Related papers: Fluctuations and control in the Vlasov-Poisson equ…
Fluctuations of the excess heat in an out of equilibrium steady state are experimentally investigated in two stochastic systems : an electric circuit with an imposed mean current and a harmonic oscillator driven out of equilibrium by a…
The work fluctuations of an oscillator in contact with a thermostat and driven out of equilibrium by an external force are studied experimentally and theoretically within the context of Fluctuation Theorems (FTs). The oscillator dynamics is…
In this paper, we present a fluctuation analysis of a type of parabolic equations with large, highly oscillatory, random potentials around the homogenization limit. With a Feynman-Kac representation, the Kipnis-Varadhan's method, and a…
From the laws of macroscopic electrostatics of conductors (in particular the existence of screening) taken for granted, one can deduce universal properties for the thermal fluctuations in a classical Coulomb system at equilibrium. The…
This study investigates the interplay between a high-frequency external forcing and the intrinsic dynamics of a quantum nonlinear parametric oscillator. To analyze this system, classical equations of motion of the averages of quantum…
The effect of external fluctuations on the formation of spatial patterns is analysed by means of a stochastic Swift-Hohenberg model with multiplicative space-correlated noise. Numerical simulations in two dimensions show a shift of the…
The linearized problem of plasma oscillations in layer (particularly, in thin films) in external longitudinal alternating electric field is solved analytically. Specular - accommodative boundary conditions of electron reflection from the…
We present an analysis of the quantum fluctuations around the electroweak sphaleron and calculate the associated determinant which gives the 1--loop correction to the sphaleron transition rate. The calculation differs in various technical…
Starting from the kinetic equations for the fluctuations and correlations of a dilute gas of inelastic hard spheres or disks, a Boltzmann-Langevin equation for the one-particle distribution function of the homogeneous cooling state is…
We present Vlasov's equation and its association with Poisson's equation in the context of modelling self-gravitating systems such as Globular Clusters or Galaxies. We first review the classical hypotheses of the model. We continue with a…
Magnetoconductance fluctuations are used to study the effect of an applied bias on an electron billiard. At lower bias, nonlinear effects can be well described by electron heating alone, while at higher bias (V > 2mV, ~5% of the electron…
An interesting analog circuit for simulating a signal with fluctuations having a probability density function with a power tail has recently been proposed and constructed. The exponent of the power law can be fixed by tuning an appropriate…
In the study of complex networks (systems), the scaling phenomenon of flow fluctuations refers to a certain power-law between the mean flux (activity) $<F_i>$ of the $i$th node and its variance $\sigma_i$ as $\sigma_i \propto < F_{i} >…
We perform quantum calculations of fluctuations of the electromagnetic fields in $AA$ collisions at RHIC and LHC energies. The analysis is based on the fluctuation-dissipation theorem. We find that in the quantum picture the field…
We study the effects of thermal fluctuations on a small elastic ring. We derive analytical expressions for the correlation functions of the Euler angles, for the real space two--point correlation functions and for the probability…
We consider a one-dimensional symmetric simple exclusion process in contact with slowed reservoirs: at the left (resp. right) boundary, particles are either created or removed at rates given by $\alpha/n$ or $(1-\alpha)/n$ (resp. $\beta/n$…
We show that the general two-variable Langevin equations with inhomogeneous noise and friction can generate many different forms of power-law distributions. By solving the corresponding stationary Fokker-Planck equation, we can obtain a…
Stabilizing plasma dynamics through externally applied electric and magnetic fields is a fundamental control problem. We study this question for a plasma evolving under a uniform external magnetic field. Although the governing dynamics are…
We consider the Vlasov-Poisson system that is equipped with an external magnetic field to describe the time evolution of the distribution function of a plasma. An optimal control problem where the external magnetic field is the control…
This paper is devoted to the approximation of the linear Boltzmann equation by fractional diffusion equations. Most existing results address this question when there is no external acceleration field. The goal of this paper is to…