Related papers: Diffusion limit for a kinetic equation with a ther…
A linear Boltzmann equation is interpreted as the forward equation for the probability density of a Markov process (K(t), i(t), Y(t)), where (K(t), i(t)) is an autonomous reversible jump process, with waiting times between two jumps with…
We consider the D1Q3 lattice Boltzmann scheme with an acoustic scale for the simulation of diffusive processes. When the mesh is refined while holding the diffusivity constant, we first obtain asymptotic convergence. When the mesh size…
Thermal boundary resistance is a critical quantity that controls heat transfer at the nanoscale, which is primarily related to interfacial phonon scattering. Here, we combine lattice dynamics calculations and inputs from first principles ab…
Developing simplified, but accurate, theoretical approaches to treat heat transport on all length and time scales is needed to further enable scientific insight and technology innovation. Using a simplified form of the Boltzmann transport…
We investigate the fractional diffusion approximation of a kinetic equation in the upper-half plane with diffusive reflection conditions at the boundary. In an appropriate singular limit corresponding to small Knudsen number and long time…
We report finite-volume simulations of the phonon Boltzmann transport equation (BTE) for heat conduction across the heterogeneous interfaces in SiGe superlattices. The diffuse mismatch model incorporating phonon dispersion and polarization…
A new method is introduced for calculation of interfacial thermal resistance in the case of heat transport through the interface by phonons. A unique feature of the method is taking into account all the consequences of a non-equilibrium…
We derive the continuum equations and boundary conditions governing phonon-mediated heat transfer in the limit of small but finite mean free path from asymptotic solution of the linearized Boltzmann equation in the relaxation time…
In this paper, we study the diffusive limit of the steady state radiative heat transfer system for non-homogeneous Dirichlet boundary conditions in a bounded domain with flat boundaries. A composite approximate solution is constructed using…
We investigate the fractional diffusion limit of a Linear Boltzmann equation with heavy-tailed velocity equilibrium in a half-space with Maxwell boundary conditions. We derive a new confined version of the fractional Laplacian and show…
We study nondiffusive thermal transport by phonons at small distances within the framework of the Boltzmann transport equation (BTE) and demonstrate that the transport is significantly affected by the distribution of phonons emitted by the…
Deviations from diffusive heat transport in high thermal conductivity crystalline insulators are generally understood within the framework of the phonon Boltzmann Transport Equation. However, for low thermal conductivity materials with…
Controlling heat flow at the nanoscales is pivotal to several applications, including thermal energy harvesting and heat management. However, engineering nanostructures is challenging because phonon-boundary interaction, not contemplated by…
This paper is devoted to diffusion limits of linear Boltzmann equations. When the equilibrium distribution function is Maxwellian distribution, it is well known that for an appropriate time scale, the small mean free path limit gives rise…
We present high-resolution thermal diffusivity measurements on several near optimally doped electron- and hole-doped cuprate systems in a temperature range that passes through the Mott-Ioffe-Regel limit, above which the quasiparticle…
A nonlinear Poisson--Boltzmann equation with transmission boundary conditions at the interface between two materials is investigated. The model describes the electrostatic potential generated by a vector of ion concentrations in a periodic…
Recent THz spectroscopy of the quantum paraelectric SrTiO$_3$ (arXiv:2501.15771) and a high-$T_c$ cuprate (arXiv:2503.15646) has renewed interest in energy relaxation in correlated electron systems. We consider a situation in which…
As nanostructured devices become prevalent, interfaces often play an important role in thermal transport phenomena. However, interfacial thermal transport remains poorly understood due to complex physics across a wide range of length scales…
Multi-species Boltzmann equations for gaseous mixtures, with analytic cross sections and under Grad's angular cutoff assumption, are considered under diffusive scaling. In the limit, we formally obtain an explicit expression for the binary…
We consider an infinite chain of coupled harmonic oscillators with a Poisson thermostat at the origin. In the high frequency limit, we establish the reflection-transmission-scattering coefficients for the wave energy scattered off the…