Related papers: Averaging lemmas and hypoellipticity
An Enskog-Landau kinetic equation for a many-component system of charged hard spheres is proposed. It has been obtained from the Liouville equation with modified boundary conditions by the method of nonequilibrium statistical operator. On…
We consider linear and nonlinear transport equations with irregular velocity fields, motivated by models coming from mean field games. The velocity fields are assumed to increase in each coordinate, and the divergence therefore fails to be…
Kinetic equations are analyzed for thermal degradation of polymers. The governing relations are based on the fragmentation-annihilation concept. Explicit solutions to these equations are derived in two particular cases of interest. For…
We present a machine learning based approach to address the study of transport processes, ubiquitous in continuous mechanics, with particular attention to those phenomena ruled by complex micro-physics, impractical to theoretical…
We shall deal with the periodic problem for nonlinear perturbations of abstract hyperbolic evolution equations generating an evolution system of contractions. We prove an averaging principle for the translation along trajectories operator…
We study symplectic deformations of Gabor frames using the covariance properties of the Heisenberg operators. This allows us to recover in a very simple way known results. We thereafter propose a general deformation scheme by Hamiltonian…
We show that the ideal (nondissipative) form of the dynamical equations for the Lipps-Hemler formulation of the anelastic fluid model follow as Euler-Poincar\'{e} equations, obtained from a constrained Hamilton's principle expressed in the…
We derive the equilibrium and transport properties of metals using renormalization group equations and finite-size scaling. Particular attention is given to the well-known cases of Fermi and Luttinger liquids. An important subtlety is that…
We review various numerical approaches to compute transport coefficients in molecular dynamics. These approaches can be broadly classified into three groups: (i) nonequilibrium methods based on applying an external driving field to the…
A novel approach is developed for analytic orbit propagation based on asymptotic expansion with respect to a small perturbative acceleration. The method improves upon existing first order asymptotic expansions by leveraging on linear…
We use the relative trace formula to obtain exact formulas for central values of certain twisted quadratic base change L-functions averaged over Hilbert modular forms of a fixed weight and level. We apply these formulas to the subconvexity…
We study time averages for the norm of solutions to kinetic Fokker--Planck equations associated with general Hamiltonians. We provide fully explicit and constructive decay estimates for systems subject to a confining potential, allowing…
We study general linear transport-reaction systems on an arbitrary dimensional hypercube with periodic boundary conditions. Transport-reaction systems are often used to model the finite speed movement and interaction of particles, bacteria…
We present a generalization of AEMD approach, routinely applied to estimate thermal conductivity, to the more general case in which Soret and Dufour effects determine a coupled heat-mass transfer. We show that, by starting from…
Intrinsically stable magnetic levitation between superconductors and permanent magnets can be exploited in a variety of applications of great technical interest in the field of transportation (rail transportation), energy (flywheels) and…
Here, we study quantitative homogenization of first-order convex Hamilton-Jacobi equations with $(u/\varepsilon)$-periodic Hamiltonians which typically appear in dislocation dynamics. Firstly, we establish the optimal convergence rate by…
The distribution of finite time observable averages and transport in low dimensional Hamiltonian systems is studied. Finite time observable average distributions are computed, from which an exponent $\alpha$ characteristic of how the…
We compute the transport properties of one dimensional interacting electrons, also known as a Luttinger liquid. We show that a renormalization group study allows to obtain the temperature dependence of the conductivity in an intermediate…
We study the averaging method for flows perturbed by a dynamical system preserving an infinite measure. Motivated by the case of perturbation by the collision dynamic on the finite horizon $\mathbb Z$-periodic Lorentz gas and in view of…
The continuum equations of fluid mechanics are rederived with the intention of keeping certain mechanical and thermodynamic concepts separate. A new "mechanical" mass density is created to be used in computing inertial quantities, whereas…