187 research outputs found
The asymmetric Exclusion Process and Brownian Excursions
We consider the totally asymmetric exclusion process (TASEP) in one dimension
in its maximal current phase. We show, by an exact calculation, that the
non-Gaussian part of the fluctuations of density can be described in terms of
the statistical properties of a Brownian excursion. Numerical simulations
indicate that the description in terms of a Brownian excursion remains valid
for more general one dimensional driven systems in their maximal current phase.Comment: 23 pages, 1 figure, in latex, e-mail addresses: [email protected],
[email protected], [email protected]
Large deviation functional of the weakly asymmetric exclusion process
We obtain the large deviation functional of a density profile for the
asymmetric exclusion process of L sites with open boundary conditions when the
asymmetry scales like 1/L. We recover as limiting cases the expressions derived
recently for the symmetric (SSEP) and the asymmetric (ASEP) cases. In the ASEP
limit, the non linear differential equation one needs to solve can be analysed
by a method which resembles the WKB method
Fluctuations in the weakly asymmetric exclusion process with open boundary conditions
accepted in Journal of Statistical PhysicsWe investigate the fluctuations around the average density profile in the weakly asymmetric exclusion process with open boundaries in the steady state. We show that these fluctuations are given, in the macroscopic limit, by a centered Gaussian field and we compute explicitly its covariance function. We use two approaches. The first method is dynamical and based on fluctuations around the hydrodynamic limit. We prove that the density fluctuations evolve macroscopically according to an autonomous stochastic equation, and we search for the stationary distribution of this evolution. The second approach, which is based on a representation of the steady state as a sum over paths, allows one to write the density fluctuations in the steady state as a sum over two independent processes, one of which is the derivative of a Brownian motion, the other one being related to a random path in a potential
Action functional and quasi-potential for the Burgers equation in a bounded interval
Consider the viscous Burgers equation on
the interval with the inhomogeneous Dirichlet boundary conditions
, . The flux is the function , is the viscosity, and the boundary data satisfy
. We examine the quasi-potential corresponding to an action
functional, arising from non-equilibrium statistical mechanical models,
associated to the above equation. We provide a static variational formula for
the quasi-potential and characterize the optimal paths for the dynamical
problem. In contrast with previous cases, for small enough viscosity, the
variational problem defining the quasi potential admits more than one
minimizer. This phenomenon is interpreted as a non-equilibrium phase transition
and corresponds to points where the super-differential of the quasi-potential
is not a singleton
Work and heat probability distributions in out-of-equilibrium systems
We review and discuss the equations governing the distribution of work done
on a system which is driven out of equilibrium by external manipulation, as
well as those governing the entropy flow to a reservoir in a nonequilibrium
system. We take advantage of these equations to investigate the path phase
transition in a manipulated mean-field Ising model and the large-deviation
function for the heat flow in the asymmetric exclusion process with
periodically varying transition probabilities.Comment: Contribution to Proceedings of "Work, Dissipation, and Fluctuations
in Nonequilibrium Physics", Brussels, 200
Sample-Dependent Phase Transitions in Disordered Exclusion Models
We give numerical evidence that the location of the first order phase
transition between the low and the high density phases of the one dimensional
asymmetric simple exclusion process with open boundaries becomes sample
dependent when quenched disorder is introduced for the hopping rates.Comment: accepted in Europhysics Letter
Phase diagram and edge effects in the ASEP with bottlenecks
We investigate the totally asymmetric simple exclusion process (TASEP) in the
presence of a bottleneck, i.e. a sequence of consecutive defect sites with
reduced hopping rate. The influence of such a bottleneck on the phase diagram
is studied by computer simulations and a novel analytical approach. We find a
clear dependence of the current and the properties of the phase diagram not
only on the length of the bottleneck, but also on its position. For bottlenecks
near the boundaries, this motivates the concept of effective boundary rates.
Furthermore the inclusion of a second, smaller bottleneck far from the first
one has no influence on the transport capacity. These results will form the
basis of an effective description of the disordered TASEP and are relevant for
the modelling of protein synthesis or intracellular transport systems where the
motion of molecular motors is hindered by immobile blocking molecules.Comment: accepted by Physica
Single-Bottleneck Approximation for Driven Lattice Gases with Disorder and Open Boundary Conditions
We investigate the effects of disorder on driven lattice gases with open
boundaries using the totally asymmetric simple exclusion process as a
paradigmatic example. Disorder is realized by randomly distributed defect sites
with reduced hopping rate. In contrast to equilibrium, even macroscopic
quantities in disordered non-equilibrium systems depend sensitively on the
defect sample. We study the current as function of the entry and exit rates and
the realization of disorder and find that it is, in leading order, determined
by the longest stretch of consecutive defect sites (single-bottleneck
approximation, SBA). Using results from extreme value statistics the SBA allows
to study ensembles with fixed defect density which gives accurate results, e.g.
for the expectation value of the current. Corrections to SBA come from
effective interactions of bottlenecks close to the longest one. Defects close
to the boundaries can be described by effective boundary rates and lead to
shifts of the phase transitions. Finally it is shown that the SBA also works
for more complex models. As an example we discuss a model with internal states
that has been proposed to describe transport of the kinesin KIF1A.Comment: submitted to J. Stat. Mec
Driven Diffusive Systems with Disorder
We discuss recent work on the static and dynamical properties of the
asymmetric exclusion process, generalized to include the effect of disorder. We
study in turn: random disorder in the properties of particles; disorder in the
spatial distribution of transition rates, both with a single easy direction and
with random reversals of the easy direction; dynamical disorder, where
particles move in a disordered landscape which itself evolves in time. In every
case, the system exhibits phase separation; in some cases, it is of an unusual
sort. The time-dependent properties of density fluctuations are in accord with
the kinematic wave criterion that the dynamical universality class is
unaffected by disorder if the kinematic wave velocity is nonzero.Comment: To appear in Physica A, Proc. of International Workshop on Common
Trends in Traffic Systems (IIT, Kanpur,2006
The gut-lung axis in the CFTR modulator era
The advent of CFTR modulators represents a turning point in the history of cystic fibrosis (CF) management, changing profoundly the disease’s clinical course by improving mucosal hydration. Assessing changes in airway and digestive tract microbiomes is of great interest to better understand the mechanisms and to predict disease evolution. Bacterial and fungal dysbiosis have been well documented in patients with CF; yet the impact of CFTR modulators on microbial communities has only been partially deciphered to date. In this review, we aim to summarize the current state of knowledge regarding the impact of CFTR modulators on both pulmonary and digestive microbiomes. Our analysis also covers the inter-organ connections between lung and gut communities, in order to highlight the gut-lung axis involvement in CF pathophysiology and its evolution in the era of novel modulators therapies
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