Other Physical Sciences and Mathematics Commons^™

Equivalence Of Contact Gluing Maps In Sutured Floer Homology, Federico Salmoiraghi

LSU Doctoral Dissertations

The contact invariant from Heegaard Floer homology is a useful tool for studying

contact structures. This invariant is preserved under cut-and-paste operations

by contact gluing maps of Honda, Kazez, and Matic. However, these maps are

difficult to compute in practice, even in simple cases.

We show that the contact gluing map of Honda, Kazez, and Matic

has a natural description in terms of bordered sutured Floer homology. In

particular, we establish Zarev’s conjecture that his pairing on sutured Floer

homology is equivalent to the contact gluing map.

Design Of Metamaterials For Optics, Abiti Adili

LSU Doctoral Dissertations

First part of this dissertation studies the problem of designing metamaterial crystals with double negative effective properties for applications in optics by investigating the conditions necessary for generating novel dispersion properties in a metamaterial crystal with subwavelength microstructure. This provides novel optical properties created through local resonances tied to the geometry of the media in subwavelength regime.

In the second part, this dissertation studies the representation formula used to describe band structures in photonic crystals with plasmonic inclusions. By using layer potential techniques, a magnetic dipole operator describing the tangential component of the electrical field generated by magnetic distribution is …

Bipartite Quantum Interactions: Entangling And Information Processing Abilities, Siddhartha Das

LSU Doctoral Dissertations

The aim of this thesis is to advance the theory behind quantum information processing tasks, by deriving fundamental limits on bipartite quantum interactions and dynamics. A bipartite quantum interaction corresponds to an underlying Hamiltonian that governs the physical transformation of a two-body open quantum system. Under such an interaction, the physical transformation of a bipartite quantum system is considered in the presence of a bath, which may be inaccessible to an observer. The goal is to determine entangling abilities of such arbitrary bipartite quantum interactions. Doing so provides fundamental limitations on information processing tasks, including entanglement distillation and secret key …

Shifting Niche Space In Coastal Landscapes: Spatio-Temporal Patterns Driving Submerged Aquatic Vegetation Across The Northern Gulf Of Mexico, Kristin Elise Demarco

LSU Doctoral Dissertations

Identifying distributions of submerged aquatic vegetation (SAV) across the northern Gulf of Mexico (NGOM) coastal landscape necessitates describing ecological processes in estuarine gradients. SAV assemblages are ecological indicators of aquatic ecosystem health; spatial and temporal distributions are strongly correlated to environmental conditions. Many wildlife species, including waterfowl, are dependent on SAV and seeds in NGOM coastal marshes for food and habitat. To understand SAV distributions at multiple spatial and temporal scales a multi-tiered project was designed to collect SAV presence, species assemblage, and cover data, and cores to describe seed food. The first tier sampled inter-annually in the growing seasons …