Applied Mathematics Commons^™

The Truth About Lie Symmetries: Solving Differential Equations With Symmetry Methods, Ruth A. Steinhour

Senior Independent Study Theses

Differential equations are vitally important in numerous scientific fields. Oftentimes, they are quite challenging to solve. This Independent Study examines one method for solving differential equations. Norwegian mathematician Sophus Lie developed this method, which uses groups of symmetries, called Lie groups. These symmetries map one solution curve to another. They can be used to determine a canonical coordinate system for a given differential equation. Writing the differential equation in terms of a different coordinate system can make the equation simpler to solve. This I.S. explores techniques for finding a canonical coordinate system and using it to solve a given differential …

Population Models, Jessica Hauer

EWU Masters Thesis Collection

This thesis will examine mathematical interpretations of biological situations through the study of differential equations. It will first explore the interactions of the lynx and hare populations in Canada based on data retrieved by the Hudson Bay Company. The purpose of this study is to find a suitable mathematical model, namely that of a three-variable Lotka-Volterra system. Also, the paper will explore short-term infectious disease models as they relate to particular epidemics throughout history, including the Iowa Mumps outbreak of 1966 and the Bubonic Plaque. The thesis will then work to make sense of the rise and fall patterns in …

Mathematical Modelling Of Internal Heat Recovery In Flash Tank Heat Exchanger Cascades, Andrei Korobeinikov, John E. Mccarthy, Emma Mooney, Krum Semkov, James Varghese

Mathematics Faculty Research

Flash tank evaporation combined with a condensing heat exchanger can be used when heat exchange is required between two streams and where at least one of these streams is difficult to handle (tends severely to scale, foul, causing blockages). To increase the efficiency of heat exchange, a cascade of these units in series can be used. Heat transfer relationships in such a cascade are very complex due to their interconnectivity, thus the impact of any changes proposed is difficult to predict. Moreover, the distribution of loads and driving forces in different stages and the number of designed stages faces tradeoffs …

Generalized Analytic Fourier-Feynman Transform Of Functionals In A Banach Algebra F_(A1,A2)^(A,B), Jae Gil Choi, David Skough, Seung Jun Chang

Department of Mathematics: Faculty Publications

We introduce the Fresnel type class F_(A1,A2)^(a,b).We also establish the existence of the generalized analytic Fourier-Feynman transform for functionals in the Banach algebra F_(A1,A2)^(a,b).

Global Attracting Equilibria For Coupled Systems With Ceiling Density Dependence, Eric A. Eager, Mary Hebert, Elise Hellwig, Francisco Hernandez, Richard Rebarber, Brigitte Tenhumberg, Bryan Wigianto

School of Biological Sciences: Faculty Publications

In this paper, we present a system of two difference equations modeling the dynamics of a coupled population with two patches. Each patch can house only a limited number of individuals (called a carrying capacity) because resources like food and breeding sites are limited in each patch. We assume that the population in each patch is governed by a linear model until reaching a carrying capacity in each patch, resulting in map which is nonlinear and not sublinear. We analyze the global attractors of this model.

A Study Of Nonlinear Dynamics In Mathematical Biology, Joseph Ferrara

UNF Graduate Theses and Dissertations

We first discuss some fundamental results such as equilibria, linearization, and stability of nonlinear dynamical systems arising in mathematical modeling. Next we study the dynamics in planar systems such as limit cycles, the Poincaré-Bendixson theorem, and some of its useful consequences. We then study the interaction between two and three different cell populations, and perform stability and bifurcation analysis on the systems. We also analyze the impact of immunotherapy on the tumor cell population numerically.

