Practical Green’s function approach to the simulation of elastic semi-infinite solids
Bibliographic record
Abstract
This paper is concerned with the principles of Green's function-based molecular dynamics (GFMD) simulations of semi-infinite elastic solids and their application to various contact mechanical problems. A methodology to compute the (renormalized) elastic interactions of surface atoms is presented first. It is based on the fluctuation-dissipation theorem, with the help of which thermal fluctuations of atomic displacements can be related to the elastic Green's functions and thus to the effective coupling between surface atoms. We suggest a sparse representation of these renormalized spring constants and present numerical results for some simple two- and three-dimensional lattices. The renormalized elastic interactions can be obtained for relatively small systems and then be extrapolated to large systems. They incorporate the full elastic response of semi-infinite solids in a way that only surface atoms have to be considered in molecular dynamics simulations. The usefulness of GFMD is demonstrated by applying it to various idealized contact models, such as nonadhesive Hertzian contacts as well as nonadhesive contacts between flat, semi-infinite elastic solids and a self-affine, rigid substrate. In all cases, a zero probability density $P(p)$ for infinitesimally small contact pressures $p$ is found, as predicted theoretically. If the self-affine, nonadhesive surfaces are under such high loads that the contact is complete, the pressure histogram can be represented by a Gaussian also in accordance with theoretical predictions. However, if the topography of the substrate resembles that of industrial steel surfaces and the loads are moderate, $P(p)$ decays exponentially for medium and large $p$ in contradiction to theoretical predictions for randomly rough surfaces.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".