13 research outputs found
Frozen shuffle update for an asymmetric exclusion process on a ring
We introduce a new rule of motion for a totally asymmetric exclusion process
(TASEP) representing pedestrian traffic on a lattice. Its characteristic
feature is that the positions of the pedestrians, modeled as hard-core
particles, are updated in a fixed predefined order, determined by a phase
attached to each of them. We investigate this model analytically and by Monte
Carlo simulation on a one-dimensional lattice with periodic boundary
conditions. At a critical value of the particle density a transition occurs
from a phase with `free flow' to one with `jammed flow'. We are able to
analytically predict the current-density diagram for the infinite system and to
find the scaling function that describes the finite size rounding at the
transition point.Comment: 16 page
Non equilibrium steady states: fluctuations and large deviations of the density and of the current
These lecture notes give a short review of methods such as the matrix ansatz,
the additivity principle or the macroscopic fluctuation theory, developed
recently in the theory of non-equilibrium phenomena. They show how these
methods allow to calculate the fluctuations and large deviations of the density
and of the current in non-equilibrium steady states of systems like exclusion
processes. The properties of these fluctuations and large deviation functions
in non-equilibrium steady states (for example non-Gaussian fluctuations of
density or non-convexity of the large deviation function which generalizes the
notion of free energy) are compared with those of systems at equilibrium.Comment: 35 pages, 9 figure
Statistical Theory for the Kardar-Parisi-Zhang Equation in 1+1 Dimension
The Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimension dynamically develops
sharply connected valley structures within which the height derivative {\it is
not} continuous. There are two different regimes before and after creation of
the sharp valleys. We develop a statistical theory for the KPZ equation in 1+1
dimension driven with a random forcing which is white in time and Gaussian
correlated in space. A master equation is derived for the joint probability
density function of height difference and height gradient when the forcing correlation length is much smaller than
the system size and much bigger than the typical sharp valley width. In the
time scales before the creation of the sharp valleys we find the exact
generating function of and . Then we express the time
scale when the sharp valleys develop, in terms of the forcing characteristics.
In the stationary state, when the sharp valleys are fully developed, finite
size corrections to the scaling laws of the structure functions are also obtained.Comment: 50 Pages, 5 figure