Effects of Inertia on the Steady-Shear Rheology of Disordered Solids
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Bibliographic record
Abstract
We study the finite-shear-rate rheology of disordered solids by means of molecular dynamics simulations in two dimensions. By systematically varying the damping strength $\ensuremath{\zeta}$ in the low-temperature limit, we identify two well-defined flow regimes, separated by a thin (temperature-dependent) crossover region. In the overdamped regime, the athermal rheology is governed by the competition between elastic forces and viscous forces, whose ratio gives the Weissenberg number $\mathrm{Wi}\ensuremath{\propto}\ensuremath{\zeta}\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{\ensuremath{\gamma}}$; the macroscopic stress $\mathrm{\ensuremath{\Sigma}}$ follows the frequently encountered Herschel-Bulkley law $\mathrm{\ensuremath{\Sigma}}={\mathrm{\ensuremath{\Sigma}}}_{0}+k\sqrt{\mathrm{Wi}}$, with yield stress ${\mathrm{\ensuremath{\Sigma}}}_{0}>0$. In the underdamped (inertial) regime, dramatic changes in the rheology are observed for low damping: the flow curve becomes nonmonotonic. This change is not caused by longer-lived correlations in the particle dynamics at lower damping; instead, for weak dissipation, the sample heats up considerably due to, and in proportion to, the driving. By thermostating more or less underdamped systems, we are able to link quantitatively the rheology to the kinetic temperature and the shear rate, rescaled with Einstein's vibration frequency.
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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 | 0.000 | 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 it