Fractional order theory of a perfect conducting thermoelastic medium
Bibliographic record
Abstract
In this work, a new mathematical model of magneto-thermoelasticity theory is constructed in the context of a new consideration of heat conduction law with time-fractional order. This model is applied to a one-dimensional application for a perfect conducting half-space of elastic material, which is thermally shocked in the presence of magnetic field. Laplace transforms and state-space techniques (Ezzat. Can. J. Phys. 86, 1242, (2008)) will be used to obtain the general solution for any set of boundary conditions. According to numerical results and graphs, it is found that introducing a fractional derivative of order α has a significant effect on the temperature, stress, and heat flux distributions as well as the induced electric and magnetic fields; the curves are smoother in the case of 0 < α < 1 due to weak thermal conductivity. Some comparisons are made and shown in figures to estimate the effects of the fractional order parameter on all the studied fields.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".