Note on the solutions of the model of coupled oscillators in crystalline optical activity for the direction perpendicular to the optic axis
Bibliographic record
Abstract
In the past, Chandrasekhar's method of two coupled oscillators was successfully used for the interpretation of crystalline optical activity. The optical activity dispersion relations were obtained in the direction of the optic axis and also in the direction perpendicular to the optic axis. However, Chandrasekhar's approach to the solution method is based on a mistake in his calculations. This mistake does not influence the character of the dispersion relations in the direction of the optic axis, which was proved by the solution of the model of coupled oscillators using the Condon relations. Similar conclusions have not been introduced for the direction perpendicular to the optic axis. For that reason, the model of coupled oscillators, using the Condon relations, is presented also for the direction perpendicular to the optic axis. The considered model of coupled oscillators is more complicated and therefore corresponds to the structure of real crystals more closely. It can be proved that, in spite of Chandrasekhar's mistake in the calculations, his conclusions hold. The character of the dispersion relations in the directions parallel and perpendicular to the optic axis is the same and differs only by a constant multiplicative factor. However, Chandrasekhar's factor differs from the derived form of this factor, which is presented in this paper. It is also presented for the example of an atomic crystal of tellurium that the form of Chandrasekhar's factor is incorrect. The mistakes in Chandrasekhar's derivations are also discussed.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".