Beyond dust survival: the inner regions of protoplanetary disks
Using generative adversarial networks to represent geometries of vertical-axis win...
Evolution of the radius of analyticity for dispersive equations and systems involv...
| Full text | |
| Author(s): |
Birgin, Ernesto G.
;
Gardenghi, John L.
;
Laurain, Antoine
Total Authors: 3
|
| Document type: | Journal article |
| Source: | MATHEMATICS OF OPERATIONS RESEARCH; v. N/A, p. 36-pg., 2023-09-12. |
| Abstract | |
The problem of covering a two-dimensional bounded set with a fixed number of minimum-radius identical disks is studied in the present work. Bounds on the optimal radius are obtained for a certain class of nonsmooth domains, and an asymptotic expansion of the bounds as the number of disks goes to infinity is provided. The proof is based on the approximation of the set to be covered by hexagonal honeycombs and on the thinnest covering property of the regular hexagonal lattice arrangement in the whole plane. The dependence of the optimal radius on the number of disks is also investigated numerically using a shape-optimization approach, and theoretical and numerical convergence rates are compared. An initial point construction strategy is introduced, which, in the context of a multistart method, finds good-quality solutions to the problem under consideration. Extensive numerical experiments with a variety of polygonal regions and regular polygons illustrate the introduced approach. (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: | 19/25258-7 - A nonlinear optimization approach to the covering problem |
| Grantee: | Rafael Massambone de Oliveira |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| 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 |