COULOMB FRICTION AND OTHER SLIDING LAWS IN A HIGHER-ORDER GLACIER FLOW MODEL
Bibliographic record
Abstract
We consider a widely used higher-order glacier flow model with a variety of parametrizations of wall slip, including Coulomb friction, regularized Coulomb friction laws and a power law. Mathematically, the Coulomb friction problem is found to be analogous to a classical friction problem in elasticity theory. We specifically analyze the case in which slip is possible everywhere at the boundary, in which case the weak formulation becomes a semi-coercive convex minimization problem which has a solution only if a solvability condition representing force and torque balance is satisfied. Going beyond previous work, we study the uniqueness of solutions in depth, finding that non-unique solutions are possible under very specialized circumstances. Further, in an extension of work by Campos, Oden and Kikuchi, we show that solutions to the regularized Coulomb friction and power law problems converge to the Coulomb friction problem in appropriate parametric limits, provided the latter is unique, and briefly discuss the implications of possible non-unique solutions for a priori error estimation in numerical approximations.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".