Modeling quasi-ballistic transient thermal transport with spatially sinusoidal heating: A McKelvey-Shockley flux approach
Bibliographic record
Abstract
Ballistic phonon effects, arising on length scales comparable to the mean-free-path, result in non-diffusive heat flow and alter the thermal properties of materials. Simple theoretical models that accurately capture non-diffusive transport physics are valuable for experimental analysis, technology design, and providing physical insight. In this work, we utilize and extend the McKelvey-Shockley (McK-S) flux method, a simple and accurate framework, to investigate ballistic effects in transient phonon transport submitted to a spatially sinusoidal heating profile, simulating a transient thermal grating. We begin by extending a previous McK-S formulation to include inelastic scattering, then obtain an analytical solution in the single phonon energy case (gray approximation), and after show how this approach can readily support a full phonon dispersion and mean-free-path distribution. The results agree with experimental data and compare very well to solutions of the phonon Boltzmann transport equation in the diffusive and weakly quasi-ballistic transport regimes. We discuss the role of ballistic and non-equilibrium physics, and show that inelastic scattering is key to retrieving the heat equation solution in the diffusive limit. Overall the McK-S flux method, which takes the form of a diffusion-like equation, proves to be a simple and accurate framework that is applicable from the ballistic to diffusive transport regime.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".