Bibliographic record
Abstract
The existence and dynamics of interfaces played a central role in the description of the domain-coarsening phenomena considered in the previous chapters. In the late stages of domain growth the random forces in the order parameter kinetic equations were suppressed and the interface dynamics was treated deterministically. In this chapter we provide a more detailed treatment of the effects of noise and diffusion on the structure of the interface. One may capture the essential physics of diffusively rough interfaces in a general model often called the Kardar–Parisi–Zhang (KPZ) equation (Kardar et al ., 1986). KPZ equation Consider a front in a ( d + 1)-dimensional system extended along x and moving, on average, in the x 1 direction (see Fig. 16.1). The system is assumed to be infinitely extended along x1 and has linear dimension L along x . In contrast to the description in Chapter 7, we neglect the intrinsic thickness of the interface and investigate the effects of diffusion and noise on the dynamics of the interfacial profile. Referring to Fig. 16.1, let h( x , t ) be the position of the interface as a function of x at time t , relative to an arbitrarily selected origin. Its mean position at time t is. We assume that the front propagates with velocity v in a direction normal to its interface; noise provides a destabilizing influence on the front while diffusion tends to remove any surface roughness. A sketch of a portion of the interface profile h ( x , t ) as a function of x at time t is shown in Fig. 16.2.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 0.002 |
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".