Variational approach to extracting the phonon mean free path distribution from the spectral Boltzmann transport equation
Open accessAbstract
The phonon Boltzmann transport equation (BTE) is a powerful tool for studying nondiffusive thermal transport. Here, we develop a new universal variational approach to solving the BTE that enables extraction of phonon mean free path (MFP) distributions from experiments exploring nondiffusive transport. By utilizing the known Fourier heat conduction solution as a trial function, we present a direct approach to calculating the effective thermal conductivity from the BTE. We demonstrate this technique on the transient thermal grating experiment, which is a useful tool for studying nondiffusive thermal transport and probing the MFP distribution of materials. We obtain a closed form expression for a suppression function that is materials dependent, successfully addressing the nonuniversality of the suppression function used in the past, while providing a general approach to studying thermal properties in the nondiffusive regime.
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Reconstructing the phonon MFP spectrum from the measured KA(Lc) and the derived suppression function is an inverse problem that involves complex optimization.
“Reconstructing the phonon MFP spectrum [ i.e . ߶ ሺΛሻ or ߙ ሺΛሻ ] from the measured ܭ ሺ ܮ ሻ and the derived ܵ ቀ ஃ ቁ is thus an inverse problem of Eq.(4.14) that involves complex optimization. 203-205”
From Tutorial: Time-domain thermoreflectance (TDTR) for thermal property characterization of bulk and thin film materials (2018) · cites this paper as [205]
The discussion on p. 2 says a phonon MFP distribution can be obtained from experimentally measured thermal conductivity using a suppression function. The optimization described on p. 7 concerns a trial function for solving the BTE, not optimization of the inverse MFP reconstruction. The paper therefore supports the reconstruction premise but not the claim that this inverse problem involves complex optimization. (LLM, conf=0.86)
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- Authors
- Chiloyan, V., Zeng, L., Huberman, S., Maznev, A. A., Nelson, K. A., & Chen, G.
- Affiliations
- Massachusetts Institute of Technology (US)
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2016-04-06
- Volume
- 93
- Issue
- 15
- ISSN
- 2469-9950 (ISSN-L)
- 2469-9969
- OpenAlex
- W2183171309
- Cited by
- 26
- References
- 37
- Citations by year
- 2025: 2 · 2024: 1 · 2023: 1 · 2022: 1 · 2020: 1 · 2019: 3 · 2018: 2 · 2017: 8 · 2016: 7
- FWCI
- 2.97
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Physical review. B./Physical review. B (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- DSpace@MIT (Massachusetts Institute of Technology) (submittedVersion, cc-by-nc)
- arXiv (Cornell University)
- Physical Review Letters
- Funders
- U.S. Department of Energy (DE-SC0001299/DE-FG02-09ER46577)
- Office of Science
- Basic Energy Sciences
- Topics
- Physical Sciences › Materials Science › Materials Chemistry › Thermal properties of materials
- Physical Sciences › Engineering › Mechanics of Materials › Thermoelastic and Magnetoelastic Phenomena
- Physical Sciences › Mathematics › Applied Mathematics › Gas Dynamics and Kinetic Theory
- Keywords
- variational methods, transient thermal grating, effective thermal conductivity, Fourier heat conduction, phonon transport
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