Sharp interface limit of a two-time scale phase field model of a binary mixture
Bibliographic record
Abstract
Abstract Due to its analytical flexibility and thermodynamic consistency, the phase field methodology is widely used in the analysis of equilibrium states and transformation between phases. The present review is devoted to a class of hyperbolic phase field models, which applies to slow and fast phase transformations. Focusing on the example of solidification of metastable liquid, an analysis is presented for the important procedure of reducing the diffuse interface to the sharp interface. An asymptotic analysis is discussed for application to solidifying binary mixture with diffuse phase interface under arbitrary concentration of species and isothermal and isobaric conditions. The analysis reveals that the hyperbolic phase field model can be mapped onto the known hyperbolic Stefan problem within the sharp interface limit. This result, together with the common tangent construction, allows us to analyze ( i ) nonequilibrium effects in the form of solute trapping and ( ii ) the complete transition from the diffusion-limited to the diffusionless (chemically partitionless) solidification at finite interface velocity. A comparison with other theoretical models is summarized and a discussion, which is attributed to experimental results, is given.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot 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.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
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".