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Record W2161029367 · doi:10.1002/mma.898

Shock formation in a chemotaxis model

2007· article· en· W2161029367 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.
fundA Canadian funder is recorded on the work.

Bibliographic record

VenueMathematical Methods in the Applied Sciences · 2007
Typearticle
Languageen
FieldMathematics
TopicMathematical Biology Tumor Growth
Canadian institutionsUniversity of Alberta
FundersNatural Sciences and Engineering Research Council of Canada
KeywordsUniquenessMathematicsShock waveParameterized complexityShock (circulatory)Riemann problemChemotaxisTraveling waveEntropy (arrow of time)Applied mathematicsRiemann hypothesisMathematical analysisCombinatoricsPhysicsMechanicsThermodynamics

Abstract

fetched live from OpenAlex

Abstract In this paper, we establish the existence of shock solutions for a simplified version of the Othmer–Stevens chemotaxis model ( SIAM J. Appl. Math. 1997; 57 :1044–1081). The existence of these shock solutions was suggested by Levine and Sleeman ( SIAM J. Appl. Math. 1997; 57 :683–730). Here, we consider the general Riemann problem and derive the shock curves in parameterized forms. By studying the travelling wave solutions, we examine the shock structure for the chemotaxis model and prove that the travelling wave speed is identical to the shock speed. Moreover, we explicitly derive an entropy–entropy flux pair to prove the uniqueness of the weak shock solutions. Some discussion is given for further study. Copyright © 2007 John Wiley & Sons, Ltd.

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.

Full frame distilled prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.028
metaresearch head score (Gemma)0.004
Version: codex-gemma-dda1882f352aValidation 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: Methods · Consensus signal: Methods
Teacher disagreement score0.253
Threshold uncertainty score0.982

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0280.004
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0000.001
Science and technology studies0.0000.001
Scholarly communication0.0000.000
Open science0.0010.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

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 head0.164
GPT teacher head0.458
Teacher spread0.295 · 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