Applied Mathematics Commons^™

Random Number Generation: Types And Techniques, David F. Dicarlo

Senior Honors Theses

What does it mean to have random numbers? Without understanding where a group of numbers came from, it is impossible to know if they were randomly generated. However, common sense claims that if the process to generate these numbers is truly understood, then the numbers could not be random. Methods that are able to let their internal workings be known without sacrificing random results are what this paper sets out to describe. Beginning with a study of what it really means for something to be random, this paper dives into the topic of random number generators and summarizes the key …

Determining Angular Frequency From A Video With A Generalized Fast Fourier Transform, Lindsay N. Smith

Theses and Dissertations

Suppose we are given a video of a rotating object and suppose we want to determine the rate of rotation solely from the video itself and its known frame rate. In this thesis, we present a new mathematical operator called the Geometric Sum Transform (GST) that can help one determine the angular frequency of the object in question. The GST is a generalization of the discrete Fourier transform (DFT) and as such, the two transforms have much in common. However, whereas the DFT is applied to a sequence of scalars, the GST can be applied to a sequence of vectors. …

Local Histograms For Per-Pixel Classification, Melody L. Massar

Theses and Dissertations

We introduce a rigorous mathematical theory for the analysis of local histograms, and study how they interact with textures that can be modeled as occlusions of simpler components. We first show how local histograms can be computed as a system of convolutions and discuss some basic local histogram properties. We then introduce a probabilistic, occlusion-based model for textures and formally demonstrate that local histogram transforms are natural tools for analyzing the textures produced by our model. Next, we characterize all nonlinear transforms which satisfy the three key properties of local histograms and consider the appropriateness of local histogram features in …

On Soliton Interactions For A Hierarchy Of Generalized Heisenberg Ferromagnetic Models On Su(3)/S(U(1) $\Times$ U(2)) Symmetric Space, Vladimir Gerdjikov, Georgi Grahovski, Alexander Mikhailov, Tihomir Valchev

Articles

We consider an integrable hierarchy of nonlinear evolution equations (NLEE) related to linear bundle Lax operator L. The Lax representation is Z2 \times Z2 reduced and is naturally associated with the symmetric space SU(3)/S(U(1) \times U(2)). The simplest nontrivial equation in the hierarchy is a generalization of Heisenberg ferromagnetic model. We construct the N-soliton solutions for an arbitrary member of the hierarchy by using the Zakharov-Shabat dressing method with an appropriately chosen dressing factor. Two types of soliton solutions: quadruplet and doublet solitons are found. The one-soliton solutions of NLEEs with even and odd dispersion laws have different properties. In …

Preconditioning Visco-Resistive Mhd For Tokamak Plasmas, Daniel R. Reynolds, Ravi Samtaney, Hilari C. Tiedeman

Mathematics Research

No abstract provided.

Ball Remotality In Banach Spaces And Related Topics., Tanmoy Paul

Doctoral Theses

In this project we aim to study Ball Remotality and densely Ball Remotality of subspaces in Banach spaces. We study this property in many classical spaces of type c0, c,\\â„“p and C(K) where K is a compact Hausdorff space. The said problem also discussed for Banach spaces when considered as a subspace in its bidual. It is observed M-ideals in C(K) are densely ball remotal. It is shown that a particular type of M-ideal in A(K) where K is a Choquet simplex is densely ball remotal.

The Immersed Interface Method For Two-Fluid Problems, Miguel Uh, Sheng Xu

Mathematics Research

No abstract provided.

Numerical Solution Of Integral Equations In Solidification And Laser Melting, Elizabeth Case, Johannes Tausch

Mathematics Research

No abstract provided.

Heterogeneous Multiscale Modeling Of Advection-Diffusion Problems, David J. Gardner, Daniel R. Reynolds

Mathematics Research

No abstract provided.

Multilevel Schur Complement Preconditioner For Multi-Physics Simulations, Hilari Tiedeman, Daniel Reynolds

Mathematics Research

No abstract provided.

Effects Of Stochastic Freshwater Flux On The Atlantic Thermohaline Circulation, Alyssa Pampell, Alejandra Aceves

Mathematics Research

No abstract provided.

Block Preconditioning Of Stiff Implicit Models For Radiative Ionization In The Early Universe, Daniel R. Reynolds, Robert Harkness, Geoffrey So, Michael L. Norman

Mathematics Research

No abstract provided.

On The Stability Of A Microstructure Model, Mihhail Berezovski, Arkadi Berezovski

Publications

Abstract

The asymptotic stability of solutions of the Mindlin-type microstructure model for solids is analyzed in the paper. It is shown that short waves are asymptotically stable even in the case of a weakly non-convex free energy dependence on microdeformation.

Research highlights

The Mindlin-type microstructure model cannot describe properly short wave propagation in laminates. A modified Mindlin-type microstructure model with weakly non-convex free energy resolves this discrepancy. It is shown that the improved model with weakly non-convex free energy is asymptotically stable for short waves.

Estimation Of Performance Indices For The Planning Of Sustainable Transportation Systems, Pankaj Maheshwari, Alexander Paz, Pushkin Kachroo

Graduate Publications & Presentations

What is sustainable transportation system?

