Applied Mathematics Commons^™

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 …

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.

Lefschetz Properties And Enumerations, David Cook Ii

Theses and Dissertations--Mathematics

An artinian standard graded algebra has the weak Lefschetz property if the multiplication by a general linear form induces maps of maximal rank between consecutive degree components. It has the strong Lefschetz property if the multiplication by powers of a general linear form also induce maps of maximal rank between the appropriate degree components. These properties are mainly studied for the constraints they place, when present, on the Hilbert series of the algebra. While the majority of research on the Lefschetz properties has focused on characteristic zero, we primarily consider the presence of the properties in positive characteristic. We study …

The Radon Transform And The Mathematics Of Medical Imaging, Jen Beatty

Honors Theses

Tomography is the mathematical process of imaging an object via a set of finite slices. In medical imaging, these slices are defined by multiple parallel X-ray beams shot through the object at varying angles. The initial and final intensity of each beam is recorded, and the original image is recreated using this data for multiple slices. I will discuss the central role of the Radon transform and its inversion formula in this recovery process.

Development Of New Mathematical Methods For Post-Pareto Optimality, Victor Manuel Carrillo

Open Access Theses & Dissertations

Many real-world applications of multi-objective optimization involve a large number of objectives. A multi-objective optimization task involving multiple conflicting objectives ideally demands finding a multi-dimensional Pareto-optimal front. Although the classical methods have dealt with finding one preferred solution with the help of a decision-maker, evolutionary multi-objective optimization (EMO) methods have been attempted to find a representative set of solutions in the Pareto-optimal front. Multiple objective evolutionary algorithms (MOEAs), which are biologically-inspired optimization methods, have become popular approaches to solve problems with multiple objective functions. With the use of MOEAs, multiple objective optimization becomes a two-part problem. First, the multiple objective …

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 Schrodinger (MNLS) equations and the corresponding gauge-equivalent multi-component Heisenberg ferromagnetic (MHF) type …

Consensus-Type Stochastic Approximation Algorithms, Yu Sun

Wayne State University Dissertations

This work is concerned with asymptotic properties of consensus-type algorithms for networked systems whose topologies switch randomly. The regime-switching process is modeled as a discrete-time Markov chain with a nite state space. The consensus control is achieved by designing stochastic approximation algorithms. In the setup, the regime-switching process (the Markov chain) contains a rate parameter

"Ε> 0 in the transition probability matrix that characterizes how frequently the topology switches. On the other hand, the consensus control algorithm uses a step-size Μ that denes how fast the network states are updated. Depending on their relative values, three distinct scenarios emerge. Under …

Eulerian Polynomials And B-Splines, Tian-Xiao He

Scholarship

Here presented is the interrelationship between Eulerian polynomials, Eulerian fractions and Euler-Frobenius polynomials, Euler-Frobenius fractions, B-splines, respectively. The properties of Eulerian polynomials and Eulerian fractions and their applications in B-spline interpolation and evaluation of Riemann-zeta function values at odd integers are given. The relation between Eulerian numbers and B-spline values at knot points are also discussed.

Study Of Vortex Ring Dynamics In The Nonlinear Schrödinger Equation Utilizing Gpu-Accelerated High-Order Compact Numerical Integrators, Ronald Meyer Caplan

CGU Theses & Dissertations

We numerically study the dynamics and interactions of vortex rings in the nonlinear Schrödinger equation (NLSE). Single ring dynamics for both bright and dark vortex rings are explored including their traverse velocity, stability, and perturbations resulting in quadrupole oscillations. Multi-ring dynamics of dark vortex rings are investigated, including scattering and merging of two colliding rings, leapfrogging interactions of co-traveling rings, as well as co-moving steady-state multi-ring ensembles. Simulations of choreographed multi-ring setups are also performed, leading to intriguing interaction dynamics.

