Maximum Entropy Methods in the Mechanics of Quasi-Static Deformation of Granular Materials
Bibliographic record
Abstract
In statistical physics of dilute gases maximum entropy methods are widely used for theoretical predictions of macroscopic quantities in terms of microscopic quantities. In this study an analogous approach to the mechanics of quasi-static deformation of granular materials is proposed. The reasoning is presented that leads to the definition of an entropy that is appropriate to quasi-static deformation of granular materials. This entropy is formulated in terms of contact quantities, since contacts constitute the relevant microscopic level for granular materials that consist of semirigid particles. The proposed maximum entropy approach is then applied to two cases. The first case deals with the probability density functions of contact forces in a two-dimensional assembly with frictional contacts under prescribed hydrostatic stress. The second case deals with the elastic behaviour of two-dimensional assemblies of non-rotating particles with bonded contacts. For both cases the probability density functions of contact forces are determined from the proposed maximum entropy method, under the constraints appropriate to the case. These constraints form the macroscopic information available about the system. With the probability density functions for contact forces thus determined, theoretical predictions of macroscopic quantities can be made. These theoretical predictions are then compared with results obtained from two-dimensional Discrete Element simulations and from experiments.
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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 | 0.001 | 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".