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Record W2049235379 · doi:10.1093/qjmam/56.1.139

The Stefan Problem with Nonlinear Kinetic Undercooling

2003· article· en· W2049235379 on OpenAlex
Jonathan D. Evans

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.

fundA Canadian funder is recorded on the work.
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

VenueThe Quarterly Journal of Mechanics and Applied Mathematics · 2003
Typearticle
Languageen
FieldEarth and Planetary Sciences
Topicnanoparticles nucleation surface interactions
Canadian institutionsnot available
FundersMemorial University of NewfoundlandNuffield FoundationLeverhulme Trust
KeywordsSupercoolingStefan problemKinetic energyNonlinear systemThermodynamicsPower lawBoundary value problemDiffusionLimit (mathematics)Phase (matter)Boundary (topology)Materials scienceMathematicsStatistical physicsMathematical analysisPhysicsClassical mechanics

Abstract

fetched live from OpenAlex

The behaviour of the one‐phase Stefan problem with nonlinear kinetic undercooling is studied. This system is physically relevant in a number of contexts, in particular as the sharp‐interface (fast‐reaction) limit of a variety of reaction–diffusion systems. The similarities and differences with the linear kinetic condition (studied by Evans and King (2000)) are highlighted for both one‐ and two‐dimensional problems. Asymptotic results (both in time and in the Stefan number) are obtained for the power‐law form of the kinetic condition. Significantly, the one‐dimensional growth behaviour of the moving boundary is seen to be relatively insensitive to the precise form of the nonlinear kinetic condition, and this in effect has hindered its experimental determination in applications such as silicon oxidation. By contrast, the two‐dimensional development of the moving boundary around a mask edge depends strongly on the form of the kinetic condition and consequently a method, similar to the Boltzmann–Matano method for determining nonlinear diffusivities, is described to determine the kinetic undercooling relation from experiment.

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)0.001
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 score0.124
Threshold uncertainty score0.234

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.000
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 head0.012
GPT teacher head0.209
Teacher spread0.196 · 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