension of the known
square-triangle tiling by the addition of a'thin rhombus'.
This tiling model is identified with a 10-vertex model. The eigenvalue was
found using Algebraic Bethe Ansatz and the model is solved on the line
parametrised by a single parameter $$\gamma$$.