Hua, Chengyun and Minnich, Austin J. (2014) Analytical Green’s function of the multidimensional frequency-dependent phonon Boltzmann equation. Physical Review B, 90 (21). Art. No. 214306. ISSN 1098-0121. http://resolver.caltech.edu/CaltechAUTHORS:20150320-133005322
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Abstract
Thermal phonon transport at length scales comparable to mean free paths is governed by the Boltzmann equation, which is challenging to solve due to its high dimensionality. Here, we present an analytical Green's function for the frequency-dependent, multidimensional Boltzmann equation under the relaxation-time approximation. The new analytical solution is valid from diffusive to ballistic transport regimes and rigorously includes frequency dependence of phonon properties. We demonstrate that our result enables simple closed-form solutions for a number of multidimensional problems for which the only prior solution methods have been computationally expensive numerical simulations.
| Item Type: | Article | |||||||||
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| Additional Information: | © 2014 American Physical Society. Received 19 August 2014; revised manuscript received 20 November 2014; published 31 December 2014. This work was sponsored in part by Robert Bosch, LLC, through Bosch Energy Research Network Grant No. 13.01.CC11, by the National Science Foundation under Grant No. CBET CAREER 1254213, and by Boeing under the Boeing-Caltech Strategic Research and Development Relationship Agreement. | |||||||||
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| Classification Code: | PACS: 65.40.−b | |||||||||
| Record Number: | CaltechAUTHORS:20150320-133005322 | |||||||||
| Persistent URL: | http://resolver.caltech.edu/CaltechAUTHORS:20150320-133005322 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 55948 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 20 Mar 2015 23:01 | |||||||||
| Last Modified: | 20 Mar 2015 23:01 |
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