Reduced surface integral equations for Laplacian fields in the presence of layered bodies
Bibliographic record
Abstract
Laplacian potential fields in stratified media are usually analyzed using an integral equation for an unknown function over the union of all the interfaces between regions with different homogeneous materials. In this paper, the field problem is solved using a reduced integral equation involving a single unknown function over only the boundary of the source region. The new integral equation is derived by introducing surface operators to express the potential and its normal derivative on each interface in terms of a single unknown function over the same interface. These operators and the corresponding single functions are obtained recursively, from one interface to the next. Thus, a substantial decrease in the amount of necessary numerical computation and computer memory is achieved especially for systems containing identical layered bodies where the reduction operators are only constructed for one of the bodies. The purpose of this paper is to derive reduced integral equations by directly applying the interface conditions and to show their high computational efficiency for systems of layered bodies.PACS Nos.: 02.30.Rz, 02.70.Pt, 41.20.Cv
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| 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 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".