Trefethen, Lloyd N. and Betcke, Timo (2005) Computed eigenmodes of planar regions. AMS Contemporary Mathematics. (In Press)
![[thumbnail of trefethen_updated.pdf]](https://eprints.maths.manchester.ac.uk/style/images/fileicons/application_pdf.png) |
PDF
trefethen_updated.pdf Download (1MB) |
Abstract
Recently developed numerical methods make possible the high-accuracy computation of eigenmodes of the Laplacian for a variety of "drums" in two dimensions. A number of computed examples are presented together with a discussion of their implications concerning bound and continuum states, isospectrality, symmetry and degeneracy, eigenvalue avoidance, resonance, localization, eigenvalue optimization, perturbation of eigenvalues and eigenvectors, and other matters.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | billiards, drums, Helmholtz equation, level repulsion, membranes, quantum chaos, Schrödinger operator |
| Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis |
| Depositing User: | Dr. Timo Betcke |
| Date Deposited: | 14 Sep 2006 |
| Last Modified: | 20 Oct 2017 14:12 |
| URI: | https://eprints.maths.manchester.ac.uk/id/eprint/594 |
Actions (login required)
 |
View Item |