Physical Sciences and Mathematics Commons^™

Interplay Of Quantum Size Effect, Anisotropy And Surface Stress Shapes The Instability Of Thin Metal Films, Mikhail Khenner

Mathematics Faculty Publications

Morphological instability of a planar surface ([111], [011], or [001]) of an ultra-thin metal film is studied in a parameter space formed by three major effects (the quantum size effect, the surface energy anisotropy and the surface stress) that influence a film dewetting. The analysis is based on the extended Mullins equation, where the effects are cast as functions of the film thickness. The formulation of the quantum size effect (Z. Zhang et al., PRL 80, 5381 (1998)) includes the oscillation of the surface energy with thickness caused by electrons confinement. By systematically comparing the effects, their contributions into the …

Information Theoretic Study Of Gaussian Graphical Models And Their Applications, Ali Moharrer

LSU Doctoral Dissertations

In many problems we are dealing with characterizing a behavior of a complex stochastic system or its response to a set of particular inputs. Such problems span over several topics such as machine learning, complex networks, e.g., social or communication networks; biology, etc. Probabilistic graphical models (PGMs) are powerful tools that offer a compact modeling of complex systems. They are designed to capture the random behavior, i.e., the joint distribution of the system to the best possible accuracy. Our goal is to study certain algebraic and topological properties of a special class of graphical models, known as Gaussian graphs. First, …

Numerical Methods For Nonlinear Optimal Control Problems And Their Applications In Indoor Climate Control, Runxin He

McKelvey School of Engineering Theses & Dissertations

Efficiency, comfort, and convenience are three major aspects in the design of control systems for residential Heating, Ventilation, and Air Conditioning (HVAC) units. In this dissertation, we study optimization-based algorithms for HVAC control that minimizes energy consumption while maintaining a desired temperature, or even human comfort in a room. Our algorithm uses a Computer Fluid Dynamics (CFD) model, mathematically formulated using Partial Differential Equations (PDEs), to describe the interactions between temperature, pressure, and air flow. Our model allows us to naturally formulate problems such as controlling the temperature of a small region of interest within a room, or to control …

Time Varying Parameter Estimation Scheme For A Linear Stochastic Differential Equation.Pdf, Michael Otunuga

Olusegun Michael Otunuga

On The Ramberg-Osgood Stress-Strain Model And Large Deformations Of Cantilever Beams, Ronald J. Giardina Jr

University of New Orleans Theses and Dissertations

In this thesis the Ramberg-Osgood nonlinear model for describing the behavior of many different materials is investigated. A brief overview of the model as it is currently used in the literature is undertaken and several misunderstandings and possible pitfalls in its application is pointed out, especially as it pertains to more recent approaches to finding solutions involving the model. There is an investigation of the displacement of a cantilever beam under a combined loading consisting of a distributed load across the entire length of the beam and a point load at its end and new solutions to this problem are …

Simulation Of Driven Elastic Spheres In A Newtonian Fluid, Shikhar M. Dwivedi

Electronic Thesis and Dissertation Repository

Simulations help us test various restrictions/assumptions placed on physical systems that would otherwise be difficult to efficiently explore experimentally. For example, the Scallop Theorem, first stated in 1977, places limitations on the propulsion mechanisms available to microscopic objects in fluids. In particular, the theorem states that when the viscous forces in a fluid dominate the inertial forces associated with a physical body, such a physical body cannot generate propulsion by means of reciprocal motion. The focus of this thesis is to firstly, explore an adaptive Multiple-timestep(MTS) scheme for faster molecular dynamics(MD) simulations, and secondly, use hybrid MD-LBM(Lattice-Boltzman Method) to test …

On Honey Bee Colony Dynamics And Disease Transmission, Matthew I. Betti

Electronic Thesis and Dissertation Repository

The work herein falls under the umbrella of mathematical modeling of disease transmission. The majority of this document focuses on the extent to which infection undermines the strength of a honey bee colony. These studies extend from simple mass-action ordinary differential equations models, to continuous age-structured partial differential equation models and finally a detailed agent-based model which accounts for vector transmission of infection between bees as well as a host of other influences and stressors on honey bee colony dynamics. These models offer a series of predictions relevant to the fate of honey bee colonies in the presence of disease …

