Asymptotic theory for disc-like crystal growth (II): interfacial instability and pattern formation at early stage of growth
Bibliographic record
Abstract
This paper is a continuation of the paper ([1] ), which is called paper (I) afterward. In the present paper, which we shall call paper (II), we study the interfacial instability property of the side interface of a growing disc-like crystal at the early stage of growth by using the approach developed in the interfacial wave (IFW) theory of dendritic growth. Our analysis show that the system allows two types of unstable modes over theside-interface: (1). The axi-symmetric $(m=0)$ modes. The mostdangerous axi-symmetric mode is the base mode $A_0$, which isresponsible for formation of the axi-symmetric pattern over theside-interface, anti-symmetric about the central plane of thedisc; (2). The non-axi-symmetric modes, which are responsible for non-axi-symmetric pattern formation around theedge of the disc. The growth rates of these non-axi-symmetricmodes are much smaller than the growth rate of the base mode$A_0$. During the course of disc growth, the unstable $A_0$-modemerges first. It leads to the formation of anti-symmetric patternabout the central plane over the side-interface. Following the onset of unstable base mode$A_0$, a set of non-axi-symmetric growing modes also appear.However, due to the smallness of growth rate of these unstable modes, the non-axi-symmetric patternaround the edge of the disc becomes observable, only after asufficiently long time. Our theoretical predictions are in goodagreement with the available experimental data.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot 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.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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.
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 source (direct Gemma or distilled Codex), 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".