On the scaling from statistical to representative volume element in thermoelasticity of random materials
Bibliographic record
Abstract
Under consideration is the finnite-size scaling of effective thermoelastic properties of random microstructures from a Statistical Volume Element(SVE) to a Representative Volume Element (RVE), without invoking any periodic structure assumptions, but only assuming the microstructure's statisticsto be spatially homogeneous and ergodic. The SVE is set up on a mesoscale,i.e. any scale finite relative to the microstructural length scale. The Hill condition generalized to thermoelasticity dictates uniform Neumann and Dirichletboundary conditions, which, with the help of two variational principles, lead toscale dependent hierarchies of mesoscale bounds on effective (RVE level) properties: thermal expansion and stress coefficients, effective stiffness, and specificheats. Due to the presence of a non-quadratic term in the energy formulas,the mesoscale bounds for the thermal expansion are more complicated thanthose for the stiffness tensor and the heat capacity. To quantitatively assessthe scaling trend towards the RVE, the hierarchies are computed for a planarmatrix-inclusion composite, with inclusions (of circular disk shape) located atpoints of a planar, hard-core Poisson point field. Overall, while the RVE isattained exactly on scales infinitely large relative to the microscale, depending on the microstructural parameters, the random fluctuations in the SVEresponse may become very weak on scales an order of magnitude larger thanthe microscale, thus already approximating the RVE.
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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 | 0.003 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| 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".