Synthetic iterative scheme for thermal applications in hotspot systems with large temperature variance
Bibliographic record
Abstract
A synthetic iterative scheme is developed for thermal applications in hotspot systems with large temperature variance. Different from previous work with linearized equilibrium state and small temperature difference assumption, the phonon equilibrium distribution shows a nonlinear relationship with temperature and mean free path changes with the spatial temperature when the temperature difference of system is large, so that the same phonon mode may suffer different transport processes in different geometric regions. In order to efficiently capture nonlinear and multiscale thermal behaviors, the Newton method is used and a macroscopic iteration is introduced for preprocessing based on the iterative solutions of the stationary phonon BTE. Macroscopic and mesoscopic physical evolution processes are connected by the heat flux, which is no longer calculated by classical Fourier's law but obtained by taking the moment of phonon distribution function. These two processes exchange information from different scales, such that the present scheme could efficiently deal with heat conduction problems from ballistic to diffusive regime. Numerical tests show that the present scheme could efficiently capture the multiscale heat conduction in hotspot systems with large temperature variances. In addition, a comparison is made between the solutions of the present scheme and effective Fourier's law by several heat dissipations problems under different sizes or selective phonon excitation. Numerical results show that compared to the classical Fourier's law, the results of the effective Fourier's law could be closer to the BTE solutions by adjusting effective coefficients. However, it is still difficult to capture some local nonlinear phenomena in complex geometries.
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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 | 0.000 |
| Open science | 0.001 | 0.001 |
| 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".