Pure & Applied Mathematics (Theses and Dissertations): Recent submissions
Now showing items 41-60 of 71
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Anisotropic discretisations and practical all-to-all 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 ... -
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 finite-dimensional ... -
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 recently-derived nonlinear models for shallow water waves are presented. In the first part ... -
Novel methods for heavy-quark 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 mass-dependent errors ... -
Methods for calculating option prices with early-exercise features
(Trinity College (Dublin, Ireland). School of Mathematics, 2006)In this dissertation we deal with two distinct methods for pricing financial options with early-exercise features. First we use finite difference methods to calculate the prices, examining in particular two new schemes ... -
Robust layer-resolving 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 ... -
Towards Excited Radiative Transitions in Charmonium
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2019)In this thesis lattice QCD is utilised to investigate the spectrum of charmonium and charmed mesons with the aim of working towards investigating radiative transitions between excited states in the charmonium spectrum. ... -
Complexity of Holographic Flavours and causality in QFTs with Gauss-Bonnet dual
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2019)This thesis is the compilation of two different projects undertaken during my PhD programme. Chapter 2 covers the work on quantum complexity. Quantum complexity of a thermofield double state in a strongly coupled quantum ... -
String breaking from Lattice QCD with Nf=2+1 dynamical fermions
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2019)In quantum chromodynamics (QCD), the static potential V (r) is defined as the energy of the ground state of the system containing a static quark and a static antiquark, separated by a distance r. As a consequence of confinement, ... -
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 ... -
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 the ... -
Interferometry and non-equilibrium 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 non-trivial topological order. ... -
Pion-pion scattering amplitudes and timelike pion form factor from Nf=2+1 Lattice QCD
(Trinity College (Dublin, Ireland). School of Mathematics, 2017)We study isovector pion-pion 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 = ... -
Higher Spin Theories in Twistor Space
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2018)In this thesis we formulate an action principle for conformal higher spin theory on twistor space. For this theory, and for a unitary sub-sector that we identify, we construct an MHV amplitude expansion by considering ... -
Form Factors, Integrability and the AdS/CFT Correspondence
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2018)Form factors are matrix elements of local operators between scattering states, and are interesting off-shell objects in any QFT. In this thesis we will focus on the world-sheet theory describing strings in AdS5xS5, the ... -
Charmed tetraquarks from lattice QCD
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2018) -
The Ads/CFT spectrum via Integrability-based algorithms
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2017)The spectral problem of the AdS/CFT correspondence is believed to be integrable in the planar limit. The Quantum Spectral Curve captures the underlying mathematical structure in a relatively simple Riemann-Hilbert problem. ... -
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 lower-semicontinuous C*-bundles not ... -
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 ... -
Spectral functions from lattice QCD at finite temperature
(Trinity College (Dublin, Ireland). School of Mathematics, 2015)An investigation of the bottonionium spectrum above and below the QCD deconfinement crossover temperature, Tc, was performed using a non-relativistic treatment of the heavy quark on anisotropic lattices with Nf = 2 + 1 ...
