Mathematics Commons^™

An Analysis Of Capillary Flow In Finite Length Interior Corners, Samuel Shaw Mohler

Dissertations and Theses

We analyze the mathematical robustness of slow massively parallel interior corner flows in low gravity environments. An interior corner provides a preferential orientation in low gravity environments. This is a luxury usually only found on earth. It also provides a passive pumping mechanism due to geometry of a conduit. The driving force for this flow is a pressure difference due to local surface curvature gradients. An alternative reasoning is that due to the geometrical constraints the interior corner surface energy is unbounded below. This results in the liquid wicking into corners indefinitely. Interior corner flow's main quantity of interest is …

A Bayesian Nonparametric Multiple Testing Procedure For Comparing Several Treatments Against A Control, Luis Gutiérrez, Andrés Barrientos, Jorge González, Daniel Taylor-Rodríguez

Mathematics and Statistics Faculty Publications and Presentations

We propose a Bayesian nonparametric strategy to test for differences between a control group and several treatment regimes. Most of the existing tests for this type of comparison are based on the differences between location parameters. In contrast, our approach identifies differences across the entire distribution, avoids strong modeling assumptions over the distributions for each treatment, and accounts for multiple testing through the prior distribution on the space of hypotheses. The proposal is compared to other commonly used hypothesis testing procedures under simulated scenarios. Two real applications are also analyzed with the proposed methodology.

Keyword-Based Patent Citation Prediction Via Information Theory, Farshad Madani, Martin Zwick, Tugrul U. Daim

Engineering and Technology Management Faculty Publications and Presentations

Patent citation shows how a technology impacts other inventions, so the number of patent citations (backward citations) is used in many technology prediction studies. Current prediction methods use patent citations, but since it may take a long time till a patent is cited by other inventors, identifying impactful patents based on their citations is not an effective way. The prediction method offered in this article predicts patent citations based on the content of patents. In this research, Reconstructability Analysis (RA), which is based on information theory and graph theory, is applied to predict patent citations based on keywords extracted from …

Generalized Differential Calculus And Applications To Optimization, R. Blake Rector

Dissertations and Theses

This thesis contains contributions in three areas: the theory of generalized calculus, numerical algorithms for operations research, and applications of optimization to problems in modern electric power systems. A geometric approach is used to advance the theory and tools used for studying generalized notions of derivatives for nonsmooth functions. These advances specifically pertain to methods for calculating subdifferentials and to expanding our understanding of a certain notion of derivative of set-valued maps, called the coderivative, in infinite dimensions. A strong understanding of the subdifferential is essential for numerical optimization algorithms, which are developed and applied to nonsmooth problems in operations …

Shift-Symmetric Configurations In Two-Dimensional Cellular Automata: Irreversibility, Insolvability, And Enumeration, Peter Banda, John S. Caughman Iv, Martin Cenek, Christof Teuscher

Mathematics and Statistics Faculty Publications and Presentations

The search for symmetry as an unusual yet profoundly appealing phenomenon, and the origin of regular, repeating configuration patterns have been for a long time a central focus of complexity science, and physics.

Here, we introduce group-theoretic concepts to identify and enumerate the symmetric inputs, which result in irreversible system behaviors with undesired effects on many computational tasks. The concept of so-called configuration shift-symmetry is applied on two-dimensional cellular automata as an ideal model of computation. The results show the universal insolvability of “non-symmetric” tasks regardless of the transition function. By using a compact enumeration formula and bounding the number …

A Parabolic Equation Analysis Of The Underwater Noise Radiated By Impact Pile Driving, Nathan Laws

Dissertations and Theses

Impact pile driving can produce extremely high underwater sound levels, which are of increasing environmental concern due to their deleterious effects on marine wildlife. Prediction of underwater sound levels is important to the assessment and mitigation of the environmental impacts caused by pile driving. Current prediction methods are limited and do not account for the dynamic pile driving source, inhomogeneities in bathymetry and sediment, or physics-based sound wave propagation.

In this thesis, a computational model is presented that analyzes and predicts the underwater noise radiated by pile driving and is suitable for shallow, inhomogeneous environments and long propagation ranges. The …

A Class Of Discontinuous Petrov–Galerkin Methods. Part Iii: Adaptivity, Leszek Demkowicz, Jay Gopalakrishnan, Antti H. Niemi

Mathematics and Statistics Faculty Publications and Presentations

We continue our theoretical and numerical study on the Discontinuous Petrov–Galerkin method with optimal test functions in context of 1D and 2D convection-dominated diffusion problems and hp-adaptivity. With a proper choice of the norm for the test space, we prove robustness (uniform stability with respect to the diffusion parameter) and mesh-independence of the energy norm of the FE error for the 1D problem. With hp-adaptivity and a proper scaling of the norms for the test functions, we establish new limits for solving convection-dominated diffusion problems numerically: for 1D and for 2D problems. The adaptive process is fully automatic and starts …

Determination Of The Electric Field Intensity And Space Charge Density Versus Height Prior To Triggered Lightning, Christopher J. Biagi, Martin A. Uman, Jay Gopalakrishnan, J. D. Hill, Vladimir A. Rakov, T. Ngin, Douglas M. Jordan

Mathematics and Statistics Faculty Publications and Presentations

We infer the vertical profiles of space charge density and electric field intensity above ground by comparing modeling and measurements of the ground-level electric field changes caused by elevating grounded lightning-triggering wires. The ground-level electric fields at distances of 60 m and 350 m were measured during six wire launches that resulted in triggered lightning. The wires were launched when ground-level electric fields ranged from 3.2 to 7.6 kV m⁻¹ and the triggering heights ranged from 123 to 304 m. From wire launch time to lightning initiation time, the ground-level electric field reduction at 60 m ranged from 2.2 …

Polynomial Extension Operators. Part Iii, Leszek Demkowicz, Jay Gopalakrishnan, Joachim Schöberl

Mathematics and Statistics Faculty Publications and Presentations

In this concluding part of a series of papers on tetrahedral polynomial extension operators, the existence of a polynomial extension operator in the Sobolev space H(div) is proven constructively. Specifically, on any tetrahedron K, given a function w on the boundary ∂K that is a polynomial on each face, the extension operator applied to w gives a vector function whose components are polynomials of at most the same degree in the tetrahedron. The vector function is an extension in the sense that the trace of its normal component on the boundary ∂K coincides with w. Furthermore, the extension operator is …