Cox–Merz rules from general rigid bead-rod theory
Bibliographic record
Abstract
The value of this work is in its macromolecular explanations of both Cox–Merz rules, thus of when to expect them to work. For polymeric liquids and their solutions, the measured values of the steady shear viscosity and the magnitude of the complex viscosity often equate, within experimental error, when compared at common shear rate (in units of t−1) and angular frequency (in units of rad t−1). Called the first Cox–Merz rule, this remarkable empiricism, with one exception, has defied most macromolecular explanations. This one exception is the suspension of multi-bead rods and its special case of rigid dumbbells. The second Cox–Merz rule equates approximately the slope of the first derivative of steady shear viscosity with respect to shear rate with the real part of the complex viscosity when compared at common shear rate (in units of t−1) and angular frequency (in units of rad t−1). In this paper, we explain both Cox–Merz rules for all axisymmetric macromolecules, be they prolate or oblate, of almost any lopsidedness. Furthermore, through the lens of general rigid bead-rod theory, we define under what conditions these rules do not apply. Specifically, the first Cox–Merz rule fails when the macromolecules are too oblate.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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".