Green's functions of the Boltzmann transport equation with the full scattering matrix for phonon nanoscale transport beyond the relaxation-time approximation

Quantitative validation of the Boltzmann transport equation phonon thermal conductivity model under the single-mode relaxation time approximation

The phonon thermal conductivity of the Lennard-Jones argon face-centered cubic crystal is predicted between temperatures of 20 K and 80 K using the Boltzmann transport equation under the single-mode relaxation time approximation. The temperature and frequency dependencies of the phonon dispersion and phonon relaxation times are obtained from lattice-dynamics calculations based on the results of...

Variance-reduced particle simulation of the Boltzmann transport equation in the relaxation-time approximation.

We present an efficient variance-reduced particle simulation technique for solving the linearized Boltzmann transport equation in the relaxation-time approximation used for phonon, electron, and radiative transport, as well as for kinetic gas flows. The variance reduction is achieved by simulating only the deviation from equilibrium. We show that in the limit of small deviation from equilibrium...

determinant of the hankel matrix with binomial entries

abstract in this thesis at first we comput the determinant of hankel matrix with enteries a_k (x)=?_(m=0)^k??((2k+2-m)¦(k-m)) x^m ? by using a new operator, ? and by writing and solving differential equation of order two at points x=2 and x=-2 . also we show that this determinant under k-binomial transformation is invariant.

Reconstruction of the phonon relaxation times using solutions of the Boltzmann transport equation

We present a method for reconstructing the phonon relaxation time distribution τω = τ (ω) (including polarization) in a material from thermal spectroscopy data. The distinguishing feature of this approach is that it does not make use of the effective thermal conductivity concept and associated approximations. The reconstruction is posed as an optimization problem in which the relaxation times τ...

Thermal transport at the nanoscale: A Fourier's law vs. phonon Boltzmann equation study