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Record W2066764747 · doi:10.1137/s0036144502409007

A Hyperbolic PDE with Parabolic Behavior

2004· article· en· W2066764747 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.

Bibliographic record

VenueSIAM Review · 2004
Typearticle
Languageen
FieldMathematics
TopicFractional Differential Equations Solutions
Canadian institutionsWestern University
FundersDeakin University
KeywordsHyperbolic partial differential equationParabolic partial differential equationPartial differential equationFTCS schemeMathematicsElliptic partial differential equationDimension (graph theory)Heat equationMathematical analysisFirst-order partial differential equationHyperbolic functionEvolution equationApplied mathematicsDifferential equationPure mathematicsOrdinary differential equation

Abstract

fetched live from OpenAlex

In this paper we present a hyperbolic partial differential equation (PDE) in one space and one time dimension. This equation arose in a study of numerical schemes for simulating evolving river topographies. The solution of this PDE, whose initial data are specified along a characteristic, is very similar to that of the canonical diffusion equation. This interesting example provides insight into the solution of hyperbolic PDEs when data is specified in this pathological way as well as illustrating some connections between the parabolic and hyperbolic classes of evolution equations.

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)0.000
metaresearch head score (Gemma)0.000
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: Empirical · Consensus signal: Empirical
Teacher disagreement score0.512
Threshold uncertainty score0.791

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.001

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 head0.083
GPT teacher head0.368
Teacher spread0.286 · 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