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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…

Mesoscale and Nanoscale Physics · Physics 2015-06-23 Jesse Maassen , Mark Lundstrom

The phonon Boltzmann transport equation (BTE) is a powerful tool for studying non-diffusive thermal transport. Here, we develop a new universal variational approach to solving the BTE that enables extraction of phonon mean free path (MFP)…

Mesoscale and Nanoscale Physics · Physics 2016-04-13 Vazrik Chiloyan , Lingping Zeng , Samuel Huberman , Alexei A. Maznev , Keith A. Nelson , Gang Chen

The phonon Boltzmann transport equation (BTE) is widely utilized to study non-diffusive thermal transport. We find a solution of the BTE in the thin film transient thermal grating (TTG) experimental geometry by using a recently developed…

Mesoscale and Nanoscale Physics · Physics 2016-07-15 Vazrik Chiloyan , Lingping Zeng , Samuel Huberman , Alexei A. Maznev , Keith A. Nelson , Gang Chen

Understanding ballistic phonon transport effects in transient thermoreflectance experiments and explaining the observed deviations from classical theory remains a challenge. Diffusion equations are simple and computationally efficient but…

Mesoscale and Nanoscale Physics · Physics 2016-03-23 Jesse Maassen , Mark Lundstrom

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

In this paper, a fast synthetic iterative scheme is developed to accelerate convergence for the implicit DOM based on the stationary phonon BTE. The key innovative point of the present scheme is the introduction of the macroscopic synthetic…

Computational Physics · Physics 2018-12-18 Chuang Zhang , Songze Chen , Zhaoli Guo , Lei Wu

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…

Mesoscale and Nanoscale Physics · Physics 2017-10-05 Vazrik Chiloyan , Samuel Huberman , Alexei A. Maznev , Keith A. Nelson , Gang Chen

Mesoscopic numerical simulation has become an important tool in thermal management and energy harvesting at the micro/nano scale, where the Fourier's law failed. However, it is not easy to efficiently solve the phonon Boltzmann transport…

Computational Physics · Physics 2022-12-13 Chuang Zhang , Samuel Huberman , Xinliang Song , Jin Zhao , Songze Chen , Lei Wu

In this paper analysis is performed on a computational method for thermal radiative transfer (TRT) problems based on the multilevel quasidiffusion (variable Eddington factor) method with the method of long characteristics (ray tracing) for…

Numerical Analysis · Mathematics 2026-03-18 Joseph M. Coale , Dmitriy Y. Anistratov

The theory of heat transfer by electromagnetic radiation is based on the radiative transfer equation (RTE) for the radiation intensity, or equivalently on the Boltzmann transport equation (BTE) for the photon distribution. We focus in this…

Statistical Mechanics · Physics 2010-09-17 Thomas Christen , Frank Kassubek , Rudolf Gati

Predicting nanoscale thermal transport in dielectrics requires models, such as the Boltzmann transport equation (BTE), that account for phonon boundary scattering in structures with complex geometries. Although the BTE has been validated…

Materials Science · Physics 2023-08-03 S. Aria Hosseini , Alex Greaney , Giuseppe Romano

Boltzmann transport theory, the standard framework for predicting thermal conductivity, assumes that every vibrational mode eventually scatters, acquiring a finite lifetime that yields a convergent, length-independent thermal conductivity:…

Mesoscale and Nanoscale Physics · Physics 2026-05-22 P. M. Martinez , O. Mateos-Lopez , J. C. Cuevas , J. G. Vilhena

Hydrodynamic second sound can be generated by heat pulses when the phonon-phonon interaction is dominantly momentum conserving, and the propagation of the temperature field becomes wavelike rather than diffusive. While the Boltzmann…

Materials Science · Physics 2025-01-08 Xin Qian , Chuang Zhang , Te-Huan Liu , Ronggui Yang

Suitably superimposed grey-medium solutions of the Boltzmann transport equation (BTE) provide a simple yet accurate description of non-grey quasiballistic heat conduction in transient thermal grating experiments. Recent applications of…

Mesoscale and Nanoscale Physics · Physics 2016-08-22 Bjorn Vermeersch , Ali Shakouri

In crystals, macroscopic technological properties such as thermal conductivity originate from the microscopic drift and scattering of phonons, commonly described by the Boltzmann Transport Equation (BTE). Despite its widespread use, the…

Materials Science · Physics 2026-03-18 Enrico Di Lucente , Nicola Marzari , Michele Simoncelli

In this article, we address lattice heat transport in single-walled carbon nanotubes (CNTs) by a quantum mechanical calculation of three-phonon scattering rates in the framework of the Boltzmann transport equation (BTE) and classical…

Mesoscale and Nanoscale Physics · Physics 2020-05-06 Daniel Bruns , Alireza Nojeh , A. Srikantha Phani , Jörg Rottler

We report computational uncertainties in Boltzmann Transport Equation (BTE)-based lattice thermal conductivity prediction of 50 diverse semiconductors from the use of different BTE solvers (ShengBTE, Phono3Py, and in-house code) and…

Materials Science · Physics 2025-09-19 Yagyank Srivastava , Amey G. Gokhale , Ankit Jain

Cross-plane heat transport in thin films with thickness comparable to the phonon mean free paths is of both fundamental and practical interest. However, physical insight is difficult to obtain for the cross-plane geometry due to the…

Mesoscale and Nanoscale Physics · Physics 2014-10-13 Chengyun Hua , Austin J. Minnich

We present a formula for thermal transport in the bulk of Bose systems based on the quantum Boltzmann equation (QBE). First, starting from the quantum kinetic equation and using the Born approximation for impurity scattering, we derive the…

Mesoscale and Nanoscale Physics · Physics 2021-08-09 Kouki Nakata , Yuichi Ohnuma

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
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