Exact Solution to the Contact Problem in a Quarter-Plane of a Multilayer Medium by the Universal Simulation Method
Bibliographic record
Abstract
Abstract In this paper, for the first time, an exact solution to the contact problem posed on the surface of a multilayer medium in a quarter-plane is constructed. This is achieved by applying a new universal modeling method developed for studying and solving boundary value problems for partial differential equations. In this paper, the method is applied to two-dimensional Wiener–Hopf integral equations in the quarter-plane arising in mixed problems of deformable solid mechanics, in contact problems. A feature of mixed problems for layered media is the presence of meromorphic functions in Fourier transformations of the kernels of integral equations. As in differential equations, this made it possible to find fragments of differential equations in the representation of Wiener–Hopf integral equations and to find a way to reduce a two-dimensional integral equation to one-dimensional. This makes it possible to reduce integral equations in this field to infinite systems of linear algebraic equations having an inverse infinite matrix. This type of integral equations is not available for numerical solution, due to the unlimited scope of the equation, and has not been studied analytically before. The exact solution to the two-dimensional Wiener–Hopf equation in a quarter-plane makes it possible to construct high-precision solutions to contact problems in limited domains, just like in the one-dimensional case. Wiener–Hopf integral equations are widely used in various fields for materials with complex rheology, including strength theory, diffraction, flaw detection, and tribology.
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How this classification was reachedexpand
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 | 0.001 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".