Henyey-Greenstein Model in the Shape Relaxation of Dilute Gas Mixtures
Bibliographic record
Abstract
Abstract We study the relaxation of Li+ ions dilutely dispersed in He at equilibrium. We employ the Henyey-Greenstein phase function to model the angular dependence of the differential scattering cross section for Li+-He collisions. We solve the spatially homogeneous linear Boltzmann equation for this model cross section with the collision operator explicitly given in terms of the scattering kernel. With the Quadrature Discretization Method based on the speed polynomials, the Boltzmann equation is reduced to a set of ordinary differential equations. This numerical method provides a rapid convergence for the Li+ distribution function. We study the relaxation of the shape of the Li+ distribution function in terms of the Kullback-Leibler information relative to the steady state and local in time Maxwellians. A comparison of the relaxation times of these two functionals show that there is no formation of a local Maxwellian during the relaxation process. This was verified for several values of the g-parameter in the Henyey-Greenstein phase function model and the initial average energies investigated. Keywords: Boltzmann equationshape relaxationKullback-Leibler informationHenyey-Greenstein ACKNOWLEDGMENTS This research is supported by grants to BDS from the Natural Sciences and Engineering Research Council of Canada and the Canadian Space Agency.
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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".