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498
We introduce and discuss a one-dimensional kinetic model of the Boltzmann equation with dissipative collisions and variable coefficient of restitution. Then, the behavior of the Boltzmann equation in the quasi elastic limit is investigated for a wide range of the rate function. By this limit procedure we obtain a class of nonlinear equations classified as nonlinear friction equations. The analysis of the cooling process shows that the nonlinearity on the relative velocity is of paramount importance...
We present an interacting particle system methodology for the numerical solving of the Lyapunov exponent of Feynman–Kac semigroups and for estimating the principal eigenvalue of Schrödinger generators. The continuous or discrete time models studied in this work consists of interacting particles evolving in an environment with soft obstacles related to a potential function . These models are related to genetic algorithms and Moran type particle schemes. Their choice is not unique. We will examine...
We present an interacting particle system
methodology for the numerical solving of the Lyapunov exponent
of Feynman–Kac semigroups and for estimating the principal
eigenvalue of Schrödinger generators. The continuous or discrete time
models studied in this work
consists of N interacting particles evolving in an environment
with soft obstacles related to a potential function V. These
models are related to genetic algorithms and Moran type particle
schemes. Their choice
is not unique. We...
Recent technological advances including brain imaging (higher resolution in space and
time), miniaturization of integrated circuits (nanotechnologies), and acceleration of
computation speed (Moore’s Law), combined with interpenetration between neuroscience,
mathematics, and physics have led to the development of more biologically plausible
computational models and novel therapeutic strategies. Today, mathematical models of
irreversible medical conditions...
We consider the hexagonal circle packing with radius and perturb it by letting the circles move as independent Brownian motions for time . It is shown that, for large enough , if is the point process given by the center of the circles at time , then, as , the critical radius for circles centered at to contain an infinite component converges to that of continuum percolation (which was shown – based on a Monte Carlo estimate – by Balister, Bollobás and Walters to be strictly bigger than...
Using probabilistic tools, this work states a pointwise convergence of function solutions of the 2-dimensional Boltzmann equation to the function solution of the Landau equation for Maxwellian molecules when the collisions become grazing. To this aim, we use the results of Fournier (2000) on the Malliavin calculus for the Boltzmann equation. Moreover, using the particle system introduced by Guérin and Méléard (2003), some simulations of the solution of the Landau equation will be given. This result...
Using probabilistic tools, this work states a pointwise convergence of
function solutions of the 2-dimensional Boltzmann equation to the function
solution of the Landau equation for Maxwellian molecules when the collisions become grazing. To this aim, we use the results of
Fournier (2000) on the Malliavin calculus for the Boltzmann
equation. Moreover, using the particle system introduced by Guérin and
Méléard (2003), some simulations of the solution of the Landau equation will be given. This result...
We consider the parabolic Anderson model, the Cauchy problem for the heat equation with random potential in ℤd. We use i.i.d. potentials ξ:ℤd→ℝ in the third universality class, namely the class of almost bounded potentials, in the classification of van der Hofstad, König and Mörters [Commun. Math. Phys.267 (2006) 307–353]. This class consists of potentials whose logarithmic moment generating function is regularly varying with parameter γ=1, but do not belong to the class of so-called double-exponentially...
We establish circumstances under which the dispersion of passive contaminants in a forced flow can be consistently interpreted as a Markovian diffusion process.
We consider a bounded step size random walk in an ergodic random environment with some ellipticity, on an integer lattice of arbitrary dimension. We prove a level 3 large deviation principle, under almost every environment, with rate function related to a relative entropy.
We consider a stochastic system of particles, usually called vortices in that setting, approximating the 2D Navier-Stokes equation written in vorticity. Assuming that the initial distribution of the position and circulation of the vortices has finite (partial) entropy and a finite moment of positive order, we show that the empirical measure of the particle system converges in law to the unique (under suitable a priori estimates) solution of the 2D Navier-Stokes equation. We actually prove a slightly...
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498