Simulations Of Newtonian And Non-Newtonian Flows In Deformable Tubes, Abdallah A. Al-Habahbeh

Dissertations, Master's Theses and Master's Reports - Open

Computational models for the investigation of flows in deformable tubes are developed and implemented in the open source computing environment OpenFOAM. Various simulations for Newtonian and non-Newtonian fluids under various flow conditions are carried out and analyzed. First, simulations are performed to investigate the flow of a shear-thinning, non-Newtonian fluid in a collapsed elastic tube and comparisons are made with experimental data. The fluid is modeled by means of the Bird-Carreau viscosity law. The computational domain of the deformed tube is constructed from data obtained via computer tomography imaging. Comparison of the computed velocity fields with the ultrasound Doppler velocity …

Influence Of Mechanical And Thermal Boundary Conditions On Stabilizing/Destabilizing Mechanisms In Evaporating Liquid Films, Aneet Dharmavaram Narendranath

Dissertations, Master's Theses and Master's Reports - Open

Liquid films, evaporating or non-evaporating, are ubiquitous in nature and technology. The dynamics of evaporating liquid films is a study applicable in several industries such as water recovery, heat exchangers, crystal growth, drug design etc. The theory describing the dynamics of liquid films crosses several fields such as engineering, mathematics, material science, biophysics and volcanology to name a few.

Interfacial instabilities typically manifest by the undulation of an interface from a presumed flat state or by the onset of a secondary flow state from a primary quiescent state or both. To study the instabilities affecting liquid films, an evaporating/non-evaporating Newtonian …

The Machete Number, David Freund

Senior Independent Study Theses

Knot theory is a branch of topology that deals with the structure and properties of links. Employing a variety of tools, including surfaces, graph theory, and polynomials, we develop and explore classical link invariants. From this foundation, we de fine two novel link invariants, braid height and machete number, and investigate their properties and connection to classical invariants.

Creating A User Satisfaction Index From A Parsimonious Survey Instrument, Brian Barthel

All Graduate Theses, Dissertations, and Other Capstone Projects

In this paper we present a comprehensive method for creating a user satisfaction index using a survey instrument. First we construct a parsimonious survey instrument, using the PageRank Centrality, to measure attributes of user satisfaction. Then confirmatory factor analysis is applied to extract ``weights'' on the questions that are used in a linear model of computing the user satisfaction index. Throughout the paper an analysis of an existing data set is implemented to illustrate the proposed method. In addition the validity of the confirmatory factor model is tested using bootstrap sampling.

Hydrodynamic Modeling Of Ns-Laser Ablation, David Autrique, Vasilios Alexiades, Harihar Khanal

Publications

Laser ablation is a versatile and widespread technique, applied in an increasing number of medical, industrial and analytical applications. A hydrodynamic multiphase model describing nanosecond-laser ablation (ns- LA) is outlined. The model accounts for target heating and mass removal mechanisms as well as plume expansion and plasma formation. A copper target is placed in an ambient environment consisting of helium and irradiated by a nanosecond-laser pulse. The effect of variable laser settings on the ablation process is explored in 1-D numerical simulations.

Time-Stepping For Laser Ablation, Harihar Khanal, David Autrique, Vasilios Alexiades

Publications

Nanosecond laser ablation is a popular technique, applied in many areas of science and technology such as medicine, archaeology, chemistry, environmental and materials sciences. We outline a computational model for radiative and collisional processes occurring during ns-laser ablation, and compare the performance of various low and high order time-stepping algorithms.

Reduced-Order Modeling Using Orthogonal And Bi-Orthogonal Wavelet Transforms, Miguel Hernandez Iv

Open Access Theses & Dissertations

It is well known that model reduction methods borrow techniques typically found in data compression, and current state-of-the-art techniques for data compression are based on the wavelet transform. Given these facts, it is surprising that model reduction using wavelets has not received much attention and has not been adequately addressed in the literature. This research seeks to determine if wavelets can be used for model reduction and if wavelet model reduction is a viable alternative to existing model reduction methods.

In this work we propose a novel method for model reduction using wavelets. Specifically, we introduce techniques for deriving wavelet …

Automatic Elucidation Of Gpi Molecular Structures With Grid Computing Technology, Juan Clemente Aguilar Bonavides

Open Access Theses & Dissertations

Glycosylphosphatidylinositol (GPI)-anchored proteins are involved in many biological processes and are of medical importance. The identification and analysis of the entire collection of free and protein-linked GPIs within an organism (i.e., GPIomics) requires highly sensitive instruments. At present, liquid chromatography-tandem mass spectrometry (LC-MS/MS or -MSⁿ) is the most efficient laboratory technique for these tasks. As a typical MSⁿ experiment produces hundreds of thousands of spectra, the data analysis creates a major bottleneck in high-throughput GPIomic projects. Yet, no computational tool for characterizing the chemical structures of GPI is available to date. We propose a library-search algorithm to …

