Nonhydrodynamic aspects of electron transport near a boundary: The Milne problem
Bibliographic record
Abstract
The nonhydrodynamic behavior of electrons near a boundary is studied with the Milne problem of transport theory. A system of electrons dilutely dispersed in a heat bath of atomic moderators is considered in the positive one-dimensional spatial half-space with an absorbing boundary at the origin which mimics an electrode. A flux of electrons is assumed to originate at an infinite distance from the boundary. The Fokker-Planck equation for the electron distribution function in space and velocity is considered. The density and temperature profiles are determined, and the departure from hydrodynamic behavior near the boundary is studied. Argon and helium are chosen as the moderators, and results with different cross sections are obtained. The Fokker-Planck equation is solved with an expansion in Legendre and Speed polynomials, and compared wherever possible with results obtained with a Monte Carlo simulation. The behavior near the boundary is shown to be strongly influenced by the Ramsauer-Townsend minimum in the electron-Ar momentum transfer cross section.
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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) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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".