Exact coefficients for rigid dumbbell suspensions for steady shear flow material function expansions
Bibliographic record
Abstract
From kinetic molecular theory, we can attribute the elasticity of polymeric liquids to macromolecular orientation. For a suspension of rigid dumbbells, subject to a particular flow field, we must first solve the diffusion equation for the orientation distribution function. From this distribution, we then calculate physical properties such as the steady shear flow material functions. We thus arrive at power series expansions in the shear rate for both the orientation distribution function and for the steady shear flow material functions. Analytical work on many viscoelastic material functions must be checked for consistency, in their steady shear flow limits, against these power series. For instance, for large-amplitude oscillatory shear flow, we recover the coefficients of these expansions in the limits of low test frequency. The coefficients of the steady shear viscosity and the first normal stress coefficient functions are not known exactly beyond the fourth power. In this work, for both of these functions, we arrive at exact expressions for the first 20 coefficients. We close with five worked examples illustrating uses for our new coefficients.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 0.002 |
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".