Thermodynamics Of Coherent Structures Near Phase Transitions, Julia M. Meyer, Ivan Christov

The Summer Undergraduate Research Fellowship (SURF) Symposium

Phase transitions within large-scale systems may be modeled by nonlinear stochastic partial differential equations in which system dynamics are captured by appropriate potentials. Coherent structures in these systems evolve randomly through time; thus, statistical behavior of these fields is of greater interest than particular system realizations. The ability to simulate and predict phase transition behavior has many applications, from material behaviors (e.g., crystallographic phase transformations and coherent movement of granular materials) to traffic congestion. Past research focused on deriving solutions to the system probability density function (PDF), which is the ground-state wave function squared. Until recently, the extent to which …

Evolution Of Delayed Dispersal And Subsequent Emergence Of Helping, With Implications For Cooperative Breeding., Geoff Wild, Judith Korb

Applied Mathematics Publications

Cooperative breeding occurs when individuals help raise the offspring of others. It is widely accepted that help displayed by cooperative breeders emerged only after individuals' tendency to delay dispersal had become established. We use this idea as a basis for two inclusive-fitness models: one for the evolution of delayed dispersal, and a second for the subsequent emergence of helpful behavior exhibited by non-breeding individuals. We focus on a territorial species in a saturated environment, and allow territories to be inherited by non-breeding individuals who have delayed dispersal. Our first model predicts that increased survivorship and increased fecundity both provide an …

Math Department Newsletter, 2017, University Of Dayton. Department Of Mathematics

Department of Mathematics Newsletters

No abstract provided.

Regularized Solutions For Terminal Problems Of Parabolic Equations., Sujeewa Indika Hapuarachchi

Electronic Theses and Dissertations

The heat equation with a terminal condition problem is not well-posed in the sense of Hadamard so regularization is needed. In general, partial differential equations (PDE) with terminal conditions are those in which the solution depends uniquely but not continuously on the given condition. In this dissertation, we explore how to find an approximation problem for a nonlinear heat equation which is well-posed. By using a small parameter, we construct an approximation problem and use a modified quasi-boundary value method to regularize a time dependent thermal conductivity heat equation and a quasi-boundary value method to regularize a space dependent thermal …

Prediction Of Stress Increase In Unbonded Tendons Using Sparse Principal Component Analysis, Eric Mckinney

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

While internal and external unbonded tendons are widely utilized in concrete structures, the analytic solution for the increase in unbonded tendon stress, Δ���, is challenging due to the lack of bond between strand and concrete. Moreover, most analysis methods do not provide high correlation due to the limited available test data. In this thesis, Principal Component Analysis (PCA), and Sparse Principal Component Analysis (SPCA) are employed on different sets of candidate variables, amongst the material and sectional properties from the database compiled by Maguire et al. [18]. Predictions of Δ��� are made via Principal Component Regression models, and the method …

Exponential Integrator Methods For Nonlinear Fractional Reaction-Diffusion Models, Olaniyi Samuel Iyiola

Theses and Dissertations

Nonlocality and spatial heterogeneity of many practical systems have made fractional differential equations very useful tools in Science and Engineering. However, solving these type of models is computationally demanding. In this work, we propose an exponential integrator method for nonlinear fractional reaction-diffusion equations. This scheme is based on using a real distinct poles discretization for the underlying matrix exponentials. Due to these real distinct poles, the algorithm could be easily implemented in parallel to take advantage of multiple processors for increased computational efficiency. The method is established to be second-order convergent; and proven to be robust for problems involving non-smooth/mismatched …

Transcriptome Of Neonatal Prebotzinger Complex Neurones In Dbx1 Reporter Mice, John A. Hayes, (…), Ronald D. Smith, Gregory D. Smith, Margaret S. Saha, Christopher A. Del Negro

Arts & Sciences Articles

We sequenced the transcriptome of brainstem interneurons in the specialized respiratory rhythmogenic site dubbed preBotzinger Complex (preBotC) from newborn mice. To distinguish molecular characteristics of the core oscillator we compared preBotC neurons derived from Dbx1-expressing progenitors that are respiratory rhythmogenic to neighbouring non-Dbx1-derived neurons, which support other respiratory and non-respiratory functions. Results in three categories are particularly salient. First, Dbx1 preBotC neurons express kappa-opioid receptors in addition to mu-opioid receptors that heretofore have been associated with opiate respiratory depression, which may have clinical applications. Second, Dbx1 preBotC neurons express the hypoxia-inducible transcription factor Hif1a at levels three-times higher than non-Dbx1 …