Fulfill the needs of current generations without compromising the ability of future generations

Utilize resources without compromising their health and productivity Leads to development that improves quality of life

Assimilate economic, ecological, social, and bio-physical components of resource ecosystems

Minimize the use of renewable and non-renewable resources, provide affordability and equity between generations

A Local Radial Basis Function Method For The Numerical Solution Of Partial Differential Equations, Maggie Elizabeth Chenoweth

Theses, Dissertations and Capstones

Most traditional numerical methods for approximating the solutions of problems in science, engineering, and mathematics require the data to be arranged in a structured pattern and to be contained in a simply shaped region, such as a rectangle or circle. In many important applications, this severe restriction on structure cannot be met, and traditional numerical methods cannot be applied. In the 1970s, radial basis function (RBF) methods were developed to overcome the structure requirements of existing numerical methods. RBF methods are applicable with scattered data locations. As a result, the shape of the domain may be determined by the application …

A Study Of The Gam Approach To Solve Laminar Boundary Layer Equations In The Presence Of A Wedge, Rahmat Ali Khan, Muhammad Usman

Mathematics Faculty Publications

We apply an easy and simple technique, the generalized ap- proximation method (GAM) to investigate the temperature field associated with the Falkner-Skan boundary-layer problem. The nonlinear partial differ- ential equations are transformed to nonlinear ordinary differential equations using the similarity transformations. An iterative scheme for the non-linear ordinary differential equations associated with the velocity and temperature profiles are developed via GAM. Numerical results for the dimensionless ve- locity and temperature profiles of the wedge flow are presented graphically for different values of the wedge angle and Prandtl number.

Proceedings Of The Graduate Student Symposium Of The 7th International Conference On The Theory And Application Of Diagrams, July 5 2012, Ozge Alacam, Farrukh Arslan, Andrew Blake, Lillian Fanjoy, Luke Macneill, Gorkem Pacaci, Alistair Stead, Peter Vivian, Cengiz Acarturk, Gem Stapleton, Peter Rodgers, John Howse, Andreas Hamfelt, Nathan Miller

Mathematical Sciences Faculty Publications

Proceedings of the Graduate Student Symposium held at the 7th International Conference on the Theory and Application of Diagrams, ("Diagrams 2012"), held at the University of Kent on July 5, 2012. Dr. Nathaniel Miller, professor of in the School of Mathematical Sciences at UNC, served on the symposium organizing committee.

The Secretary Problem From The Applicant's Point Of View, Darren B. Glass

Math Faculty Publications

Searching for a job is always stressful and, with unemployment rates at their highest levels in years, never more so than now. Applicants can and should use every advantage at their disposal to obtain a job which is rewarding, financially and otherwise. While this author believes a math major gives applicants many advantages as they search for their dream job, one often overlooked is the ability to strategize and schedule their interviews to maximize the chance of landing that job.

Second Gradient Viscoelastic Fluids: Dissipation Principle And Free Energies, G. Amendola, M. Fabrizio, John Murrough Golden

Articles

We consider a generalization of the constitutive equation for an incompressible second order fluid, by including thermal and viscoelastic effects in the expression for the stress tensor. The presence of the histories of the strain rate tensor and its gradient yields a non-simple material, for which the laws of thermodynamics assume a modified form. These laws are expressed in terms of the internal mechanical power which is evaluated, using the dynamical equation for the fluid. Generalized thermodynamic constraints on the constitutive equation are presented. The required properties of free energy functionals are discussed. In particular, it is shown that they …

Large Eddy Simulation Of Dispersed Multiphase Flow, Yejun Gong

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

This thesis covers two main topics. The first is the comparison between the Reynoldsaveraged Navier-Stokes (RANS) simulation and the Large Eddy Simulation (LES) of high injection pressure diesel sprays under non-evaporating or evaporating conditions. The second topic is the comparison of the fuel behavior in the spray process between the hydrotreated vegetable oil (HVO) and the conventional EN 590, diesel #2 and n-heptane fuels.

To validate the RANS and LES spray simulations, comparisons were made with experimental data. The LES turbulence model, the initial drop size distribution (IDSD), the Levich jet breakup model and the CAB drop breakup model are …

Controlling Nanoparticles Formation In Molten Metallic Bilayers By Pulsed-Laser Interference Heating, Mikhail Khenner, Sagar Yadavali, Ramki Kalyanaraman

Mathematics Faculty Publications

The impacts of the two-beam interference heating on the number of core-shell and embedded nanoparticles and on nanostructure coarsening are studied numerically based on the non-linear dynamical model for dewetting of the pulsed-laser irradiated, thin (< 20 nm) metallic bilayers. The model incorporates thermocapillary forces and disjoining pressures, and assumes dewetting from the optically transparent substrate atop of the reflective support layer, which results in the complicated dependence of light reflectivity and absorption on the thicknesses of the layers. Stabilizing thermocapillary effect is due to the local thickness-dependent, steady- state temperature profile in the liquid, which is derived based on the mean substrate temperature estimated from the elaborate thermal model of transient heating and melting/freezing. Linear stability analysis of the model equations set for Ag/Co bilayer predicts the dewetting length scales in the qualitative agreement with experiment.

