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Spring 2017
We explore the connection between Eynard-Orantin Topological Recursion (EOTR) and the asymptotic solutions to differential equations constructed with the WKB method (named for its creators Wentzel, Kramers and Brillouin). Using the Airy spectral curve as an initial example, we propose a general...
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Fall 2021
Topological Recursion began its life as a series of recursive equations aimed at solving constraints which occur in matrix models of Quantum Field Theory. After its inception, Topological Recursion was given a more abstract formulation in terms of Quantum Airy Structures and has since been of...
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Fall 2012
This thesis is interested in the topological recursion first introduced in \cite{CEO} and generalized to algebraic curves in \cite{Eynard:2007,Eynard:2008}. A presentation of the Hermitian matrix model is given and includes a derivation of this topological recursion. The second part introduces a...
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Fall 2022
The topological recursion is a construction in algebraic geometry that takes in the data of a so-called spectral curve, $\mathcal{S}=\left(\Sigma,x,y\right)$ where $\Sigma$ is a Riemann surface and $x,y:\Sigma\to\mathbb{C}_\infty$ are meromorphic, and recursively constructs correlators which, in...
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Spring 2024
Additive Manufacturing (AM) is a transformative method in industrial manufacturing, facilitating the creation of lighter, stronger, and smarter parts and systems. Both plastic and metal AM technologies are extensively employed in various fields, including medical, automotive, and aeronautical...
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Fall 2010
Deformation of the orthodontic bracket upon wire engagement may result in torque dissipation within the bracket rather than transmission to the tooth and its supporting structures. The purpose of this study was: 1) quantify the amount of torque expression and 2) quantify any deformation as a...
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Fall 2017
To fully utilize magnetic structures, a rich understanding of their physical properties and magnetic interactions is required. As device sizes shrink to the nanoscale, it is also important to acquire characterization information in the presence of inevitable intrinsic pinning sites....