105 research outputs found
Exact joint density-current probability function for the asymmetric exclusion process
We study the asymmetric exclusion process with open boundaries and derive the
exact form of the joint probability function for the occupation number and the
current through the system. We further consider the thermodynamic limit,
showing that the resulting distribution is non-Gaussian and that the density
fluctuations have a discontinuity at the continuous phase transition, while the
current fluctuations are continuous. The derivations are performed by using the
standard operator algebraic approach, and by the introduction of new operators
satisfying a modified version of the original algebra.Comment: 4 pages, 3 figure
Exact probability function for bulk density and current in the asymmetric exclusion process
We examine the asymmetric simple exclusion process with open boundaries, a
paradigm of driven diffusive systems, having a nonequilibrium steady state
transition. We provide a full derivation and expanded discussion and digression
on results previously reported briefly in M. Depken and R. Stinchcombe, Phys.
Rev. Lett. {\bf 93}, 040602, (2004). In particular we derive an exact form for
the joint probability function for the bulk density and current, both for
finite systems, and also in the thermodynamic limit. The resulting distribution
is non-Gaussian, and while the fluctuations in the current are continuous at
the continuous phase transitions, the density fluctuations are discontinuous.
The derivations are done by using the standard operator algebraic techniques,
and by introducing a modified version of the original operator algebra. As a
byproduct of these considerations we also arrive at a novel and very simple way
of calculating the normalization constant appearing in the standard treatment
with the operator algebra. Like the partition function in equilibrium systems,
this normalization constant is shown to completely characterize the
fluctuations, albeit in a very different manner.Comment: 10 pages, 4 figure
Continuum approach to wide shear zones in quasi-static granular matter
Slow and dense granular flows often exhibit narrow shear bands, making them
ill-suited for a continuum description. However, smooth granular flows have
been shown to occur in specific geometries such as linear shear in the absence
of gravity, slow inclined plane flows and, recently, flows in split-bottom
Couette geometries. The wide shear regions in these systems should be amenable
to a continuum description, and the theoretical challenge lies in finding
constitutive relations between the internal stresses and the flow field. We
propose a set of testable constitutive assumptions, including
rate-independence, and investigate the additional restrictions on the
constitutive relations imposed by the flow geometries. The wide shear layers in
the highly symmetric linear shear and inclined plane flows are consistent with
the simple constitutive assumption that, in analogy with solid friction, the
effective-friction coefficient (ratio between shear and normal stresses) is a
constant. However, this standard picture of granular flows is shown to be
inconsistent with flows in the less symmetric split-bottom geometry - here the
effective friction coefficient must vary throughout the shear zone, or else the
shear zone localizes. We suggest that a subtle dependence of the
effective-friction coefficient on the orientation of the sliding layers with
respect to the bulk force is crucial for the understanding of slow granular
flows.Comment: 11 pages, 7 figure
The Grand-Canonical Asymmetric Exclusion Process and the One-Transit Walk
The one-dimensional Asymmetric Exclusion Process (ASEP) is a paradigm for
nonequilibrium dynamics, in particular driven diffusive processes. It is
usually considered in a canonical ensemble in which the number of sites is
fixed. We observe that the grand-canonical partition function for the ASEP is
remarkably simple. It allows a simple direct derivation of the asymptotics of
the canonical normalization in various phases and of the correspondence with
One-Transit Walks recently observed by Brak et.al.Comment: Published versio
Wide shear zones and the spot model: Implications from the split-bottom geometry
The spot model has been developed by Bazant and co-workers to describe
quasistatic granular flows. It assumes that granular flow is caused by the
opposing flow of so-called spots of excess free volume, with spots moving along
the slip lines of Mohr-Coulomb plasticity. The model is two-dimensional and has
been successfully applied to a number of different geometries. In this paper we
investigate whether the spot model in its simplest form can describe the wide
shear zones observed in experiments and simulations of a Couette cell with
split bottom. We give a general argument that is independent of the particular
description of the stresses, but which shows that the present formulation of
the spot model in which diffusion and drift terms are postulated to balance on
length scales of order of the spot diameter, i.e. of order 3-5 grain diameters,
is difficult to reconcile with the observed wide shear zones. We also discuss
the implications for the spot model of co-axiality of the stress and strain
rate tensors found in these wide shear flows, and point to possible extensions
of the model that might allow one to account for the existence of wide shear
zones.Comment: 6 pages, 6 figures, to be published in EPJ
Dyck Paths, Motzkin Paths and Traffic Jams
It has recently been observed that the normalization of a one-dimensional
out-of-equilibrium model, the Asymmetric Exclusion Process (ASEP) with random
sequential dynamics, is exactly equivalent to the partition function of a
two-dimensional lattice path model of one-transit walks, or equivalently Dyck
paths. This explains the applicability of the Lee-Yang theory of partition
function zeros to the ASEP normalization.
In this paper we consider the exact solution of the parallel-update ASEP, a
special case of the Nagel-Schreckenberg model for traffic flow, in which the
ASEP phase transitions can be intepreted as jamming transitions, and find that
Lee-Yang theory still applies. We show that the parallel-update ASEP
normalization can be expressed as one of several equivalent two-dimensional
lattice path problems involving weighted Dyck or Motzkin paths. We introduce
the notion of thermodynamic equivalence for such paths and show that the
robustness of the general form of the ASEP phase diagram under various update
dynamics is a consequence of this thermodynamic equivalence.Comment: Version accepted for publicatio
Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
We consider the general problem of determining the steady state of stochastic
nonequilibrium systems such as those that have been used to model (among other
things) biological transport and traffic flow. We begin with a broad overview
of this class of driven diffusive systems - which includes exclusion processes
- focusing on interesting physical properties, such as shocks and phase
transitions. We then turn our attention specifically to those models for which
the exact distribution of microstates in the steady state can be expressed in a
matrix product form. In addition to a gentle introduction to this matrix
product approach, how it works and how it relates to similar constructions that
arise in other physical contexts, we present a unified, pedagogical account of
the various means by which the statistical mechanical calculations of
macroscopic physical quantities are actually performed. We also review a number
of more advanced topics, including nonequilibrium free energy functionals, the
classification of exclusion processes involving multiple particle species,
existence proofs of a matrix product state for a given model and more
complicated variants of the matrix product state that allow various types of
parallel dynamics to be handled. We conclude with a brief discussion of open
problems for future research.Comment: 127 pages, 31 figures, invited topical review for J. Phys. A (uses
IOP class file
Enforcement and Public Corruption: Evidence from US States
We use high-quality panel data on corruption convictions, new panels of assistant U.S. attorneys and relative public sector wages, and careful attention to the consequences of modeling endogeneity to estimate the impact of prosecutorial resources on criminal convictions of those who undertake corrupt acts. Consistent with system capacity arguments, we find that greater prosecutor resources result in more convictions for corruption, other things equal. We find more limited, recent evidence for the deterrent effect of increased prosecutions. We control for and confirm in a panel context the effects of many previously identified correlates and causes of corruption. By explicitly determining the allocation of prosecutorial resources endogenously from past corruption convictions and political considerations, we show that this specification leads to larger estimates of the effect of resources on convictions. The results are robust to various ways of measuring the number of convictions as well as to various estimators
Monte Carlo Simulations indicate that Chromati: Nanostructure is accessible by Light Microscopy
A long controversy exists about the structure of chromatin. Theoretically, this structure could be resolved by scattering experiments if one determines the scattering function - or equivalently the pair distribution function - of the nucleosomes. Unfortunately, scattering experiments with live cells are very difficult and limited to only a couple of nucleosomes
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