Multiple-quantum nuclear magnetic resonance spin dynamics in disordered rigid chains and rings
Bibliographic record
Abstract
Multiple-quantum (MQ) nuclear magnetic resonance (NMR) spin dynamics are investigated in rigid linear chains and rings with nearest neighbor dipole–dipole interactions with different coupling constants due to spatial disorder. It is shown that MQ NMR spectra, for such one-dimensional systems initially at thermal equilibrium followed by evolution under a 2-quantum/2-spin average dipolar Hamiltonian, only consist of 0- and 2-quantum coherences. A new constant of motion for the systems under consideration is found and used in the numerical analysis of MQ NMR spin dynamics to factorize the Hamiltonian into distinct blocks corresponding to different eigenvalues of the constant of motion. Only one of these blocks of dimension N×N (where N is the number of spins) completely determines the MQ NMR spin dynamics. Supercomputer calculations of MQ NMR spin dynamics in rigid linear chains containing up to 1000 spins are presented. The possibility to obtain structural information from the time evolution of MQ coherences is also discussed.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| 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 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".