Parallel superposition of small-amplitude oscillatory shear flow upon steady shear flow from rotarance theory
Bibliographic record
Abstract
The power of a macromolecular theory for the transport properties of a polymeric liquid increases with the number of analytical expressions for its most important material functions. In this work, we add another of these canonical function to our recent series of material function derivations for rotarance theory. By rotarance theory, we mean the explanation of the elasticity of polymeric liquids by use of (i) the diffusion equation to get the orientation distribution in Euler coordinates, and (ii) the integration in phase space using this distribution to get the target material function. In this paper, we target parallel superposition of oscillatory shear flow upon steady shear flow. We arrive at analytical expressions for both parts of the complex viscosity in parallel superposition. We find that these explain the classic experimental observations in parallel superposition: (a) the maximum in the real part of the complex viscosity, and (b) the negative values of minus its imaginary part, and (c) the independence of the steady mean shear stress from the superposed oscillation.
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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".