Browsing Pure & Applied Mathematics (Theses and Dissertations) by Subject "Mathematics, Ph.D."
Now showing items 120 of 26

A dynamical study of the chirally rotated Schrödinger functional in lattice QCD
(Trinity College (Dublin, Ireland). School of Mathematics, 2015)In this work, we present first results from dynamical simulations of the chirally rotated Schrödinger functional (SF) in lattice QCD. More specifically, we discuss the determination of renormalization constants of ... 
A formulation of discrete differential geometry applied to fermionic lattice field theory and its implications for chiral symmetry
(Trinity College (Dublin, Ireland). School of Mathematics, 2008)In this thesis, we develop the Geometric Discretization formulation of DiracKahler fermions. We note that the naive definition of chiral synnnetry is only approximately captured in the formulation. However, we show that ... 
A theoretical study of spin filtering and its application to polarizing antiprotons
(Trinity College (Dublin, Ireland). School of Mathematics, 2008)There has been much recent research into possible methods of polarizing an antiproton beam, the most promising being spin filtering, the theoretical understanding of which is currently incomplete. The method of polarization ... 
Anisotropic discretisations and practical alltoall propagators for lattice QCD
(Trinity College (Dublin, Ireland). School of Mathematics, 2006)In this thesis, we concern ourselves primarily with improving the accuracy of the determination of correlation functions in lattice QCD. We detail two avenues of improvement and implement them both, separately and in ... 
Aspects of the mathematical theory of water waves
(Trinity College (Dublin, Ireland). School of Mathematics, 2007)In this thesis we study various aspects of the mathematical theory of water waves. In Chapter 2 some qualitative results for two recentlyderived nonlinear models for shallow water waves are presented. In the first part ... 
CFTs on Riemann surfaces of genus g ≥ 1
(Trinity College (Dublin, Ireland). School of Mathematics, 2014)The purpose of this thesis is to argue that Npoint functions of holomorphic fields in rational conformal field theories can be calculated by methods from algebraic geometry. We establish explicit formulae for the 2point ... 
CR Singularities in condimension 2
(Trinity College (Dublin, Ireland). School of Mathematics, 2013)In this thesis we study the real submanifolds of codimension 2 in a complex manifold near a CR singularity. The thesis has 3 chapters. In Chapter 1 we shall make a small introduction where we will remind some basic notions ... 
Cₒ(X)structure in C*algebras, multiplier algebras and tensor products
(Trinity College (Dublin, Ireland). School of Mathematics, 2015)We begin in Chapter 2 with an introduction to the various notions of a bundle of C*algebras that have appeared throughout the literature, and clarify the definitions of upper and lowersemicontinuous C*bundles not ... 
Discrete exterior calculus with applications to flows and spinors
(Trinity College (Dublin, Ireland). School of Mathematics, 2005) 
Elements of an operator calculus
(Trinity College (Dublin, Ireland). School of Mathematics, 2001)The operational calculus developed by the Irish School of the Vienna Development Method (VDM) has a life of its own independent of its applications. This thesis is interested in the operational calculus that arose from ... 
Free Field Representation and Form Factors of the Chiral GrossNeveu Model
(Trinity College (Dublin, Ireland). School of Mathematics, 2013)The process of using the free field representation to construct form factors of two dimensional integrable models is very promising. In this thesis, this procedure is analysed and adapted for application to the chiral ... 
Integrable lattice models for strongly correlated electrons
(Trinity College (Dublin, Ireland). School of Mathematics, 2013)This thesis is dedicated to the study of a new family of integrable lattice models for strongly correlated electrons, namely the Hubbard Shastry models. The techniques of exactly solvable models, and in particular those ... 
Interferometry and nonequilibrium noise in the fractional quantum Hall effect
(Trinity College (Dublin, Ireland). School of Mathematics, 2014)We study theoretical aspects of fractional quantum Hall devices based on tunnelling point contacts. The fractional quantum Hall effect is the prime example of a (2 + 1) dimensional system with nontrivial topological order. ... 
Methods for calculating option prices with earlyexercise features
(Trinity College (Dublin, Ireland). School of Mathematics, 2006)In this dissertation we deal with two distinct methods for pricing financial options with earlyexercise features. First we use finite difference methods to calculate the prices, examining in particular two new schemes ... 
Novel methods for heavyquark physics from lattice QCD
(Trinity College (Dublin, Ireland). School of Mathematics, 2006)The application of 3+1 anisotropic lattices to numerical simulations of hadrons containing heavy quarks is investigated. It is expected that using a fine temporal lattice spacing will suppress large massdependent errors ... 
Peturbative study of the Chirally Rotated Schrödinger Functionality in Lattice QCD
(Trinity College (Dublin, Ireland). School of Mathematics, 2014)In this thesis we study the renormalisation and O(a) improvement of the Chirally Rotated Schrödinger Functional (xSF) in perturbation theory. The xSF was originally proposed in [1] as a way of rehabiliting the mechanism ... 
Pionpion scattering amplitudes and timelike pion form factor from Nf=2+1 Lattice QCD
(Trinity College (Dublin, Ireland). School of Mathematics, 2017)We study isovector pionpion scattering and extract the electromagnetic pion form factor in the timelike region from Nf = 2 + 1 Lattice QCD ensembles at a single lattice spacing and two pion masses mπ = 200MeV and mπ = ... 
Random sampling and large deviations
(Trinity College (Dublin, Ireland). School of Mathematics, 2001)In this thesis, we are concerned with the effect of randomly sampling a stochastic process. We consider two stochastic processes: the underlying process, {Xt}tεT and the observation process {Tn}nεN, a strictly increasing ... 
Robust layerresolving methods for various Prandtl problems
(Trinity College (Dublin, Ireland). School of Mathematics, 2005)In this thesis we deal with four Prandtl boundary layer problems for incompressible laminar flow. When the Reynolds and Prandtl numbers are large the solution of each problem has parabolic boundary layers. For each problem ... 
Simulated annealing of Skyrme model configurations
(Trinity College (Dublin, Ireland). School of Mathematics, 2006)The Skyrme model is a topological field theory that has been shown to be a good low energy approximation to QCD. A particular quantum theoretical treatment of the model reduces the quantization to a finitedimensional ...