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Record W1972417825 · doi:10.3934/dcdsb.2005.5.299

On the $L^2$-moment closure of transport equations: The general case

2005· article· en· W1972417825 on OpenAlexaff
Thomas Hillen

Bibliographic record

VenueDiscrete and Continuous Dynamical Systems - B · 2005
Typearticle
Languageen
FieldMathematics
TopicNonlinear Partial Differential Equations
Canadian institutionsUniversity of Alberta
Fundersnot available
KeywordsClosure (psychology)Norm (philosophy)Moment (physics)Moment closureMathematicsClosure problemSpace (punctuation)Convection–diffusion equationMathematical analysisApplied mathematicsPhysicsClassical mechanicsComputer scienceLawThermodynamics

Abstract

fetched live from OpenAlex

Transport equations are intensively used in Mathematical Biology.In this article the moment closure for transport equations for an arbitraryfinite number of moments is presented. With use of a variational principle theclosure can be obtained by minimizing the $L^2(V)$-norm with constraints. An$H$-Theorem for the negative $L^2$-norm is shown and the existence of Lagrangemultipliers is proven. The Cattaneo closure is a special case for two momentsand was studied in Part I (Hillen 2003). Here the general theory is given andthe three moment closure for two space dimensions is calculated explicitly. Itturns out that the steady states of the two and three moment systems aredetermined by the steady states of a corresponding diffusion problem.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

How this classification was reachedexpand

Full frame machine prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.002
metaresearch head score (Gemma)0.003
Version: metacan-v3-hybrid-931329e0061cValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.002
Threshold uncertainty score0.009

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0020.003
Meta-epidemiology (narrow)0.0010.000
Meta-epidemiology (broad)0.0010.002
Bibliometrics0.0010.001
Science and technology studies0.0010.004
Scholarly communication0.0020.004
Open science0.0010.002
Research integrity0.0020.002
Insufficient payload (model declined to judge)0.0020.000

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.

Opus teacher head0.029
GPT teacher head0.298
Teacher spread0.269 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Classification

machine, unvalidated

Machine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designTheoretical or conceptual
Domainnot available
GenreEmpirical

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".

Quick stats

Citations21
Published2005
Admission routes1
Has abstractyes

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Same venueDiscrete and Continuous Dynamical Systems - BSame topicNonlinear Partial Differential EquationsFrench-language works237,207