On the application of maximum-entropy-inspired multi-Gaussian moment closure for multi-dimensional non-equilibrium gas kinetics
Bibliographic record
Abstract
Maximum -entropy moment closures for describing non -equilibrium rare fied gaseous flows have previously been shown to provide accurate and computationally efficient descriptions oftransition -regime flows .Unfortunately ,forhigh -order variants ofthese closuresabovesecondorderinvelocityspace,therearenoanalyticalclosuresforthesystemsofhyperbolicpartialdifferentialequations( PDEs ) which govern the transport of the macroscopic moment quantities and instead approximate closures have been sought .In this study ,abi-Gaussian approximation for the number density function (NDF )is considered both for approximating the NDF and closing moment fluxes of the resulting fourth -order 14 -moment maximum -entropy closure associated with fully three -dimensional kinetic theory .Prior investigations of the bi -Gaussian approximation applied to simpli fi ed one -dimensional univariate kinetic theory has yielded excellent results when compared to the actual maximum -entropy solutions as well a similar interpolative -based maximumentropy -based (IBME )closure .Inthe one -dimensional univariate case ,the bi-Gaussian closure isequivalent tothe so-called extended quadrature method of moments (EQMOM ) with a normal or Gaussian kernel basis function .A potential bene fi t of the bi -Gaussian approach proposed hereinisthatanessentially closed-formanalytical expression resultsfortheNDF.Inthisstudy,theextension ofthebi -Gaussian closure to the multi -dimensional case is considered and compared to the equivalent multi -dimensional IBME closure .The approximate form for the NDF and closing fluxes in terms of the relevant moments are derived and the validity and hyperbolicity of the closure for the space of realizable predicted moments are all explored and compared tothose ofthe IBME closure .Itisshown that the bi-Gaussian closure in the multi -dimensional case unfortunately suffers from several de ficiencies :firstly ,the valid region of realizable moment space forthebi-Gaussian closure isasmall subset ofthefullrealizable 14-moment space;andsecondly,theclosure andmoment equation eigenstructure for solutions associated with zero heat fluxbecome undefined.The findings herein suggest that the proposed bi-Gaussian closure may not be a good choice for practical multi -dimensional rare fi ed fl ow predictions despite the promising results exhibitedintheone-dimensionalcase.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 source (direct Gemma or distilled Codex), 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".