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Record W2163048869 · doi:10.1139/cjp-2013-0231

Nonlinear diffusion in a plane surface

2013· article· en· W2163048869 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.

venuePublished in a venue whose home country is Canada.
no affNo Canadian affiliation: this work is invisible to an affiliation-only frame.
No Canadian affiliation. An affiliation-only frame, the usual design, would never have seen this work. It is one of the works that make the case for inverting the frame.

Bibliographic record

VenueCanadian Journal of Physics · 2013
Typearticle
Languageen
FieldEngineering
TopicAdvanced Materials Characterization Techniques
Canadian institutionsnot available
Fundersnot available
KeywordsPhysicsNonlinear systemDiffusionFick's laws of diffusionDiffusion equationBrownian motionPenetration (warfare)Plane (geometry)Mathematical analysisAnomalous diffusionDiffusion processImpuritySquare rootSimilarity solutionClassical mechanicsMechanicsGeometryThermodynamicsMathematicsQuantum mechanicsBoundary layerInnovation diffusion

Abstract

fetched live from OpenAlex

Diffusion is the result of Brownian motion and must occur with a finite velocity. The earlier presented nonlinear diffusion equation, with diffusion coefficients that are directly proportional to the concentration of impurities, defines the maximum depth of penetration. For nonlinear diffusion from a constant source, the depth of the impurities’ penetration is directly proportional to the square root of the diffusion time. Profiles of nonlinear solutions differ from classical linear solutions on great distances and are in good fitting with experiment. We increased the accuracy of the approximate analytical solutions for nonlinear diffusion in the plane from a square infinite source with fixed initial impurity concentrations in the corners. The nonlinear diffusion equation for the solution was transformed by introducing similarity variables.

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: Bench or experimental · Consensus signal: Bench or experimental
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.027
Threshold uncertainty score0.250

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)0.0000.000

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 head0.007
GPT teacher head0.191
Teacher spread0.185 · 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