Compressible viscoelasticity: stability of solutions for homogeneous plane-Earth models
Bibliographic record
Abstract
Recently, Purcell has discussed the influence of gravity on load-induced perturbations of compressible, viscoelastic plane-Earth models, where the contributions arising from initial stress and internal buoyancy have been distinguished in the equation of motion. According to his results, the consideration of initial stress is mandatory, whereas that of internal buoyancy has only a minor influence on the solution. We re-examine his study using a different approach. In particular, we present analytical solutions for a homogeneous half-space and discuss the associated relaxation spectra. We show that the solution to the problem involves singularities and branch cuts in the complex s-plane in addition to the singularities caused by roots of the determinant function. Furthermore, Rayleigh—Taylor instabilities arising from internal buoyancy cannot be completely balanced by initial stress. Also, the stability margin introduced by Love for an elastic continuum cannot be ignored when applying the solution. Finally, we show that the relaxation spectra can be directly related to the spectral response of a homogeneous, compressible, viscoelastic sphere as studied in recent papers by Vermeersen and Hanyk.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".