A local orientational order parameter for systems of interacting particles
Bibliographic record
Abstract
Many physical systems are well modeled as collections of interacting particles. Nevertheless, a general approach to quantifying the absolute degree of order immediately surrounding a particle has yet to be described. Motivated thus, we introduce a quantity E that captures the amount of pairwise informational redundancy among the bonds formed by a particle. Particles with larger E have less diversity in bond angles and thus simpler neighborhoods. We show that E possesses a number of intuitive mathematical properties, such as increasing monotonicity in the coordination number of Platonic polyhedral geometries. We demonstrate analytically that E is, in principle, able to distinguish a wide range of structures and conjecture that it is maximized by the icosahedral geometry under the constraint of equal sphere packing. An algorithm for computing E is described and is applied to the structural characterization of crystals and glasses. The findings of this study are generally consistent with existing knowledge on the structure of such systems. We compare E to the Steinhardt order parameter Q6 and polyhedral template matching (PTM). We observe that E has resolution comparable to Q6 and robustness similar to PTM despite being much simpler than the former and far more informative than the latter.
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".