779 research outputs found
A note on a local ergodic theorem for an infinite tower of coverings
This is a note on a local ergodic theorem for a symmetric exclusion process
defined on an infinite tower of coverings, which is associated with a finitely
generated residually finite amenable group.Comment: Final version to appear in Springer Proceedings in Mathematics and
Statistic
Vortices in the two-dimensional Simple Exclusion Process
We show that the fluctuations of the partial current in two dimensional
diffusive systems are dominated by vortices leading to a different scaling from
the one predicted by the hydrodynamic large deviation theory. This is supported
by exact computations of the variance of partial current fluctuations for the
symmetric simple exclusion process on general graphs. On a two-dimensional
torus, our exact expressions are compared to the results of numerical
simulations. They confirm the logarithmic dependence on the system size of the
fluctuations of the partialflux. The impact of the vortices on the validity of
the fluctuation relation for partial currents is also discussed.Comment: Revised version to appear in Journal of Statistical Physics. Minor
correction
Local inflammation, lethality and cytokine release in mice injected with Bothrops atrox venom.
We have provided evidence that: (a) lethality of mice to crude Bothrops venom varies according the isogenic strain (A/J > C57Bl/6 > A/Sn > BALB/c > C3H/HePas > DBA/2 > C3H/He); (b)BALB/c mice (LD50=100.0 microg) were injected i.p. with 50 microg of venom produced IL-6, IL-10, INF-gamma, TNF-alpha and NO in the serum. In vitro the cells from the mice injected and challenged with the venom only released IL-10 while peritoneal macrophages released IL-10, INF-gamma and less amounts of IL-6; (c) establishment of local inflammation and necrosis induced by the venom, coincides with the peaks of TNF-alpha, IFN-gamma and NO and the damage was neutralized when the venom was incubated with a monoclonal antibody against a 60 kDa haemorrhagic factor. These results suggest that susceptibility to Bothrops atrox venom is genetically dependent but MHC independent; that IL-6, IL-10, TNF-alpha, IFN-gamma and NO can be involved in the mediation of tissue damage; and that the major venom component inducers of the lesions are haemorrhagins
On the asymmetric zero-range in the rarefaction fan
We consider the one-dimensional asymmetric zero-range process starting from a
step decreasing profile. In the hydrodynamic limit this initial condition leads
to the rarefaction fan of the associated hydrodynamic equation. Under this
initial condition and for totally asymmetric jumps, we show that the weighted
sum of joint probabilities for second class particles sharing the same site is
convergent and we compute its limit. For partially asymmetric jumps we derive
the Law of Large Numbers for the position of a second class particle under the
initial configuration in which all the positive sites are empty, all the
negative sites are occupied with infinitely many first class particles and with
a single second class particle at the origin. Moreover, we prove that among the
infinite characteristics emanating from the position of the second class
particle, this particle chooses randomly one of them. The randomness is given
in terms of the weak solution of the hydrodynamic equation through some sort of
renormalization function. By coupling the zero-range with the exclusion process
we derive some limiting laws for more general initial conditions.Comment: 22 pages, to appear in Journal of Statistical Physic
Non equilibrium current fluctuations in stochastic lattice gases
We study current fluctuations in lattice gases in the macroscopic limit
extending the dynamic approach for density fluctuations developed in previous
articles. More precisely, we establish a large deviation principle for a
space-time fluctuation of the empirical current with a rate functional \mc
I (j). We then estimate the probability of a fluctuation of the average
current over a large time interval; this probability can be obtained by solving
a variational problem for the functional \mc I . We discuss several possible
scenarios, interpreted as dynamical phase transitions, for this variational
problem. They actually occur in specific models. We finally discuss the time
reversal properties of \mc I and derive a fluctuation relationship akin to
the Gallavotti-Cohen theorem for the entropy production.Comment: 36 Pages, No figur
Hard rod gas with long-range interactions: Exact predictions for hydrodynamic properties of continuum systems from discrete models
One-dimensional hard rod gases are explicitly constructed as the limits of
discrete systems: exclusion processes involving particles of arbitrary length.
Those continuum many-body systems in general do not exhibit the same
hydrodynamic properties as the underlying discrete models. Considering as
examples a hard rod gas with additional long-range interaction and the
generalized asymmetric exclusion process for extended particles (-ASEP),
it is shown how a correspondence between continuous and discrete systems must
be established instead. This opens up a new possibility to exactly predict the
hydrodynamic behaviour of this continuum system under Eulerian scaling by
solving its discrete counterpart with analytical or numerical tools. As an
illustration, simulations of the totally asymmetric exclusion process
(-TASEP) are compared to analytical solutions of the model and applied to
the corresponding hard rod gas. The case of short-range interaction is treated
separately.Comment: 19 pages, 8 figure
Symmetric Exclusion Process with a Localized Source
We investigate the growth of the total number of particles in a symmetric
exclusion process driven by a localized source. The average total number of
particles entering an initially empty system grows with time as t^{1/2} in one
dimension, t/log(t) in two dimensions, and linearly in higher dimensions. In
one and two dimensions, the leading asymptotic behaviors for the average total
number of particles are independent on the intensity of the source. We also
discuss fluctuations of the total number of particles and determine the
asymptotic growth of the variance in one dimension.Comment: 7 pages; small corrections, references added, final versio
Free Energy Functional for Nonequilibrium Systems: An Exactly Solvable Case
We consider the steady state of an open system in which there is a flux of
matter between two reservoirs at different chemical potentials. For a large
system of size , the probability of any macroscopic density profile
is ; thus generalizes to
nonequilibrium systems the notion of free energy density for equilibrium
systems. Our exact expression for is a nonlocal functional of ,
which yields the macroscopically long range correlations in the nonequilibrium
steady state previously predicted by fluctuating hydrodynamics and observed
experimentally.Comment: 4 pages, RevTeX. Changes: correct minor errors, add reference, minor
rewriting requested by editors and refere
Fluctuations of Current in Non-Stationary Diffusive Lattice Gases
We employ the macroscopic fluctuation theory to study fluctuations of
integrated current in one-dimensional lattice gases with a step-like initial
density profile. We analytically determine the variance of the current
fluctuations for a class of diffusive processes with a density-independent
diffusion coefficient, but otherwise arbitrary. Our calculations rely on a
perturbation theory around the noiseless hydrodynamic solution. We consider
both quenched and annealed types of averaging (the initial condition is allowed
to fluctuate in the latter situation). The general results for the variance are
specialized to a few interesting models including the symmetric exclusion
process and the Kipnis-Marchioro-Presutti model. We also probe large deviations
of the current for the symmetric exclusion process. This is done by numerically
solving the governing equations of the macroscopic fluctuation theory using an
efficient iteration algorithm.Comment: Slightly extended version. 12 pages, 6 figure
A diffusive system driven by a battery or by a smoothly varying field
We consider the steady state of a one dimensional diffusive system, such as
the symmetric simple exclusion process (SSEP) on a ring, driven by a battery at
the origin or by a smoothly varying field along the ring. The battery appears
as the limiting case of a smoothly varying field, when the field becomes a
delta function at the origin. We find that in the scaling limit, the long range
pair correlation functions of the system driven by a battery turn out to be
very different from the ones known in the steady state of the SSEP maintained
out of equilibrium by contact with two reservoirs, even when the steady state
density profiles are identical in both models
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