THE ADOMIAN DECOMPOSITION METHOD FOR THE SOLUTION OF THE TRANSIENT ENERGY EQUATION IN ROCKS SUBJECTEDTO LASER IRRADIATION
Bibliographic record
Abstract
Abstract – A 2-D heat conduction model has been solved by using the Adomian Decomposition Method to predict the transient temperature and heat flux distribution in a thick solid that is irradiated by a laser source. The laser source may operate in a continuous wave (CW) mode or repeated pulse (RP) mode and may have arbitrary, spatial and temporal profiles. A generalized solution containing five-terms approximation of a rapidly convergent series is obtained. The solution is then applied to some special cases of practical interest, such as laser irradiation of sandstones and limestones. Laser drilling of geologic formations is being considered by the petroleum industry in the foreseeable future. The 2-D transient temperature distribution is presented in a graphical form and discussed. A comparison between the results obtained from the Adomian method and those obtained numerically by using the Crank-Nicholson method is also presented.
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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".