相关论文: Diffusion limit for a kinetic equation with a ther…
We compute the contribution of phonons to the thermal conductivity in the core of superfluid neutron stars. We use effective field theory techniques to extract the phonon scattering rates, written as a function of the equation of state of…
We develop a computational framework, based on the Boltzmann transport equation, with the ability to compute the thermal transport in nanostructured materials of any geometry using as the only input the bulk thermal conductivity…
The Boltzmann equation is a fundamental equation in kinetic theory that describes the motion of rarefied gases. In this study, we examine the Boltzmann equation within a $C^1$ bounded domain, subject to a large external potential $\Phi(x)$…
We consider the spatially homogeneous Boltzmann equation for inelastic hard spheres (with constant restitution coefficient $\alpha \in (0,1)$) under the thermalization induced by a host medium with a fixed Maxwellian distribution. We prove…
High temperature thermal transport in insulators has been conjectured to be subject to a Planckian bound on the transport lifetime $\tau \gtrsim \tau_\text{Pl} \equiv \hbar/(k_B T)$, despite phonon dynamics being entirely classical at these…
The breakdown of translational symmetry at heterointerfaces leads to the emergence of new phonon modes localized near the interface. These interface phonons play an essential role in thermal/electrical transport properties in devices…
The heat current across a quantum harmonic system connected to reservoirs at different temperatures is given by the Landauer formula, in terms of an integral over phonon frequencies \omega, of the energy transmittance T(\omega). There are…
We resolve a long standing question regarding the suitable effective diffusion coefficient of the spherically-symmetric transport equation, which is valid at long times. To that end, we generalize a transport solution in three dimensions…
This paper is devoted to the derivation of a macroscopic fractional diffusion equation describing heat transport in an anharmonic chain. More precisely, we study here the so-called FPU-$\beta$ chain, which is a very simple model for a…
Numerical prediction of multiscale heat transfer is a challenging problem due to the wide range of time and length scales involved. In this work a discrete unified gas kinetic scheme (DUGKS) is developed for heat transfer in materials with…
The grand canonical ensemble formulation of the van der Waals equation of state that includes the effects of Bose statistics is applied to an equilibrium system of interacting pions. If the attractive interaction between pions is large…
Bulk matter produced in heavy ion collisions has multiple conserved quantum numbers like baryon number, strangeness and electric charge. The diffusion process of these charges can be described by a diffusion matrix describing the…
We study the one-dimensional diffusion process which takes place between two reflecting boundaries and which is acted upon by a time-dependent and spatially-constant force. The assumed force possesses both the harmonically oscillating and…
Heat transport in nanoscale systems is both hard to measure microscopically, and hard to interpret. Ballistic and diffusive heat flow coexist, adding confusion. This paper looks at a very simple case: a nanoscale crystal repeated…
We consider a stochastically perturbed reaction diffusion equation in a bounded interval, with boundary conditions imposing the two stable phases at the endpoints. We investigate the asymptotic behavior of the front separating the two…
Nanostructured semiconducting materials are promising candidates for thermoelectrics due to their potential to suppress phonon transport while preserving electrical properties. Modeling phonon-boundary scattering in complex geometries is…
We consider a class of reaction-diffusion equations with a stochastic perturbation on the boundary. We show that in the limit of fast diffusion, one can rigorously approximate solutions of the system of PDEs with stochastic Neumann boundary…
We derive the hydrodynamic limit of a kinetic equation with a stochastic, short range perturbation of the velocity operator. Under some mixing hypotheses on the stochastic perturbation, we establish a diffusion-approximation result: the…
We consider the Poisson-Boltzmann equation in a periodic cell, representative of a porous medium. It is a model for the electrostatic distribution of $N$ chemical species diluted in a liquid at rest, occupying the pore space with charged…
The hydrodynamic limit for the Boltzmann equation is studied in the case when the limit system, that is, the system of Euler equations contains contact discontinuities. When suitable initial data is chosen to avoid the initial layer, we…