Browsing by Author "Larry Norris, Committee Member"

Now showing 1 - 4 of 4

Fermat Curves on Weighted Projective Planes
(2007-05-03) Kermes, Jeremiah Mitchell; Amassa Fauntleroy, Committee Chair; Tom Lada, Committee Member; Larry Norris, Committee Member; Loek Helminck, Committee Member
This paper takes the classical result that a homogeneous polynomial of degree d≥2 defines a curve of genus
Geometric Invariant Theory Compactification of Quintic Threefolds.
(2010-08-17) Lakhani, Chirag; Amassa Fauntleroy, Committee Chair; Thomas Lada, Committee Member; Larry Norris, Committee Member; Seth Sullivant, Committee Member
The Lageos Satellite: A Comprehensive Spin Model and Analysis
(2002-12-19) Williams, Scott Everett; Arkady Kheyfets, Committee Chair; Ron Fulp, Committee Member; Larry Norris, Committee Member; Pierre Gremaud, Committee Member
A thorough investigation into the theoretical modeling of the Laser-Ranged Geodynamics Satellite (Lageos I) spin state evolution is presented. Starting from an existing dynamical model, we analyze in detail each of the model's assumptions and explore possible enhancements. Additional concerns not considered by the original model are also scrutinized in a bottom-up approach. In particular, we re-evaluate the orbit propagation module, survey and investigate all possible space-environment effects, assess numerical implementation concerns, and perform a number of software feature modifications. In the process, a parameterized approach is adopted and corresponding non-linear optimization tools are integrated into the revamped model. The outcome is a comprehensive, open-source model of the Lageos I spin dynamics which exhibits a significant advance in predictive accuracy. A corollary of the effort is a broad survey of the important space environment effects on the attitude of passive satellites. In addition, a thorough analysis of the model results is presented along with an expanded discussion of the interesting discoveries we made. Particularly significant is the sensitivity of the spin state evolution to small changes in the principal moments of the satellite–an idea discounted by previous efforts that nevertheless can be analytically verified. A consequence of the effort is the immediate application to a number of ongoing research activities involving the Lageos I satellite. Of particular interest is the potential role of Lageos I in a proposed experiment to measure the general relativistic force known as gravitomagnetism. A precise understanding of the evolution of Lageos' spin dynamics is required so that correlated thermal effects may be properly accounted for in the evaluation of orbital motion. A related effort is the attempt to empirically measure the spin state based on optical glint data. This process must be seeded with a quality initial estimate of the spin axis orientation for proper evaluation of the data. The model we present has implications for both of these efforts.
The Role of sh-Lie Algebras in Lagrangian Field Theory.
(2004-02-11) Al-Ashhab, Samer Shafiq; Tom Lada, Committee Member; Larry Norris, Committee Member; Steve Schecter, Committee Member; Ron Fulp, Committee Chair
The purpose of this dissertation is to study strongly homotopy Lie algebras (sh-Lie algebras) and their applications with primary emphasis on applications to field theory. Strongly homotopy Lie algebras are defined on graded vector spaces. They generally consist of an infinite sequence of mappings $l_1,l_2,l_3,cdots$, which satisfy certain identities. We show that, in the presence of appropriate hypotheses, there always exists a simplified sh-Lie algebra structure with $l_n=0$ for $n>3$. This is a special case which has occured in several applications. While it is known that sh-Lie algebras arise in field theory as a homological resolution of a Poisson bracket defined on the space of local functionals, we show how these sh-Lie algebras transform in the event of canonical transformations on the space of local functionals. Additionally, it is shown how a group which acts via canonical transformations transforms the sh-Lie structure and eventually leads to reduction theorems. Two kinds of reduction are obtained corresponding to two different kinds of group action and, in each case it is shown how to obtain an induced sh-Lie algebra on a corresponding reduced graded vector space. Several applications of the theory are considered as well.