996 research outputs found
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
Energy transport through rare collisions
We study a one-dimensional hamiltonian chain of masses perturbed by an energy
conserving noise. The dynamics is such that, according to its hamiltonian part,
particles move freely in cells and interact with their neighbors through
collisions, made possible by a small overlap of size between
near cells. The noise only randomly flips the velocity of the particles. If
, and if time is rescaled by a factor ,
we show that energy evolves autonomously according to a stochastic equation,
which hydrodynamic limit is known in some cases. In particular, if only two
different energies are present, the limiting process coincides with the simple
symmetric exclusion process.Comment: 24 pages, 2 figure
A limit result for a system of particles in random environment
We consider an infinite system of particles in one dimension, each particle
performs independant Sinai's random walk in random environment. Considering an
instant , large enough, we prove a result in probability showing that the
particles are trapped in the neighborhood of well defined points of the lattice
depending on the random environment the time and the starting point of the
particles.Comment: 11 page
Propagating the Pestalozzian: The Story of William Mcclure\u27s Involvement in Efforts to Affect Educational and Social Reforms in the Early Nineteenth Century
Hydrodynamic limit for a boundary driven stochastic lattice gas model with many conserved quantities
We prove the hydrodynamic limit for a particle system in which particles may
have different velocities. We assume that we have two infinite reservoirs of
particles at the boundary: this is the so-called boundary driven process. The
dynamics we considered consists of a weakly asymmetric simple exclusion process
with collision among particles having different velocities
Shocks in the asymmetric exclusion process with internal degree of freedom
We determine all families of Markovian three-states lattice gases with pair
interaction and a single local conservation law. One such family of models is
an asymmetric exclusion process where particles exist in two different
nonconserved states. We derive conditions on the transition rates between the
two states such that the shock has a particularly simple structure with minimal
intrinsic shock width and random walk dynamics. We calculate the drift velocity
and diffusion coefficient of the shock.Comment: 26 pages, 1 figur
On the Hydrodynamic Equilibrium of a Rod in a Lattice Fluid
We model the behavior of a big (Brazil) nut in a medium of smaller nuts with
a stochastic asymmetric simple exclusion dynamics of a polymer-monomer lattice
system. The polymer or `rod' can move up or down in an external negative field,
occupying N horizontal lattice sites where the monomers cannot enter. The
monomers (at most one per site) or `fluid particles' are moving symmetrically
in the horizontal plane and asymmetrically in the vertical direction, also with
a negative field. For a fixed position of the rod, this lattice fluid is in
equilibrium with a vertical height profile reversible for the monomers' motion.
Upon `shaking' (speeding up the monomers) the motion of the `rod' dynamically
decouples from that of the monomers resulting in a reversible random walk for
the rod around an average height proportional to log N.Comment: 19 pages, 2 figure
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
Large deviations in boundary-driven systems: Numerical evaluation and effective large-scale behavior
We study rare events in systems of diffusive fields driven out of equilibrium
by the boundaries. We present a numerical technique and use it to calculate the
probabilities of rare events in one and two dimensions. Using this technique,
we show that the probability density of a slowly varying configuration can be
captured with a small number of long wave-length modes. For a configuration
which varies rapidly in space this description can be complemented by a local
equilibrium assumption
Equilibrium fluctuations for the totally asymmetric zero-range process
We consider the one-dimensional Totally Asymmetric Zero-Range process evolving
on and starting from the Geometric product measure . On the hyperbolic time scale the
temporal evolution of the density fluctuation field is deterministic, in the sense that the limit
field at time is a translation of the initial one. We consider the system in a reference frame
moving at this velocity and we show that the limit density fluctuation field does not evolve in
time until , which implies the current across a characteristic to vanish on this longer time
scale.The author wants to express her gratitude to "Fundacao para a Ciencia e Tecnologia" for the grant /SFRH/BPD/39991/2007, to CMAT from University of Minho for support and to "Fundacao Calouste Gulbenkian" for the Prize: "Estimulo a investigacao" of the research project "Hydrodynamic limit of particle systems"
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