Confirmation of the Aharonov-Bohm effect without interaction with the solenoid border
New Eulerian methods for problems with interfaces, with emphasis in fluid mechanics
| Full text | |
| Author(s): |
Birgin, E. G.
;
Fernandez, L.
;
Haeser, G.
;
Laurain, A.
Total Authors: 4
|
| Document type: | Journal article |
| Source: | JOURNAL OF GEOMETRIC ANALYSIS; v. 33, n. 6, p. 28-pg., 2023-06-01. |
| Abstract | |
The problem of minimizing the first eigenvalue of the Dirichlet Laplacian with respect to a union of m balls with fixed identical radii and variable centers in the plane is investigated in the present work. The existence of a minimizer is shown and the shape sensitivity analysis of the eigenvalue with respect to the centers' positions is presented. With this tool, the derivative of the eigenvalue is computed and used in a numerical algorithm to determine candidates for minimizers. Candidates are also constructed by hand based on regular polygons. Numerical solutions contribute in at least three aspects. They corroborate the idea that some of the candidates based on regular polygons might be optimal. They also suggest alternative regular patterns that improve solutions associated with regular polygons. Lastly and most importantly, they delivered better quality solutions that do not follow any apparent pattern. Overall, for low values of m, candidates for minimizers of the eigenvalue are proposed and their geometrical properties as well as the appearance of regular patterns formed by the centers are discussed. (AU) | |
| FAPESP's process: | 18/24293-0 - Computational methods in optimization |
| Grantee: | Sandra Augusta Santos |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry |
| Grantee: | Francisco Louzada Neto |
| Support Opportunities: | Research Grants - Research, Innovation and Dissemination Centers - RIDC |
| FAPESP's process: | 16/01860-1 - Cutting, packing, lot-sizing, scheduling, routing and location problems and their integration in industrial and logistics settings |
| Grantee: | Reinaldo Morabito Neto |
| Support Opportunities: | Research Projects - Thematic Grants |