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Articles 1 - 9 of 9
Full-Text Articles in Physical Sciences and Mathematics
Sensitivity Analysis In Magnetic Resonance Elastography And A Local Wavelength Reconstruction Based On Wave Direction, Christopher Gillam
Sensitivity Analysis In Magnetic Resonance Elastography And A Local Wavelength Reconstruction Based On Wave Direction, Christopher Gillam
All Dissertations
or the detection of early stage cancer. MRE utilizes interior data for its inverse problems, which greatly reduces the ill-posedness from which most traditional inverse problems suffer.
In this thesis, we first establish a sensitivity analysis for viscoelastic scalar medium with complex wave number and compare it with the purely elastic case. Also we estimate the smallest detectable inclusion for breast and liver, which is about twice larger than using the purely elastic model. We also found the existence of optimal frequency (50 Hz) that maximizes the detectability when the Voigt model is used.
Second, we propose a local wavelength …
Polyhedral Approximations Of Quadratic Semi-Assignment Problems, Disjunctive Programs, And Base-2 Expansions Of Integer Variables, Frank Muldoon
Polyhedral Approximations Of Quadratic Semi-Assignment Problems, Disjunctive Programs, And Base-2 Expansions Of Integer Variables, Frank Muldoon
All Dissertations
This research is concerned with developing improved representations for special families of mixed-discrete programming problems. Such problems can typically be modeled using different mathematical forms, and the representation employed can greatly influence the problem's ability to be solved. Generally speaking, it is desired to obtain mixed 0-1 linear forms whose continuous relaxations provide tight polyhedral outer-approximations to the convex hulls of feasible solutions. This dissertation makes contributions to three distinct problems, providing new forms that improve upon published works.
The first emphasis is on devising solution procedures for the classical quadratic semi-assignment problem(QSAP), which is an NP-hard 0-1 quadratic program. …
Sensitivity Anaylsis And Detectability For Magnetic Resonance Elastography, Catherine White
Sensitivity Anaylsis And Detectability For Magnetic Resonance Elastography, Catherine White
All Dissertations
This thesis is for a sensitivity analysis of magnetic resonance elastography, a hybrid imaging technique used in early-stage cancer screening. To quantitatively analyze the sensitivity, we introduce a notion of detectability, which is dened as a relative amplitude
drop in a small sti tumor region. This analysis is accomplished in both the full elastic and viscoelastic models and compared with that of the simpler scalar model which is frequently used in the actual application.
Some of the highlights are 1) a useful formula for detectability in terms of physical parameters, which will help the design of experiments; 2) the discrepancy …
Physicic-Based Algorithms And Divergence Free Finite Elements For Coupled Flow Problems, Nicholas Wilson
Physicic-Based Algorithms And Divergence Free Finite Elements For Coupled Flow Problems, Nicholas Wilson
All Dissertations
This thesis studies novel physics-based methods for
simulating incompressible fluid flow described by the Navier-Stokes equations (NSE) and
magnetohydrodynamics equations (MHD).
It is widely accepted in computational fluid dynamics (CFD) that numerical schemes which are more
physically accurate lead to more precise flow simulations especially over long time intervals.
A prevalent theme throughout will be the inclusion of as much
physical fidelity in numerical solutions as efficiently possible. In algorithm design, model
selection/development, and element choice, subtle changes can provide better physical accuracy,
which in turn provides better overall accuracy (in any measure). To this end we develop and study …
Sparsity Regularization In Diffuse Optical Tomography, John Cooper
Sparsity Regularization In Diffuse Optical Tomography, John Cooper
All Dissertations
The purpose of this dissertation is to improve image reconstruction in Diffuse Optical Tomography (DOT), a high contrast imaging modality that uses a near infrared light source. Because the scattering and absorption of a tumor varies significantly from healthy tissue, a reconstructed spatial representation of these parameters serves as tomographic image of a medium. However, the high scatter and absorption of the optical source also causes the inverse problem to be severely ill posed, and currently only low resolution reconstructions are possible, particularly when using an unmodulated direct current (DC) source.
In this work, the well posedness of the forward …
Modular Forms, Elliptic Curves And Drinfeld Modules, Catherine Trentacoste
Modular Forms, Elliptic Curves And Drinfeld Modules, Catherine Trentacoste
All Dissertations
In this thesis we explore three different subfields in the area of number theory. The first topic we investigate involves modular forms, specifically nearly holomorphic eigenforms. In Chapter 3, we show the product of two nearly holomorphic eigenforms is an eigenform for only a finite list of examples. The second type of problem we analyze is related to the rank of elliptic curves. Specifically in Chapter 5 we give a graph theoretical approach to calculating the size of 3-Selmer groups for a given family of elliptic curves. By calculating the size of the 3-Selmer groups, we give an upper bound …
On Factoring Hecke Eigenforms, Nearly Holomorphic Modular Forms, And Applications To L-Values, Jeff Beyerl
On Factoring Hecke Eigenforms, Nearly Holomorphic Modular Forms, And Applications To L-Values, Jeff Beyerl
All Dissertations
This thesis is a presentation of some of my research activities while at Clemson University. In particular this includes joint work on the factorization of eigenforms and their relationship to Rankin- Selberg L-values, and nearly holomorphic eigenforms. The main tools used on the factorization of eigenforms are linear algebra, the j function, and the Rankin-Selberg Method. The main tool used on nearly holomorphic modular forms is the Rankin-Cohen bracket operator.
A Collection Of Problems In Combinatorics, Janine Janoski
A Collection Of Problems In Combinatorics, Janine Janoski
All Dissertations
We present several problems in combinatorics including the partition function, Graph Nim, and the evolution of strings.
Let p(n) be the number of partitions of n. We say a sequence an is log-concave if for every n, an2 &ge an+1 an-1. We will show that p(n) is log-concave for n &ge 26. We will also show that for n<26, p(n) alternatively satisfies and does not satisfy the log-concave property. We include results for the Sperner property of the partition function.
The second problem we present is the game of Graph Nim. We use the Sprague-Grundy theorem to analyze modified versions of Nim played on various graphs. We include progress made towards proving that all G-paths …
An Optimization Approach To A Geometric Packing Problem, Bradley Paynter
An Optimization Approach To A Geometric Packing Problem, Bradley Paynter
All Dissertations
We investigate several geometric packing problems (derived from an industrial setting) that involve fitting patterns of regularly spaced disks without overlap. We first derive conditions for achieving the feasible placement of a given set of patterns and construct a network formulation that, under certain conditions, allows the calculation of such a placement. We then discuss certain related optimization problems (e.g., fitting together the maximum number of patterns) and broaden the field of application by showing a connection to the well-known Periodic Scheduling Problem. In addition, a variety of heuristics are developed for solving large-scale instances of these provably difficult packing …