TRANSIENT LINEAR AND NONLINEAR HEAT CONDUCTION IN WEAKLY MODULATED DOMAINS
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Abstract Heat conduction in two-dimensional domains with spatially periodic boundary is addressed in this study. The periodic modulation is assumed to be weak, but is of arbitrary shape. A regular perturbation approach is implemented to determine the temperature and heat flux throughout the domain. It is observed that the validity of the perturbation approach extends to include geometries of practical importance. Transient linear as well as steady nonlinear heat conduction problems are examined. The periodic domain is mapped onto the rectangular domain. For both steady and transient linear heat conduction, a fully analytical spectral solution becomes possible. The nonlinear problem is shown to reduce to a set of ordinary differential equations of the two-point-boundary-value type, which is solved using a variable-step-size finite-difference scheme. The perturbation approach is validated upon comparison with conventional methods; excellent agreement is obtained against the boundary- and finite-element methods.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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 it