Numerical Solution Of Partial Differential Equations Using Polynomial Particular Solutions, Thir R. Dangal

Dissertations

Polynomial particular solutions have been obtained for certain types of partial differential operators without convection terms. In this dissertation, a closed-form particular solution for more general partial differential operators with constant coefficients has been derived for polynomial basis functions. The newly derived particular solutions are further coupled with the method of particular solutions (MPS) for numerically solving a large class of elliptic partial differential equations. In contrast to the use of Chebyshev polynomial basis functions, the proposed approach is more flexible in selecting the collocation points inside the domain. Polynomial basis functions are well-known for yielding ill-conditioned systems when their …

Large-Scale Online Feature Selection For Ultra-High Dimensional Sparse Data, Yue Wu, Steven C. H. Hoi, Tao Mei, Nenghai Yu

Research Collection School Of Computing and Information Systems

Feature selection (FS) is an important technique in machine learning and data mining, especially for large scale high-dimensional data. Most existing studies have been restricted to batch learning, which is often inefficient and poorly scalable when handling big data in real world. As real data may arrive sequentially and continuously, batch learning has to retrain the model for the new coming data, which is very computationally intensive. Online feature selection (OFS) is a promising new paradigm that is more efficient and scalable than batch learning algorithms. However, existing online algorithms usually fall short in their inferior efficacy. In this article, …

Some Problems Arising From Mathematical Model Of Ductal Carcinoma In Situ., Heng Li

Electronic Theses and Dissertations

Ductal carcinoma in situ (DCIS) is the earliest form of breast cancer. Three mathematical models in the one dimensional case arising from DCIS are proposed. The first two models are in the form of parabolic equation with initial and known moving boundaries. Direct and inverse problems are considered in model 1, existence and uniqueness are proved by using tool from heat potential theory and Volterra integral equations. Also, we discuss the direct problem and nonlocal problem of model 2, existence and uniqueness are proved. And approximation solution of these problems are implemented by Ritz-Galerkin method, which is the first attempt …

Extending Difference Of Votes Rules On Three Voting Models., Sarah Schulz King

Electronic Theses and Dissertations

In a voting situation where there are only two competing alternatives, simple majority rule outputs the alternatives with the most votes or declares a tie if both alternatives receive the same number of votes. For any non-negative integer k, the difference of votes rule M_k outputs the alternative that beats the competing alternative by more than k votes. Llamazares (2006) gives a characterization of the difference of votes rules in terms of five axioms. In this thesis, we extend Llamazares' result by completely describing the class of voting rules that satisfy only two out of his five axioms. …

Eignefunctions For Partial Differential Equations On Two-Dimensional Domains With Piecewise Constant Coefficients, Abdullah Muheel Momit Aurko

Master's Theses

In this thesis, we develop a highly accurate and efficient algorithm for computing the solution of a partial differential equation defined on a two-dimensional domain with discontinuous coefficients. An example of such a problem is for modeling the diffusion of heat energy in two space dimensions, in the case where the spatial domain represents a medium consisting of two different but homogeneous materials, with periodic boundary conditions.

Since diffusivity changes based on the material, it will be represented using a piecewise constant function, and this results in the formation of a complicated mathematical model. Such a model is impossible to …

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 …

A Stable Algorithm For Divergence-Free And Curl-Free Radial Basis Functions In The Flat Limit, Kathryn Primrose Drake

Boise State University Theses and Dissertations

Radial basis functions (RBFs) were originally developed in the 1970s for interpolating scattered topographic data. Since then they have become increasingly popular for other applications involving the approximation of scattered, scalar-valued data in two and higher dimensions, especially data collected on the surface of a sphere. In the late 2000s, matrix-valued RBFs were introduced for approximating divergence-free and curl-free vector fields on the surface of a sphere from scattered samples, which arise naturally in atmospheric and oceanic sciences. The intriguing property of these RBFs is that the resulting vector-valued approximations analytically preserve the divergence-free or curl-free properties of the field. …

Joint Inversion Of Compact Operators, James Ford

Boise State University Theses and Dissertations

The first mention of joint inversion came in [22], where the authors used the singular value decomposition to determine the degree of ill-conditioning in inverse problems. The authors demonstrated in several examples that combining two models in a joint inversion, and effectively stacking discrete linear models, improved the conditioning of the problem. This thesis extends the notion of using the singular value decomposition to determine the conditioning of discrete joint inversion to using the singular value expansion to determine the well-posedness of joint linear operators. We focus on compact linear operators related to geophysical, electromagnetic subsurface imaging.

