Fast and accurate coarsening simulation with an unconditionally stable time step
Why this work is in the frame
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Bibliographic record
Abstract
We present Cahn-Hilliard and Allen-Cahn numerical integration algorithms that are unconditionally stable and so provide significantly faster accuracy-controlled simulation. Our stability analysis is based on Eyre's theorem and unconditional von Neumann stability analysis, both of which we present. Numerical tests confirm the accuracy of the von Neumann approach, which is straightforward and should be widely applicable in phase-field modeling. For the Cahn-Hilliard case, we show that accuracy can be controlled with an unbounded time step Delta t that grows with time t as Delta t approximately t(alpha). We develop a classification scheme for the step exponent alpha and demonstrate that a class of simple linear algorithms gives alpha=1/3. For this class the speedup relative to a fixed time step grows with N, the linear size of the system, as N/ln N. With conservative choices for the parameters controlling accuracy and finite-size effects we find that an 8192(2) lattice can be integrated 300 times faster than with the Euler method.
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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) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it