Bibliographic record
Abstract
This chapter provides a brief introduction to the subject of continuum-atomistic multiscale models. The governing equations of a molecular statics (MS) simulation are described. The chapter also describes how to define an elastic continuum constitutive model based upon an underlying atomistic model. When a lattice deforms elastically and homogeneously it is possible to map the deformations and forces of the atomistic model to the displacements and stresses of an effective continuum model. This is accomplished via a simple hierarchical multiscale model commonly known as the Cauchy-Born rule, which was made popular by the quasicontinuum method of Tadmor et al., but was first considered by Johnson and Milstein. The bridging domain method (BDM) of Xiao and Belytschko and Xiao and Yang is introduced to couple an MS model with the FEM. The chapter illustrates the accuracy of the extended finite element method-BDM relative to a fully atomistic MS simulation.
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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 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.077 | 0.025 |
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".