Simple shear and small amplitude oscillatory rectilinear shear permeation flows of cholesteric liquid crystals
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Bibliographic record
Abstract
A model of rod-like cholesteric liquid crystals subjected to slow steady simple shear and low frequency small amplitude oscillatory shear flow is formulated and applied to permeation flow, also known as Helfrich permeation flow [Helfrich (1969, 1970)], when the cholesteric helix is oriented along the velocity direction and the orientation distortions retain the original planar chiral structure. In permeation flow the elastic forces exactly balance viscous forces. The presence of a small internal length scale (pitch of the helix) leads to boundary layer behavior in the velocity and orientation fields at any shear rate and at any driving frequency. The thickness of the boundary layer region is of the order of the pitch. The apparent viscosity is larger than typical nematic viscosities by a factor proportional to the ratio of the gap thickness to the pitch length. The effect is due to the Ericksen elastic stress. The response of cholesterics to small amplitude oscillatory shear corresponds to a purely viscous material. The out-of-phase stress component vanishes because the viscous force is exactly cancelled by the elastic force. In the terminal region, the loss modulus G″ exhibits a classical frequency ω dependence (G″∝ω) but its magnitude is much greater than for other cholesteric flows by a factor proportional to the ratio of the gap thickness to the pitch length.
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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 | 0.001 | 0.001 |
| 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) | 0.001 | 0.000 |
Machine scores (provisional)
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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 it