Related papers: Fokker-Planck description and diffusive phonon hea…
In this paper, we present a Hamiltonian and thermodynamic theory of heat transport on various levels of description. Transport of heat is formulated within kinetic theory of polarized phonons, kinetic theory of unpolarized phonons,…
The fractional Fokker-Planck equation, which contains a variable diffusion coefficient, is discussed and solved. It corresponds to the L\'evy flights in a nonhomogeneous medium. For the case with the linear drift, the solution is stationary…
A complex approach phonon quantum discrete model (PQDM) was developed to describe dynamics, kinetics and statistics of phonons in carbon nanostructures with zero-chirality of both zig-zag and armchair geometry. The model allows include into…
We study the time behavior of the Fokker-Planck equation in Zwanzig rule (the backward-Ito rule) based on the Langevin equation of Brownian motion with an anomalous diffusion in a complex medium. The diffusion coefficient is a function in…
The Boltzmann transport equation for phonons is recast directly in terms of the heat-flux by means of iteration followed by truncation at the second order in the spherical harmonic expansion of the distribution function. This procedure…
The Fokker-Planck equation with diffusion coefficient quadratic in space variable, linear drift coefficient, and nonlocal nonlinearity term is considered in the framework of a model of analysis of asset returns at financial markets. For…
In this work, a lattice Boltzmann scheme is developed for numerical solution of the phonon Boltzmann equation under Callaway's dual relaxation model in the hydrodynamic limit. Through a Chapman-Enskog expansion to the lattice Boltzmann…
We define the Dyson diffusion process on a curved smooth closed contour in the plane and derive the Fokker-Planck equation for probability density. Its stationary solution is shown to be the Boltzmann weight for the logarithmic gas confined…
Measurements of thermal diffusivity in several insulators have been shown to reach a Planckian bound on thermal transport that can be thought of as the limit of validity of semiclassical phonon scattering. Beyond this regime, the heat…
The~numerical solutions to a non-linear Fractional Fokker--Planck (FFP) equation are studied estimating the generalized diffusion coefficients. The~aim is to model anomalous diffusion using an FFP description with fractional velocity…
Steady-state thermal transport in nanostructures with dimensions comparable to the phonon mean-free-path is examined. Both the case of contacts at different temperatures with no internal heat generation and contacts at the same temperature…
We present a new method for predicting effective thermal conductivity ($\kappa_{\textrm{eff}}$) in materials, informed by ${ab\,initio}$ material property simulations. Using the Boltzmann transport equation in a Self-Adjoint Angular Flux…
The ab initio model for heat propagation is the phonon transport equation, a Boltzmann-like kinetic equation. When two materials are put side by side, the heat that propagates from one material to the other experiences thermal boundary…
As a fundamental physical quantity of thermal phonons, temporal coherence participates in a broad range of thermal and phononic processes, while a clear methodology for the measurement of phonon coherence is still lacking. In this Lettter,…
Starting from the recently proposed energy-based deviational formulation for solving the Boltzmann equation [J.-P. Peraud and N. G. Hadjiconstantinou, Phys. Rev. B 84, 2011], which provides significant computational speedup compared to…
We study the heat transport due to phonons in nanomechanical structures using a phase space representation of non-equilibrium Green's functions. This representation accounts for the atomic degrees of freedom making it particularly suited…
Understanding and quantifying the fundamental physical property of coherence of thermal excitations is a long-standing and general problem in physics. The conventional theory, i.e. the phonon gas model, fails to describe coherence and its…
The Fokker--Planck Equation can be used in a partially-coherent imaging context to model the evolution of the intensity of a paraxial x-ray wave field with propagation. This forms a natural generalisation of the transport-of-intensity…
Phonon heat conduction over length scales comparable to their mean free paths is a topic of considerable interest for basic science and thermal management technologies. Although the failure of Fourier's law beyond the diffusive regime is…
Nanostructured materials exhibit low thermal conductivity because of the additional scattering due to phonon-boundary interactions. As these interactions are highly sensitive to the mean free path (MFP) of a given phonon mode, MFP…