Fourier-Laplace Spectral Theory for Non-Steady-State Thermal Fields with Applications to Problems in Steady-State Photothermal Linear Frequency Modulation
Bibliographic record
Abstract
The spectral theory of thermal fields subject to arbitrary boundary surface flux conditions developed in this work establishes a universal approach to non-steady-state (photo)thermal responses of solids under transient or modulated thermal excitation through a combined Fourier-Laplace formalism. The self-consistent evolution from the nonsteady state to the steady state under single frequency or arbitrary pulsed or multifrequency thermal-wave excitation waveforms allows for defining experimental criteria in terms of excitation waveform repetition periods to attain steady state in frequency-modulated photothermal (and other general experimental) systems. This approach is crucial for ensuring accurate material property measurements using lock-in or correlation and spectral analysis demodulation of thermal waves, especially under linear frequency modulation (LFM) when the modulated steady state is time dependent. The theory is validated using experimental photothermal radiometry LFM responses from black anodized aluminum. We also define the associated thermal diffusion length in terms of linear superpositions of partial thermal waves (wavelets), which are shown to result in improved depth, lateral, and axial resolution in thermal-wave radar imaging applications compared with sequential single-modulation frequency detection.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.003 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".