The Generalised Zakharov-Shabat System And The Gauge Group Action, Georgi Grahovski

Articles

The generalized Zakharov–Shabat systems with complex-valued non-regular Cartan elements and the systems studied by Caudrey, Beals and Coifman (CBC systems) and their gauge equivalent are studied. This study includes: the properties of fundamental analytical solutions (FAS) for the gauge-equivalent to CBC systems and the minimal set of scattering data; the description of the class of nonlinear evolutionary equations, solvable by the inverse scattering method, and the recursion operator, related to such systems; the hierarchies of Hamiltonian structures. The results are illustrated on the example of the multi-component nonlinear Schr¨odinger (MNLS) equations and the corresponding gauge-equivalent multi-component Heisenberg ferromagnetic (MHF) type …

Chaos In Dynamics: The Non-Linear Waterwheel, Abraham Romerohernandez

Theses Digitization Project

In this study basic principles of Chaos in Dynamics will be presented in the context of Lorenz Equations. In particular, we will see a demonstration of chaotic behavior in the Waterwheel Experiment and show how the dynamics of that experiment are a version of the Lorenz Equations.

Singular Solutions Of Coss-Coupled Epdiff Equations: Waltzing Peakons And Compacton Pairs, Colin Cotter, Darryl Holm, Rossen Ivanov, James Percival

Conference papers

We introduce EPDiff equations as Euler-Poincare´ equations related to Lagrangian provided by a metric, invariant under the Lie Group Diff(Rⁿ). Then we proceed with a particular form of EPDiff equations, a cross coupled two-component system of Camassa-Holm type. The system has a new type of peakon solutions, 'waltzing' peakons and compacton pairs.

Two-Subspace Projection Method For Coherent Overdetermined Systems, Deanna Needell, Rachel Ward

CMC Faculty Publications and Research

We present a Projection onto Convex Sets (POCS) type algorithm for solving systems of linear equations. POCS methods have found many applications ranging from computer tomography to digital signal and image processing. The Kaczmarz method is one of the most popular solvers for overdetermined systems of linear equations due to its speed and simplicity. Here we introduce and analyze an extension of the Kaczmarz method which iteratively projects the estimate onto a solution space given from two randomly selected rows. We show that this projection algorithm provides exponential convergence to the solution in expectation. The convergence rate significantly improves upon …

Singular Points Of Reducible Sextic Curves, David A. Weinberg, Nicholas J. Willis

Faculty Publications - Department of Mathematics

No abstract provided.

Two Integration Of Faith And Mathematics Projects For Freshmen Mathematics Majors, Nicholas J. Willis

Faculty Publications - Department of Mathematics

Two projects will be presented that integrate faith and Mathematics in a freshman Introduction to Proofs class at George Fox University. The first project asks students to look at the life of a Christian Mathematician. The focus of this project is to show students that many great mathematicians also had immense faith. The second project asks students to take a close look at their own life. How do they plan to live a life of Christian faith in their chosen profession? Both projects are designed to encourage students to look at their careers in Mathematics as a vocation.

A Fire Simulation Model For Heterogeneous Environments Using The Level Set Method, Shin-En Lo

CGU Theses & Dissertations

Wildfire hazard and its destructive consequences have become a growing issue around the world especially in the context of global warming. An effective and efficient fire simulation model will make it possible to predict the fire spread and assist firefighters in the process of controlling the damage and containing the fire area. Simulating wildfire spread remains challenging due to the complexity of fire behaviors. The raster-based method and the vector-based method are two major approaches that allow one to perform computerized fire spread simulation. In this thesis, we present a scheme we have developed that utilizes a level set method …

High Tech High Touch: Lessons Learned From Project Haiti 2011, Yan Tang, Marc Compere, Yung Lun Wong, Jared Anthony Coleman, Matthew Charles Selkirk

Publications

In this paper, we will share our experiences and lessons learned from a design project for providing clean water to a Haitian orphanage (Project Haiti 2011). Supported by funds from a renewable energy company and the university president’s office, five engineering students and two faculty members from Embry-Riddle Aeronautical University successfully designed and installed a solar powered water purification system for an orphanage located in Chambellan, Haiti. This paper discusses the unique educational experiences gained from unusual design constraints, such as ambiguity of existing facilities due to limited communication, logistics of international construction at a remote village location, and cross-cultural …

Delay-Periodic Solutions And Their Stability Using Averaging In Delay-Differential Equations, With Applications, Thomas W. Carr, Richard Haberman, Thomas Erneux

Mathematics Research

Using the method of averaging we analyze periodic solutions to delay-differential equations, where the period is near to the value of the delay time (or a fraction thereof). The difference between the period and the delay time defines the small parameter used in the perturbation method. This allows us to consider problems with arbitrarily size delay times or of the delay term itself. We present a general theory and then apply the method to a specific model that has application in disease dynamics and lasers.