Green’s functions for an anisotropic half-space and bimaterial incorporating anisotropic surface elasticity and surface van der Waals forces
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Bibliographic record
Abstract
In this paper we derive explicit expressions for the Green’s functions in the case of an anisotropic elastic half-space and bimaterial subjected to a line force and a line dislocation. In contrast to previous studies in this area, our analysis includes the contributions of both anisotropic surface elasticity and surface van der Waals interaction forces. By means of the Stroh sextic formalism, analytical continuation and the state-space approach, the corresponding boundary value problem is reduced to a system of six (for a half-space) or 12 (for a bimaterial) coupled first-order differential equations. By employing the orthogonality relations among the corresponding eigenvectors, the coupled system of differential equations is further decoupled to six (for a half-space) or 12 (for a bimaterial) independent first-order differential equations. The latter is solved analytically using exponential integrals. In addition, we identify four and seven non-zero intrinsic material lengths for a half-space and a bimaterial, respectively, due entirely to the incorporation of the surface elasticity and surface van der Waal forces. We prove that these material lengths can be only either real and positive or complex conjugates with positive real parts.
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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)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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