Due to the inherent lack of a close form solution for vortex rings and the dimensionality where they live, efficient …

Lifetime Prediction And Confidence Bounds In Accelerated Degradation Testing For Lognormal Response Distributions With An Arrhenius Rate Relationship, Steven Michael Alferink

Doctoral Dissertations

"Determining the lifetime of a product is an important component of quality assurance. Traditional life testing methods are infeasible for products that have been designed to have a very long lifetime because they require a lengthy testing period. An alternative method is accelerated degradation testing, where a response variable determining the usability of the product is measured over time under multiple accelerating stress levels. The resulting data are then used to predict the life distribution of the product under the design stress level. In this dissertation, several methods are proposed and studied for obtaining prediction bounds for the lifetime of …

Lattice Residuability, Philip Theodore Thiem

Masters Theses

"Residuated lattices form the basis of certain kinds of logical interpretations. Also, complete commutative integral zero-bounded residuated lattices are used as a set of truth values for fuzzy logic values, Which are more general than the traditional bounded interval introduced by Zadeh. At times, it is important to know whether or not the lattice can be residuated in the first place. This thesis reviews the literature in lattice residuability and adds more observations. Specifically, (1) bounded chains and top-residuated lattices are show [sic] to be residuable, and (2) additional conditions necessary for residuability are established"--Abstract, page iii.

A Review Of Some Subtleties Of Practical Relevance, Keqin Gu

SIUE Faculty Research, Scholarship, and Creative Activity

This paper reviews some subtleties in time-delay systems of neutral type that are believed to be of particular relevance in practice. Both traditional formulation and the coupled differential-difference equation formulation are used. The discontinuity of the spectrum as a function of delays is discussed. Conditions to guarantee stability under small parameter variations are given. A number of subjects that have been discussed in the literature, often using different methods, are reviewed to illustrate some fundamental concepts. These include systems with small delays, the sensitivity of Smith predictor to small delay mismatch, and the discrete implementation of distributed-delay feedback control. The …

Set Ideal Topological Spaces, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book the authors for the first time introduce a new type of topological spaces called the set ideal topological spaces using rings or semigroups, or used in the mutually exclusive sense. This type of topological spaces use the class of set ideals of a ring (semigroups). The rings or semigroups can be finite or infinite order. By this method we get complex modulo finite integer set ideal topological spaces using finite complex modulo integer rings or finite complex modulo integer semigroups. Also authors construct neutrosophic set ideal toplogical spaces of both finite and infinite order as well as …

Equivariant Degenerations Of Spherical Modules For Groups Of Type A, Stavros Argyrios Papadakis, Bart Van Steirteghem

Publications and Research

Let G be a complex reductive algebraic group. Fix a Borel subgroup B of G and a maximal torus T in B. Call the monoid of dominant weights L+ and let S be a finitely generated submonoid of L+. V. Alexeev and M. Brion introduced a moduli scheme MS which classifies affine G-varieties X equipped with a T-equivariant isomorphism SpecC[X]U → SpecC[S], where U is the unipotent radical of B. Examples of MS have been obtained by S. Jansou, P. Bravi and S. Cupit-Foutou. In this paper, we prove that MS is isomorphic to an affine space when S is …

Numerical Methods For Fluid-Structure Interaction - A Review, Gene Hou, Jin Wang, Anita Layton

Mechanical & Aerospace Engineering Faculty Publications

The interactions between incompressible fluid flows and immersed structures are nonlinear multi-physics phenomena that have applications to a wide range of scientific and engineering disciplines. In this article, we review representative numerical-methods based on conforming and non-conforming meshes that are currently available for computing fluid-structure interaction problems, with an emphasis on some of the recent developments in the field. A goal is to categorize the selected methods and assess their accuracy and efficiency. We discuss challenges faced by researchers in this field, and we emphasize the importance of interdisciplinary effort for advancing the study in fluid-structure interactions

Quantization And Discretization At Large Scales, Florentin Smarandache, Victor Christianto, Pavel Pintr

