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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 OpenAlexfundno aff
Jonathan D. Evans

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.

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)0.001
metaresearch head score (Gemma)0.006
Version: metacan-v3-hybrid-931329e0061cValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Simulation or modeling · Consensus signal: none
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.007
Threshold uncertainty score0.015

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0010.006
Meta-epidemiology (narrow)0.0010.000
Meta-epidemiology (broad)0.0010.001
Bibliometrics0.0010.000
Science and technology studies0.0010.003
Scholarly communication0.0020.003
Open science0.0010.003
Research integrity0.0030.002
Insufficient payload (model declined to judge)0.0040.000

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

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 designSimulation or modeling
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

Citations19
Published2003
Admission routes1
Has abstractyes

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Same venueThe Quarterly Journal of Mechanics and Applied MathematicsSame topicnanoparticles nucleation surface interactionsFrench-language works237,207