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Related papers: A direct solution to the phonon Boltzmann equation

200 papers

We study the asymptotics of solutions of the Boltzmann equation describing the kinetic limit of a lattice of classical interacting anharmonic oscillators. We prove that, if the initial condition is a small perturbation of an equilibrium…

Mathematical Physics · Physics 2009-11-13 Jean Bricmont , Antti Kupiainen

The Boltzmann transport equation (BTE) has proven indispensable in elucidating quasiballistic heat dynamics. Experimental observations of nondiffusive thermal transients, however, are interpreted almost exclusively through purely diffusive…

Mesoscale and Nanoscale Physics · Physics 2016-11-23 Bjorn Vermeersch

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…

Numerical Analysis · Mathematics 2025-10-13 Irene M Gamba , Qin Li , Anjali Nair

Current implementations of fluctuating lattice Boltzmann equations (FLBE) describe single component fluids. In this paper, a model based on the continuum kinetic Boltzmann equation for describing multicomponent fluids is extended to…

Statistical Mechanics · Physics 2016-11-16 D. Belardinelli , M. Sbragaglia , L. Biferale , M. Gross , F. Varnik

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…

Computational Physics · Physics 2020-10-06 Yangyu Guo , Moran Wang

For low density gases the validity of the Boltzmann transport equation is well established. The central object is the one-particle distribution function, $f$, which in the Boltzmann-Grad limit satisfies the Boltzmann equation. Grad and,…

Mathematical Physics · Physics 2009-11-11 Herbert Spohn

The impact of dispersion relations, anisotropy, and Brillouin zone structure on intrinsic phonon scattering rates has been assessed within the harmonic approximation-perturbation theory approach for lattice dynamics. Anisotropic nonlinear…

Materials Science · Physics 2022-06-15 Ahmed Hamed , Anter El-Azab

Solutions to the phonon Boltzmann transport equation under the relaxation-time approximation (RTA) are fundamentally limited in that they do not account for the off-diagonal elements of the scattering matrix, which encode intermode energy…

Computational Physics · Physics 2026-05-25 Y. Sungtaek Ju

The phonon thermal conductivity of semiconducting periodic solids can be obtained using the lattice dynamics calculations along with the Boltzmann transport equation and with input from density functional theory calculations. These…

Mesoscale and Nanoscale Physics · Physics 2025-05-30 Ankit Jain , Yagyank Srivastava , Amey G. Gokhale , Nidheesh Virakante , Hardik L. Kagdada

Thermal transport in the Si/SiO$_2$ multishell nanotubes is investigated theoretically. The phonon energy spectra are obtained using the atomistic Lattice Dynamics approach. Thermal conductivity is calculated using the Boltzmann transport…

Materials Science · Physics 2021-04-30 C. Isacova , A. Cocemasov , D. L. Nika , V. M. Fomin

A Full Band Monte Carlo simulator has been developed to consider phonon transmission across interfaces that are perpendicular to the heat flux. This solver of the Boltzmann transport equation which does not require any assumption on the…

Applied Physics · Physics 2022-05-06 N. D. Le , B. Davier , N. Izitounene , P. Dollfus , J. Saint-Martin

Phonon transport of recently-fabricated $\mathrm{Na_2He}$ at high pressure is investigated from a combination of first-principles calculations and the linearized phonon Boltzmann equation within the single-mode relaxation time approximation…

Materials Science · Physics 2017-05-24 San-Dong Guo , Ai-Xia Zhang

A univariate polynomial equation is presented. It provides models of the thermal lattice Boltzmann equation. The models can be accurate up to any required level and can be applied to regular lattices, which allow efficient and accurate…

Mathematical Physics · Physics 2020-11-10 Jae Wan Shim

The lattice thermal conductivity of crystalline Si nanowires is calculated. The calculation uses complete phonon dispersions, and does not require any externally imposed frequency cutoffs. No adjustment to nanowire thermal conductivity…

Materials Science · Physics 2007-05-23 N. Mingo

In the paper, we develop spectral theory to analyze the sharp asymptotic behavior of solutions to the Boltzmann equation around global Maxwellians in a three-dimensional infinite layer $\mathbb{R}^2\times (-1,1)$. The isothermal diffuse…

Analysis of PDEs · Mathematics 2025-11-26 Hongxu Chen , Renjun Duan , Shuangqian Liu

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…

Mesoscale and Nanoscale Physics · Physics 2010-05-17 Dhruv Singh , Jayathi Y. Murthy , Timothy S. Fisher

We describe a theoretical and computational approach to calculate the vibrational, elastic, and thermal properties of materials from the low-temperature quantum regime to the high-temperature anharmonic regime. This approach is based on…

Materials Science · Physics 2024-09-20 Dylan A. Folkner , Zekun Chen , Giuseppe Barbalinardo , Florian Knoop , Davide Donadio

The lattice thermal conductivity of graphene is evaluated using a microscopic model that takes into account the lattice's discrete nature and the phonon dispersion relation within the Brillouin zone. The Boltzmann transport equation is…

Soft Condensed Matter · Physics 2024-01-18 J. Chen , Y. Liu

We derive expressions for energy flow in terms of lattice normal mode coordinates and energy transmission involving reduced group velocities. With a version of Landauer formula appropriate for lattice dynamic approach, the phonon…

Statistical Mechanics · Physics 2007-05-23 Jian Wang , Jian-Sheng Wang

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…

Materials Science · Physics 2026-05-11 Laurenz Kremeyer , Bradley J. Siwick , Samuel Huberman