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Articles 1 - 8 of 8
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Wave Scattering From Infinite Cylindrical Obstacles Of Arbitrary Cross-Section, Matthew B. Weber
Wave Scattering From Infinite Cylindrical Obstacles Of Arbitrary Cross-Section, Matthew B. Weber
Theses and Dissertations
In this work the scattering of an incident plane wave propagating along a plane perpendicular to the xy-plane is studied. The wave is scattered from an infinitely long cylindrical object of arbitrary cross-section. Due to the arbitrary geometry of the obstacle, a finite differences numerical method is employed to approximate the solution of the scattering problems. The wave equation is expressed in terms of generalized curvilinear coordinates. Boundary conforming grids are generated using elliptic grid generators. Then, a explicit marching in time scheme is implemented over these grids. It is found that as time grows the numerical solution converges to …
A Numerical Scheme For Mullins-Sekerka Flow In Three Space Dimensions, Sarah Marie Brown
A Numerical Scheme For Mullins-Sekerka Flow In Three Space Dimensions, Sarah Marie Brown
Theses and Dissertations
The Mullins-Sekerka problem, also called two-sided Hele-Shaw flow, arises in modeling a binary material with two stable concentration phases. A coarsening process occurs, and large particles grow while smaller particles eventually dissolve. Single particles become spherical. This process is described by evolving harmonic functions within the two phases with the moving interface driven by the jump in the normal derivatives of the harmonic functions at the interface. The harmonic functions are continuous across the interface, taking on values equal to the mean curvature of the interface. This dissertation reformulates the three-dimensional problem as one on the two-dimensional interface by using …
Psl(2,7)-Extensions With Certain Ramification At Two Primes, Glen E. Simpson
Psl(2,7)-Extensions With Certain Ramification At Two Primes, Glen E. Simpson
Theses and Dissertations
We conduct a parallel Hunter search in order to find a degree 7 number field K ramified at primes q and p with discriminant d(K)=q^6 p^2 where q=11 and 2
A New Approach To Lie Symmetry Groups Of Minimal Surfaces, Robert D. Berry
A New Approach To Lie Symmetry Groups Of Minimal Surfaces, Robert D. Berry
Theses and Dissertations
The Lie symmetry groups of minimal surfaces by way of planar harmonic functions are determined. It is shown that a symmetry group acting on the minimal surfaces is isomorphic with H × H^2 — the analytic functions and the harmonic functions. A subgroup of this gives a generalization of the associated family which is examined.
Ultraconnected And Critical Graphs, Jason Nicholas Grout
Ultraconnected And Critical Graphs, Jason Nicholas Grout
Theses and Dissertations
We investigate the ultraconnectivity condition on graphs, and provide further connections between critical and ultraconnected graphs in the positive definite partial matrix completion problem. We completely characterize when the join of graphs is ultraconnected, and prove that ultraconnectivity is preserved by Cartesian products. We completely characterize when adding a vertex to an ultraconnected graph preserves ultraconnectivity. We also derive bounds on the number of vertices which guarantee ultraconnectivity of certain classes of regular graphs. We give results from our exhaustive enumeration of ultraconnected graphs up to 11 vertices. Using techniques involving the Lovász theta parameter for graphs, we prove certain …
A Forbidden Subgraph Characterization Problem And A Minimal-Element Subset Of Universal Graph Classes, Michael D. Barrus
A Forbidden Subgraph Characterization Problem And A Minimal-Element Subset Of Universal Graph Classes, Michael D. Barrus
Theses and Dissertations
The direct sum of a finite number of graph classes H_1, ..., H_k is defined as the set of all graphs formed by taking the union of graphs from each of the H_i. The join of these graph classes is similarly defined as the set of all graphs formed by taking the join of graphs from each of the H_i. In this paper we show that if each H_i has a forbidden subgraph characterization then the direct sum and join of these H_i also have forbidden subgraph characterizations. We provide various results which in many cases allow us to exactly …
Problems Related To The Zermelo And Extended Zermelo Model, Benjamin Zachary Webb
Problems Related To The Zermelo And Extended Zermelo Model, Benjamin Zachary Webb
Theses and Dissertations
In this thesis we consider a few results related to the Zermelo and Extended Zermelo Model as well as outline some partial results and open problems related thereto. First we will analyze a discrete dynamical system considering under what conditions the convergence of this dynamical system predicts the outcome of the Extended Zermelo Model. In the following chapter we will focus on the Zermelo Model by giving a method for simplifying the derivation of Zermelo ratings for tournaments in terms of specific types of strongly connected components. Following this, the idea of stability of a tournament will be discussed and …
Lattices And Their Applications To Rational Elliptic Surfaces, Gretchen Rimmasch
Lattices And Their Applications To Rational Elliptic Surfaces, Gretchen Rimmasch
Theses and Dissertations
This thesis discusses some of the invariants of rational elliptic surfaces, namely the Mordell-Weil Group, Mordell-Weil Lattice, and another lattice which will be called the Shioda Lattice. It will begin with a brief overview of rational elliptic surfaces, followed by a discussion of lattices, root systems and Dynkin diagrams. Known results of several authors will then be applied to determine the groups and lattices associated with a given rational elliptic surface, along with a discussion of the uses of these groups and lattices in classifying surfaces.