On Different Techniques For The Calculation Of Bouguer Gravity Anomalies For Joint Inversion And Model Fusion Of Geophysical Data In The Rio Grande Rift, Azucena Zamora

Open Access Theses & Dissertations

Density variations in the Earth result from different material properties, which reflect the tectonic processes attributed to a region. Density variations can be identified through measurable material properties, such as seismic velocities, gravity field, magnetic field, etc. Gravity anomaly inversions are particularly sensitive to density variations but suffer from significant non-uniqueness. However, using inverse models with gravity Bouguer anomalies and other geophysical data, we can determine three dimensional structural and geological properties of the given area. We explore different techniques for the calculation of Bouguer gravity anomalies for their use in joint inversion of multiple geophysical data sets and a …

Post-Pareto Optimality Methods For The Analysis Of Large Pareto Sets In Multi-Objective Optimization, Victor Manuel Carrillo

Open Access Theses & Dissertations

Multiple objective optimization involves the simultaneous optimization of more than one, possibly conflicting, objectives. Multiple objective optimization problems arise in a variety of real-world applications. In general, the main difference between single and multi-objective optimization is that in multi-objective optimization there is usually no single optimal solution, but a set of equally good alternatives with different trade-offs, also known as Pareto-optimal solutions. There are two general approaches to solve multiple objective optimization problems: mathematical methods and meta-heuristic methods. The first approach involves the aggregation of the attributes into a linear combination of the objective functions, also known as scalarization. The …

Modeling The Human Gait Phases Using Granular Computing, Melaku Ayenew Bogale

Open Access Theses & Dissertations

Gait analysis is applied for the provision of diagnosis, evaluation, and for the design of therapeutic intervention for subjects suffering from neurological disorders. The benefits accruing from gait analysis are well established. People with neurological disorders like mild traumatic brain injury, Cerebral Palsy and Multiple Sclerosis, suffer associated functional gait problems. The symptoms and sign of these gait deficits are different from subject to subject and even for the same subject at different stage of the disease. Identifying these gait related abnormalities helps in the treatment planning and rehabilitation process.

The dynamic behavior of gait parameters is cyclic and the …

A Block Operator Splitting Method For Heterogeneous Multiscale Poroelasticity, Paul M. Delgado

Open Access Theses & Dissertations

Traditional models of poroelastic deformation in porous media assume relatively homogeneous material properties such that macroscopic constitutive relations lead to accurate results. Many realistic applications involve heterogeneous material properties whose oscillatory nature require multiscale methods to balance accuracy and efficiency in computation.

The current study develops a multiscale method for poroelastic deformation based on a fixed point iteration based operator splitting method and a heterogeneous multiscale method using finite volume and direct stiffness methods. To characterize the convergence

of the operator splitting method, we use a numerical root finding algorithm to determine a threshold surface in a non-dimensional parameter space …

Unconstrained L1 Optimization With Applications To Signal And Image Processing, Carlos Andres Ramirez

Open Access Theses & Dissertations

In recent years, the applied mathematical community has witnessed a revolution that is changing the paradigm of classical signal and image processing. Novel and e efficient numerical algorithms have emerged for solving new challenges in large scale signal retrieval, where both constrained and unconstrained L1 minimization methods play a fundamental role.

In this work, we present a new methodology for solving unconstrained L1 minimization problems in the context of image and signal processing. Our approach consists in solving a sequence of relaxed unconstrained minimization problems depending on a positive regularization parameter that converges to zero. The optimality conditions of each …

A Convex Optimization Algorithm For Sparse Representation And Applications In Classification Problems, Reinaldo Sanchez Arias

Open Access Theses & Dissertations

In pattern recognition and machine learning, a classification problem refers to finding an algorithm for assigning a given input data into one of several categories. Many natural signals are sparse or compressible in the sense that they have short representations when expressed in a suitable basis. Motivated by the recent successful development of algorithms for sparse signal recovery, we apply the selective nature of sparse representation to perform classification. Any test sample is represented in an overcomplete dictionary with the training sample as base elements. A given test sample can be expressed as a linear combination of only those training …