Physical Sciences and Mathematics Commons^™

Mathematical Modeling Of Mixtures And Numerical Solution With Applications To Polymer Physics, John Timothy Cummings

Doctoral Dissertations

We consider in this dissertation the mathematical modeling and simulation of a general diffuse interface mixture model based on the principles of energy dissipation. The model developed allows for a thermodynamically consistent description of systems with an arbitrary number of different components, each of which having perhaps differing densities. We also provide a mathematical description of processes which may allow components to source or sink into other components in a mass conserving, energy dissipating way, with the motivation of applying this model to phase transformation. Also included in the modeling is a unique set of thermodynamically consistent boundary conditions which …

Efficient Methods For Multidimensional Global Polynomial Approximation With Applications To Random Pdes, Peter A. Jantsch

Doctoral Dissertations

In this work, we consider several ways to overcome the challenges associated with polynomial approximation and integration of smooth functions depending on a large number of inputs. We are motivated by the problem of forward uncertainty quantification (UQ), whereby inputs to mathematical models are considered as random variables. With limited resources, finding more efficient and accurate ways to approximate the multidimensional solution to the UQ problem is of crucial importance, due to the “curse of dimensionality” and the cost of solving the underlying deterministic problem.

The first way we overcome the complexity issue is by exploiting the structure of the …

Numerical Methods For Non-Divergence Form Second Order Linear Elliptic Partial Differential Equations And Discontinuous Ritz Methods For Problems From The Calculus Of Variations, Stefan Raymond Schnake

Doctoral Dissertations

This dissertation consists of three integral parts. Part one studies discontinuous Galerkin approximations of a class of non-divergence form second order linear elliptic PDEs whose coefficients are only continuous. An interior penalty discontinuous Galerkin (IP-DG) method is developed for this class of PDEs. A complete analysis of the proposed IP-DG method is carried out, which includes proving the stability and error estimate in a discrete W^2;p-norm [W^2,p-norm]. Part one also studies the convergence of the vanishing moment method for this class of PDEs. The vanishing moment method refers to a PDE technique for approximating these PDEs by a …

Assessing The Economic Tradeoffs Between Prevention And Suppression Of Forest Fires, Elizabeth Trulia Heines

Doctoral Dissertations

The number of large-scale, high-severity forest fires occurring in the United States is increasing, as is the cost to suppress these fires. These trends have prompted investigations into alternative fuels methods to help prevent these large wildfires. One of the key challenges in studying the costs and benefits of forest fire prevention management is the incorporation of risk and uncertainty surrounding management decisions. We use a technique developed by William Reed to incorporate the stochasticity of the time of a forest fire into our optimal control problems. The goal of these problems is to determine the optimal fire prevention management …

Jet-Hadron Correlations Relative To The Event Plane Pb--Pb Collisions At The Lhc In Alice, Joel Anthony Mazer

Doctoral Dissertations

In relativistic heavy ion collisions at the Large Hadron Collider (LHC), a hot, dense and strongly interacting medium known as the Quark Gluon Plasma (QGP) is produced. Quarks and gluons from incoming nuclei collide to produce partons at high momenta early in the collisions. By fragmenting into collimated sprays of hadrons, these partons form 'jets'. Within the framework of perturbative Quantum Chromodynamics (pQCD), jet production is well understood in pp collisions. We can use jets measured in pp interactions as a baseline reference for comparing to heavy ion collision systems to detect and study jet quenching. The jet quenching mechanism …

Analysis Of A Market For Tradable Credits, Policy Uncertainty Effects On Investment Decisions, And The Potential To Supply A Renewable Aviation Fuel Industry With An Experimental Industrial Oilseed, Evan Lawrence Markel

Doctoral Dissertations

This research is aligned with identifying barriers throughout the alternative jet-fuel supply chain. Prices are analyzed in the market for tradable credits known as renewable identification numbers (RINs). The RIN market is a key policy instrument used in the implementation of the renewable fuel standard (RFS). The program is highly complex and drivers of RIN price are not always clear. RIN prices also exhibit multiple regimes where the price of nested RINs converge. Therefore, a smooth transition autoregressive model is employed to examine drivers of RIN price and to identify drivers of price regime change. Through research in the RIN …

Surface Energy In Bond-Counting Models On Bravais And Non-Bravais Lattices, Tim Ryan Krumwiede

Doctoral Dissertations

Continuum models in computational material science require the choice of a surface energy function, based on properties of the material of interest. This work shows how to use atomistic bond-counting models and crystal geometry to inform this choice. We will examine some of the difficulties that arise in the comparison between these models due to differing types of truncation. New crystal geometry methods are required when considering materials with non-Bravais lattice structure, resulting in a multi-valued surface energy. These methods will then be presented in the context of the two-dimensional material graphene in a way that correctly predicts its equilibrium …

Accuracy And Stability Of Integration Methods For Neutrino Transport In Core Collapse Supernovae, Kyle A. Gregory

Chancellor’s Honors Program Projects

No abstract provided.