Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- Convex hull (2)
- ALE (1)
- Absorption time (1)
- Alpha-models (1)
- Barotropic Vorticity Equations (1)
-
- Binary expansion (1)
- Combinatorics (1)
- Congestion (1)
- Detectability (1)
- Disjunctions (1)
- Eigenform (1)
- Facets (1)
- Fluid-structure interaction problem (1)
- Geometric Packing (1)
- Grad-div stabilization (1)
- Graph decompositions (1)
- Graph nim (1)
- Graphs (1)
- Hamilton cycles (1)
- Hamiltonian cycles (1)
- Hybrid imaging (1)
- Incompressible flow (1)
- Knapsack problem (1)
- L-value (1)
- Local (1)
- Magnetic resonance elastography (1)
- Magnetohydrodynamics equations (1)
- Modular form (1)
- Multi-commodity (1)
- Multicommodity (1)
- Publication
Articles 1 - 17 of 17
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. …
Convex Hull Characterization Of Special Polytopes In N-Ary Variables, Ruobing Shen
Convex Hull Characterization Of Special Polytopes In N-Ary Variables, Ruobing Shen
All Theses
This paper characterizes the convex hull of the set of n-ary vectors that are lexicographically less than or equal to a given such vector. A polynomial number of facets is shown to be sufficient to describe the convex hull. These facets generalize the family of cover inequalities for the binary case. They allow for advances relative to both the modeling of integer variables using base-n expansions, and the solving of n-ary knapsack problems with weakly super-decreasing coefficients.
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 …
Robust Parameter Estimation In The Weibull And The Birnbaum-Saunders Distribution, Jing Zhao
Robust Parameter Estimation In The Weibull And The Birnbaum-Saunders Distribution, Jing Zhao
All Theses
This paper concerns robust parameter estimation of the two-parameter Weibull distribution and the two-parameter Birnbaum-Saunders distribution. We use the proposed method to estimate the distribution parameters from (i) complete samples with and without contamination (ii) type-II censoring samples, in both distributions. Also, we consider the maximum likelihood estimation and graphical methods to compare the maximum likelihood estimation and graphical method with the proposed method based on quantile. We find the advantages and disadvantages for those three different methods.
Branching Rules For Minimum Congestion Multi-Commodity Flow Problems, Cameron Megaw
Branching Rules For Minimum Congestion Multi-Commodity Flow Problems, Cameron Megaw
All Theses
In this paper, we examine various branch and bound algorithms for a minimum congestion origin-destination integer multi-commodity flow problem.
The problem consists of finding a routing such that the congestion of the most congested arc is minimum. For our implementation, we assume that all demands are known a priori.
We provide a mixed integer linear programming formulation of our problem and propose various new branching rules to solve the model. For each rule, we provide theoretical and experimental proof of their effectiveness.
In order to solve large instances, that more accurately portray real-world applications, we outline a path formulation model …
A Set Of Tournaments With Many Hamiltonian Cycles, Hayato Ushijima-Mwesigwa
A Set Of Tournaments With Many Hamiltonian Cycles, Hayato Ushijima-Mwesigwa
All Theses
For a random tournament on $3^n$ vertices, the expected number of Hamiltonian cycles is known to be $(3^n -1)!/2^{3^n}$. Let $T_1$ denote a tournament of three vertices $ {v_1, v_2, v_3}$. Let the orientation be such that there are directed edges from $v_1 $to $v_2$ , from $v_2$ to $v_3$ and from $v_3$ to $ v_1$. Construct a tournament $T_i$ by making three copies of $T_{i-1}$, $T_{i-1}'$, $T_{i-1}''$ and $T_{i-1}'''$. Let each vertex in $T_{i-1}'$ have directed edges to all vertices in $T_{i-1}''$, similarly place directed edges from each vertex in $T_{i-1}''$ to all vertices in $T_{i-1}'''$ and from $T_{i-1}'''$ …
Local Polynomial Regression With Application To Sea Surface Temperatures, Michael Finney
Local Polynomial Regression With Application To Sea Surface Temperatures, Michael Finney
All Theses
Our problem involves methods for determining the times of a maximum or minimum for a general mean function in time series data. The methods explored here involve polynomial smoothing. In theory, the methods calculate a general number of derivatives of the estimated polynomial. Using these techniques, we wish to find a balance between error, variance, and complexity and apply it to a time series of sea surface temperatures. We will first explore the theory behind the method and then find a way to optimally apply it to our data.
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 …
Enhanced Physics Schemes For The 2d Ns-Alpha Models Of Incompressible Flow, Michael Dowling
Enhanced Physics Schemes For The 2d Ns-Alpha Models Of Incompressible Flow, Michael Dowling
All Theses
In this thesis, we study algorithms for the 2D NS-alpha model of incompressible flow. These schemes conserve both discrete energy and discrete enstrophy in the absence of viscous and external forces, and otherwise admit exact balances for them analogous to those of true fluid flow. This model belongs to a very small group that conserves both of these quantities in the continuous case, and in this work, we develop finite element algorithms for the vorticity-stream formulation of this model that will preserve numerical energy and enstrophy in the computed solutions.
Numerical Study For A Viscoelastic Fluid-Structure Interaction Problem, Shuhan Xu
Numerical Study For A Viscoelastic Fluid-Structure Interaction Problem, Shuhan Xu
All Theses
In this thesis, we consider a viscoelastic flow in a moving domain, which has significant applications in biology and industry. Numerical approximation schemes are developed based on the Arbitrary Lagrangian-Eulerian (ALE) formulation of the flow equations. A spatial discretization is accomplished by the finite element method, and the time descritization is carried by either the implicit Euler method or the Crank-Nicolson method. Numerical results are presented for a fluid in a moving domain, where the boundary movement is specified by a given function. Then, we extend our work to a fluid-structure interaction problem. This system consists of a two-dimensional viscoelastic …
Champion Primes For Elliptic Curves, Jason Hedetniemi
Champion Primes For Elliptic Curves, Jason Hedetniemi
All Theses
Let Ea,b be the elliptic curve y2 = x3 + ax + b over Fp. A well known result of Hasse states that over Fp
(p+1) - 2p½ ≤ #Ea,b ≤ (p+1)+2p½
If #Ea,b = (p+1) + floor(2p½) over Fp and Ea,b is nonsingular, then we call p a champion prime for Ea,b. We will discuss methods for finding champion primes for elliptic curves. In addition, we will show that the set of elliptic curves which have a champion prime has density one.