Dynamical Green’s function for elastic half-space, and energy losses due to collision
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Bibliographic record
Abstract
This special issue celebrates 100 years since the birth of Moisey Isaakovich Kaganov. This date is a personal event for us, since Moisey Issakovich (or Musik, for his friends and close ones) is the father of one of us, and the grandfather of the other. In addition, we have both been his students. We received the problem discussed in this paper by succession. In 1949 Ilya Mikhailovich Lifshitz was interested in studying electrodynamic and elastic properties of solids, and this analysis required knowledge of the corresponding Green’s functions. He suggested to his two graduate students, Moisey Kaganov and Victor Tsukernik, to calculate the displacement vector caused by an instant point source acting at the surface of an elastic half-space. At that time they had chosen a different topic, and the problem hibernated until the early 1990s, when Moisey Issakovich suggested it as a subject for a Master’s thesis for one of us (ML) to be conducted under the supervision of the other one (IK). The results have been published in papers I. M. Kaganova and M. L. Litinskaia, Phys. Lett. A 200, 365 (1995)1 and I. M. Kaganova and M. L. Litinskaia, Phys. Lett. A 200, 375 (1995).2 The first paper discussed the derivation of the normal component of the displacement vector. We showed that the displacement can be calculated as an integral in the complex plane, and examined the displacement at the surface of the half-space and at the direction normal to the surface. We showed that the singularities of the displacement are linked to certain changes in the shape of the integration contour. In the second paper, we applied the expression for the normal displacement to the calculation of the elastic energy due to an external load, and found the amount of energy lost by a small ball incident onto an elastic half-space. In this publication, we expand the analysis by investigating the singularities of the displacement vector in an arbitrary point of the half-space, and briefly review our previous results.
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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 | 0.000 | 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 it