The operators are …

Multi-Rate Runge-Kutta-Chebyshev Time Stepping For Parabolic Equations On Adaptively Refined Meshes, Talin Mirzakhanian

Boise State University Theses and Dissertations

In this thesis, we develop an explicit multi-rate time stepping method for solving parabolic equations on a one dimensional adaptively refined mesh. Parabolic equations are characterized by their stiffness and as a result are usually solved using implicit time stepping schemes [16]. However, implicit schemes have the disadvantage that they can be expensive in higher dimensions or complicated to implement on adaptive or otherwise non-uniform meshes. Moreover, for coupled systems of parabolic equations, it can be difficult to achieve the expected order of accuracy without using sophisticated operator splitting techniques. For these reasons, we seek to exploit the properties of …

Solution Of Pdes For First-Order Photobleaching Kinetics Using Krylov Subspace Spectral Methods, Somayyeh Sheikholeslami

Dissertations

We solve the first order reaction-diffusion equations which describe binding-diffusion kinetics using a photobleaching scanning profile of a confocal laser scanning microscope approximated by a Gaussian laser profile. We show how to solve these equations with prebleach steady-state initial conditions using a time-domain method known as a Krylov Subspace Spectral (KSS) method. KSS methods are explicit methods for solving time- dependent variable-coefficient partial differential equations (PDEs). KSS methods are advantageous compared to other methods because of their stability and their superior scalability. These advantages are obtained by applying Gaussian quadrature rules in the spectral domain developed by Golub and Meurant. …

Fluid Dynamics Of Watercolor Painting : Experiments And Modelling, David Edward Baron

Theses, Dissertations and Culminating Projects

In his classic study in 1908, A.M. Worthington gave a thorough account of splashes and their formation through visualization experiments. In more recent times, there has been renewed interest in this subject, and much of the underlying physics behind Worthington's experiments has now been clarified. One specific set of such recent studies, which motivates this thesis, concerns the fluid dynamics behind Jackson Pollock's drip paintings. The physical processes and the mathematical structures hidden in his works have received serious attention and have made the scientific pursuit of art a compelling area of exploration. Our current work explores the interaction of …

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 …

Cayley Graphs Of Groups And Their Applications, Anna Tripi

MSU Graduate Theses

Cayley graphs are graphs associated to a group and a set of generators for that group (there is also an associated directed graph). The purpose of this study was to examine multiple examples of Cayley graphs through group theory, graph theory, and applications. We gave background material on groups and graphs and gave numerous examples of Cayley graphs and digraphs. This helped investigate the conjecture that the Cayley graph of any group (except Z_2) is hamiltonian. We found the conjecture to still be open. We found Cayley graphs and hamiltonian cycles could be applied to campanology (in particular, to the …

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 Option Pricing Under The Two-Factor Models, Jiacheng Cai

UNLV Theses, Dissertations, Professional Papers, and Capstones

Pricing options under multi-factor models are challenging and important problems for financial applications. In particular, the closed form solutions are not available for the American options and some European options, and the correlations between factors increase the complexity and difficulty for the formulations and implements of the numerical methods.

In this dissertation, we first introduce a general transformation to decouple correlated stochastic processes governed by a system of stochastic differential equations. Then we apply the transformation to the popular two-factor models: the two-asset model, the stochastic volatility model, and the stochastic interest rate models. Based on our new formulations, we …

Trace Formulas For Perturbations Of Operators With Hilbert-Schmidt Resolvents, Bishnu Prasad Sedai

Mathematics & Statistics ETDs

In this dissertation, we study Taylor approximations of functions of operators with Hilbert-Schmidt resolvents. We obtain integral representations for traces of the respective Taylor remainders that are analogous to trace formulas obtained in the case of Schatten perturbations in [10, 11, 16].