Branch Mathematics and Statistics Faculty and Staff Publications

The ongoing search of extrasolar planets is one of the most attractive fields of research in astrophysics and astronomy. Up to now, 360 extrasolar planets have been discovered near stars with similar mass as the Sun. There is also discovery related to the so-called Earth-like planets. With regards to these discoveries, one intriguing question is whether there is relationship between orbit distance of the planets and their stars. Various formulas have been suggested since 1990s, and they suggest that there may be reason to accept quantization of distances of those planets both in our solar system and also in extrasolar …

Natural Product Xn On Matrices, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book the authors introduce a new product on matrices called the natural product. ...

Thus by introducing natural product we can find the product of column matrices and product of two rectangular matrices of same order. Further this product is more natural which is just identical with addition replaced by multiplication on these matrices. Another fact about natural product is this enables the product of any two super matrices of same order and with same type of partition. We see on supermatrices products cannot be defined easily which prevents from having any nice algebraic structure on the collection …

Innovative Uses Of Matrices, Florentin Smarandache, W.B. Vasantha Kandasamy, Indra Venkatbabu

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors bring out the innovative applications of matrices defined, described and developed by them. Here they do not include the natural product on matrices newly described and defined by them in the book on ‘natural product ×n on matrices’.

This book is organized into seven chapters. The first one is introductory in nature. In the second chapter authors give the unique and new way of analyzing the data which is time dependent. We construct three types of matrices called Average Time Dependent data matrix (ATD matrix), Refined Time Dependent Data matrix (RTD matrix) and Combined Effective Time …

Special Dual Like Numbers And Lattices, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book the authors introduce a new type of dual numbers called special dual like numbers. These numbers are constructed using idempotents in the place of nilpotents of order two as new element. That is x = a + bg is a special dual like number where a and b are reals and g is a new element such that g2 =g. The collection of special dual like numbers forms a ring. Further lattices are the rich structures which contributes to special dual like numbers. These special dual like numbers x = a + bg; when a and b …

Neutrosophic Super Matrices And Quasi Super Matrices, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors study neutrosophic super matrices. The concept of neutrosophy or indeterminacy happens to be one the powerful tools used in applications like FCMs and NCMs where the expert seeks for a neutral solution. Thus this concept has lots of applications in fuzzy neutrosophic models like NRE, NAM etc. These concepts will also find applications in image processing where the expert seeks for a neutral solution. Here we introduce neutrosophic super matrices and show that the sum or product of two neutrosophic matrices is not in general a neutrosophic super matrix. Another interesting feature of this book is …

Mathematical Analysis Of The Problems Faced By The People With Disabilities (Pwds), Florentin Smarandache, W.B. Vasantha Kandasamy, A. Praveen Prakash

Branch Mathematics and Statistics Faculty and Staff Publications

The authors in this book have analyzed the socio-economic and psychological problems faced by People with Disabilities (PWDs) and their families. The study was made by collecting data using both fuzzy linguistic questionnaire / by interviews in case they are not literates from 2,15,811 lakhs people. This data was collected using the five Non Government Organizations (NGOs) from northern Tamil Nadu. Now any reader would be interested to know whether the Tamils (natives of Tamil Nadu) had ever spoken about people with disability. Even before 2000 years tamils had heroic poetry Purananuru (28th poem) about the war fare methods. In …

The Geometry Of Homological Triangles, Florentin Smarandache, Ion Patrascu

Branch Mathematics and Statistics Faculty and Staff Publications

This book is addressed to students, professors and researchers of geometry, who will find herein many interesting and original results. The originality of the book The Geometry of Homological Triangles consists in using the homology of triangles as a “filter” through which remarkable notions and theorems from the geometry of the triangle are unitarily passed. Our research is structured in seven chapters, the first four are dedicated to the homology of the triangles while the last ones to their applications. In the first chapter one proves the theorem of homological triangles (Desargues, 1636), one survey the remarkable pairs of homological …