1,072 research outputs found
Second order Boltzmann-Gibbs principle for polynomial functions and applications
In this paper we give a new proof of the second order Boltzmann-Gibbs
principle. The proof does not impose the knowledge on the spectral gap
inequality for the underlying model and it relies on a proper decomposition of
the antisymmetric part of the current of the system in terms of polynomial
functions. In addition, we fully derive the convergence of the equilibrium
fluctuations towards 1) a trivial process in case of supper-diffusive systems,
2) an Ornstein-Uhlenbeck process or the unique energy solution of the
stochastic Burgers equation, in case of weakly asymmetric diffusive systems.
Examples and applications are presented for weakly and partial asymmetric
exclusion processes, weakly asymmetric speed change exclusion processes and
hamiltonian systems with exponential interactions
Crossover to the stochastic Burgers equation for the WASEP with a slow bond
We consider the weakly asymmetric simple exclusion process in the presence of
a slow bond and starting from the invariant state, namely the Bernoulli product
measure of parameter . The rate of passage of particles to the
right (resp. left) is
(resp.
) except at
the bond of vertices where the rate to the right (resp. left) is
given by (resp.
). Above,
, , . For , we show that
the limit density fluctuation field is an Ornstein-Uhlenbeck process defined on
the Schwartz space if , while for it is an
energy solution of the stochastic Burgers equation. For , it
is an Ornstein-Uhlenbeck process associated to the heat equation with Robin's
boundary conditions. For , the limit density fluctuation
field is an Ornstein-Uhlenbeck process associated to the heat equation with
Neumann's boundary conditions
Interpolation process between standard diffusion and fractional diffusion
We consider a Hamiltonian lattice field model with two conserved quantities,
energy and volume, perturbed by stochastic noise preserving the two previous
quantities. It is known that this model displays anomalous diffusion of energy
of fractional type due to the conservation of the volume [5, 3]. We superpose
to this system a second stochastic noise conserving energy but not volume. If
the intensity of this noise is of order one, normal diffusion of energy is
restored while it is without effect if intensity is sufficiently small. In this
paper we investigate the nature of the energy fluctuations for a critical value
of the intensity. We show that the latter are described by an
Ornstein-Uhlenbeck process driven by a L\'evy process which interpolates
between Brownian motion and the maximally asymmetric 3/2-stable L\'evy process.
This result extends and solves a problem left open in [4].Comment: to appear in AIHP
Nonlinear Perturbation of a Noisy Hamiltonian Lattice Field Model: Universality Persistence
In [2] it has been proved that a linear Hamiltonian lattice field perturbed
by a conservative stochastic noise belongs to the 3/2-L\'evy/Diffusive
universality class in the nonlinear fluctuating theory terminology [15], i.e.
energy superdiffuses like an asymmetric stable 3/2-L\'evy process and volume
like a Brownian motion. According to this theory this should remain valid at
zero tension if the harmonic potential is replaced by an even potential. In
this work we consider a quartic anharmonicity and show that the result obtained
in the harmonic case persists up to some small critical value of the
anharmonicity
Farming exposure and asthma phenotypes:In mice and men
Although several studies have shown that farmers and people with agricultural-related occupations have a higher risk of developing lung diseases such as nonallergic asthma, chronic bronchitis and chronic obstructive pulmonary disease (COPD), it has also been shown that exposure to the farm environment is associated with a protective effect on the development of atopy and allergic asthma.In this thesis, both effects of farm exposures on the immune system were studied: the protective effect against allergic asthma and the induction of non-allergic asthma. These studies were conducted among agricultural workers, and in mouse models of allergic and nonallergic lung disease. In addition, the presence of several macrophage phenotypes in animal models of allergic and non-allergic asthma was investigated, as well as the effects of exposure to farm dust extract on a macrophage cell line.This thesis demonstrated that occupational exposure to a farm environment and exposure to farm dust extracts in mice lead to a shift in the immune system towards non-allergic inflammation. This shift offers on the one hand protection against development of allergic diseases, such as allergic asthma, but is also associated with the risk of nonallergic asthma development. In addition, this thesis shows that, within the various phenotypes asthma, various inflammatory mediators and cells are important in the development and severity of airway hyperresponsiveness
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