Related papers: The Landau equation as a Gradient Flow
A Landau fluid model for a collisionless electron-proton magnetized plasma, that accurately reproduces the dispersion relation and the Landau damping rate of all the magnetohydrodynamic waves, is presented. It is obtained by an accurate…
We establish the gradient flow representation of diffusion with mobility $b$ with respect to the modified Wasserstein quasi-metric $W_h$, where $h(r)=rb(r)$. The appropriate selection of the free energy functional depends on the specific…
In this paper, a statistical physical derivation of thermodynamically consistent fluid mechanical equations is presented for non-isothermal viscous molecular fluids. The coarse-graining process is based on (i) the adiabatic expansion of the…
We are interested in the inhomogeneous Landau equation which describes the evolution of a particle density f = f (t, x, v) representing at time t $\ge$ 0, the density of particles at position x $\in$ R 3 and velocity v $\in$ R 3. The study…
The Poisson-Nernst-Planck system of equations used to model ionic transport is interpreted as a gradient flow for the Wasserstein distance and a free energy in the space of probability measures with finite second moment. A variational…
We propose a general method to identify nonlinear Fokker--Planck--Kolmogorov equations (FPK equations) as gradient flows on the space of probability measures on $\mathbb{R}^d$ with a natural differential geometry. Our notion of gradient…
For an electron in the plane subjected to a perpendicular constant magnetic field and a homogeneous Gaussian random potential with a Gau{ss}ian covariance function we approximate the averaged density of states restricted to the lowest…
We use the distances introduced in a previous joint paper to exhibit the gradient flow structure of some drift-diffusion equations for a wide class of entropy functionals. Functional inequalities obtained by the comparison of the entropy…
We present numerical studies of the dynamics of vortices in the Ginzburg Landau model using equations derived from the gradient flow of the free energy. These equations have previously been proposed to describe the dynamics of n-vortices…
We develop a gradient-flow theory for time-dependent functionals defined in abstract metric spaces. Global well-posedness and asymptotic behavior of solutions are provided. Conditions on functionals and metric spaces allow to consider the…
The aim of this work is to analyze the entropy, entropy flux and entropy supply rate of granular fluids within the frameworks of the Boltzmann equation and continuum thermodynamics. It is shown that the entropy inequality for a granular gas…
We calculate the probability distribution function (PDF) of an overdamped Brownian particle moving in a periodic potential energy landscape $U(x)$. The PDF is found by solving the corresponding Smoluchowski diffusion equation. We derive the…
Most inverse problems from physical sciences are formulated as PDE-constrained optimization problems. This involves identifying unknown parameters in equations by optimizing the model to generate PDE solutions that closely match measured…
A linearised kinetic equation describing electrostatic perturbations of a Maxwellian equilibrium in a weakly collisional plasma forced by a random source is considered. The problem is treated as a kinetic analogue of the Langevin equation…
We consider a transport equation of the Boltzmann-Langevin type for non-Abelian plasmas close to equilibrium to derive the spectral functions of the underlying microscopic fluctuations from the entropy. The correlator of the stochastic…
The transport coefficients of a dilute classical gas in the presence of a drag force proportional to the velocity of the particle are determined from the Boltzmann equation. The viscous drag force could model the friction of solid particles…
The diffusion coefficient--a measure of dissipation, and the entropy--a measure of fluctuation are found to be intimately correlated in many physical systems. Unlike the fluctuation dissipation theorem in linear response theory, the…
In this thesis we investigate the instabilities of superfluids at finite superflow by means of a hydrodynamical approach. We find that at a finite value of the background superfluid velocity a hydrodynamic collective mode crosses to the…
We are concerned with a mixture of Boltzmann and McKean-Vlasov type equations, this means (in probabilistic terms) equations with coefficients depending on the law of the solution itself,and driven by a Poisson point measure with the…
The blooming diffusion probabilistic models (DPMs) have garnered significant interest due to their impressive performance and the elegant inspiration they draw from physics. While earlier DPMs relied upon the Markovian assumption, recent…