Extended Dynamical Equations of the Period Vectors of Crystals under Constant External Stress to Many-body Interactions
Bibliographic record
Abstract
Since crystals are made of periodic structures in space, predicting their three period vectors starting from any values based on the inside interactions is a basic theoretical physics problem. For the general situation where crystals are under constant external stress, we derived dynamical equations of the period vectors in the framework of Newtonian dynamics, for pair potentials recently (doi:/10.1139/cjp-2014-0518). The derived dynamical equations show that the period vectors are driven by the imbalance between the internal and external stresses. This presents a physical process where when the external stress changes, the crystal structure changes accordingly, since the original internal stress can not balance the external stress. The internal stress has both a full kinetic energy term and a full interaction term. It is extended to many-body interactions in this paper. As a result, all conclusions in the pair-potential case also apply for many-body potentials.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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".