Thermal conductivity in harmonic lattices with random collisions

We review recent rigorous mathematical results about the macroscopic behaviour of harmonic chains with the dynamics perturbed by a random exchange of velocities between nearest neighbor particles. The random exchange models the effects of nonlinearities of anharmonic chains and the resulting dynamics have similar macroscopic behaviour. In particular there is a superdiffusion of energy for unpinned acoustic chains. The corresponding evolution of the temperature profile is governed by a fractional heat equation. In non-acoustic chains we have normal diffusivity, even if momentum is conserved.Comment: Review paper, to appear in the Springer Lecture Notes in Physics volume "Thermal transport in low dimensions: from statistical physics to nanoscale heat transfer" (S. Lepri ed.

Measuring device Patent

Expulsion and measuring device for determining quantity of liquid in tank under conditions of weightlessnes

From normal diffusion to superdiffusion of energy in the evanescent flip noise limit

Published online: 18 March 2015We consider a harmonic chain perturbed by an energy conserving noise depending on a parameter $\gamma$. When $\gamma$ is of order one, the energy diffuses according to the standard heat equation after a space-time diffusive scaling. On the other hand, when $\gamma=0$, the energy superdiffuses according to a $3/4$ fractional heat equation after a subdiffusive space-time scaling. In this paper, we study the existence of a crossover between these two regimes as a function of $\gamma$

Anomalous fluctuations for a perturbed Hamiltonian system with exponential interactions

A one-dimensional Hamiltonian system with exponential interactions perturbed by a conservative noise is considered. It is proved that energy superdiffuses and upper and lower bounds describing this anomalous diffusion are obtained.FCTEgid

A volume-averaged nodal projection method for the Reissner-Mindlin plate model

We introduce a novel meshfree Galerkin method for the solution of Reissner-Mindlin plate problems that is written in terms of the primitive variables only (i.e., rotations and transverse displacement) and is devoid of shear-locking. The proposed approach uses linear maximum-entropy approximations and is built variationally on a two-field potential energy functional wherein the shear strain, written in terms of the primitive variables, is computed via a volume-averaged nodal projection operator that is constructed from the Kirchhoff constraint of the three-field mixed weak form. The stability of the method is rendered by adding bubble-like enrichment to the rotation degrees of freedom. Some benchmark problems are presented to demonstrate the accuracy and performance of the proposed method for a wide range of plate thicknesses

Asymptotics of the solutions of the stochastic lattice wave equation

We consider the long time limit theorems for the solutions of a discrete wave equation with a weak stochastic forcing. The multiplicative noise conserves the energy and the momentum. We obtain a time-inhomogeneous Ornstein-Uhlenbeck equation for the limit wave function that holds both for square integrable and statistically homogeneous initial data. The limit is understood in the point-wise sense in the former case, and in the weak sense in the latter. On the other hand, the weak limit for square integrable initial data is deterministic

THERMAL CONDUCTIVITY FOR A NOISY DISORDERED HARMONIC CHAIN

We consider a $d$-dimensional disordered harmonic chain (DHC) perturbed by an energy conservative noise. We obtain uniform in the volume upper and lower bounds for the thermal conductivity defined through the Green-Kubo formula. These bounds indicate a positive finite conductivity. We prove also that the infinite volume homogenized Green-Kubo formula converges

Can translation invariant systems exhibit a Many-Body Localized phase?

This note is based on a talk by one of us, F. H., at the conference PSPDE II, Minho 2013. We review some of our recent works related to (the possibility of) Many-Body Localization in the absence of quenched disorder (in particular arXiv:1305.5127,arXiv:1308.6263,arXiv:1405.3279). In these works, we provide arguments why systems without quenched disorder can exhibit `asymptotic' localization, but not genuine localization.Comment: To appear in the Proceedings of the conference Particle systems and PDE's - II, held at the Center of Mathematics of the University of Minho in December 201