dc.contributor.advisor | Hardin, Doug | |
dc.contributor.advisor | Saff, Edward | |
dc.creator | Tenpas, Nathaniel Jay | |
dc.date.accessioned | 2024-08-15T18:19:19Z | |
dc.date.available | 2024-08-15T18:19:19Z | |
dc.date.created | 2024-08 | |
dc.date.issued | 2024-07-12 | |
dc.date.submitted | August 2024 | |
dc.identifier.uri | http://hdl.handle.net/1803/19159 | |
dc.description.abstract | We develop linear programming bounds for the energy of configurations in Euclidean space which are periodic with respect to a lattice.
In certain cases, the construction of sharp bounds can be formulated as a finite dimensional, multivariate polynomial interpolation problem. We construct sequences of such problems whose solutions would complete the Cohn-Kumar universal optimality conjecture for the hexagonal lattice.
We solve the base cases and obtain novel results about the optimality of the hexagonal lattice among certain periodic configurations for a wide range of interactions, including inverse power laws and Gaussians. | |
dc.format.mimetype | application/pdf | |
dc.language.iso | en | |
dc.subject | Point Configurations | |
dc.subject | Energy Minimization | |
dc.subject | Analysis | |
dc.subject | Metric Geometry | |
dc.subject | Mathematical Physics, Linear Programming | |
dc.subject | Lattices | |
dc.subject | Hexagonal Lattice | |
dc.subject | Universal Optimality | |
dc.subject | Computational Geometry | |
dc.subject | Potential Theory | |
dc.title | Linear Programming Bounds for Periodic Energy Problems | |
dc.type | Thesis | |
dc.date.updated | 2024-08-15T18:19:19Z | |
dc.type.material | text | |
thesis.degree.name | PhD | |
thesis.degree.level | Doctoral | |
thesis.degree.discipline | Mathematics | |
thesis.degree.grantor | Vanderbilt University Graduate School | |
dc.creator.orcid | 0000-0002-3004-1511 | |
dc.contributor.committeeChair | Hardin, Doug | |