Mathematics Commons^™

Section Abstracts: Astronomy, Mathematics, And Physics With Materials Science

Virginia Journal of Science

Abstracts of the Astronomy, Mathematics, and Physics with Materials Science Section for the 92nd Annual Meeting of the Virginia Academy of Science, May 13-15, 2014, Virginia Commonwealth University, Richmond, Virginia

Computational Solutions Of The Forward And Adjoint Euler Equations With Application To Duct Aeroacoustics, Ibrahim Kocaogul

Mathematics & Statistics Theses & Dissertations

Traditionally, the acoustic source terms are modeled by single frequency sinusoidal functions. In the present study, the acoustic sources are modeled by a broadband wave packet. Radiation of acoustic waves at all frequencies can be obtained by Time Domain Wave Packet (TDWP) method in a single time domain computation. The TDWP method is also particularly useful for computations in the ducted or waveguide environments where incident wave modes can be imposed cleanly without a potentially long transient period. Theoretical analysis as well as numerical validation are performed in this study. In addition, the adjoint equations for the linearized Euler equations …

Ray- And Wave-Theoretic Approach To Electromagnetic Scattering From Radially Inhomogeneous Spheres And Cylinders, Michael A. Pohrivchak

Mathematics & Statistics Theses & Dissertations

With applications in the areas of chemistry, physics, microbiology, meteorology, radar, astronomy, and many other fields, electromagnetic scattering is an important area of research. Many everyday phenomena that we experience are a result of the scattering of electromagnetic and acoustic waves. In this dissertation, the scattering of plane electromagnetic waves from radially inhomogeneous spheres and cylinders using both ray- and wave-theoretic principles is considered. Chapters 2 and 3 examine the use of the ray approach. The deviation undergone by an incident ray from its original direction is related to the angle through which the radius vector turns from the point …

Graph Partitioning Using Matrix Values For Preconditioning Symmetric Positive Definite Systems, Eugenr Vecharynski, Yousef Saad, Masha Sosonkina

Computational Modeling & Simulation Engineering Faculty Publications

Prior to the parallel solution of a large linear system, it is required to perform a partitioning of its equations/unknowns. Standard partitioning algorithms are designed using the considerations of the efficiency of the parallel matrix-vector multiplication, and typically disregard the information on the coefficients of the matrix. This information, however, may have a significant impact on the quality of the preconditioning procedure used within the chosen iterative scheme. In the present paper, we suggest a spectral partitioning algorithm, which takes into account the information on the matrix coefficients and constructs partitions with respect to the objective of enhancing the quality …

Toward A Formalism Of Modeling And Simulation Using Model Theory, Saikou Y. Diallo, Jose Padilla, Ross Gore, Heber Herencia-Zapana, Andreas Tolk

VMASC Publications

This article proposes a Modeling and Simulation (M&S) formalism using Model Theory. The article departs from the premise that M&S is the science that studies the nature of truth using models and simulations. Truth in models and simulations is relative as they seek to answer specific modeling questions. Consequently, truth in M&S is relative because every model is a purposeful abstraction of reality. We use Model Theory to express the proposed formalism because it is built from the premise that truth is relative. The proposed formalism allows us to: (1) deduce formal definitions and explanations of areas of study in …

Scalar Wave Scattering By Two-Layer Radial Inhomogeneities, Umaporn Nuntaplook, John Adam

Mathematics & Statistics Faculty Publications

It is shown that the iteration technique gives a better approximation for the problem with long wavelengths.

Rheological Signatures In Limit Cycle Behaviour Of Dilute, Active, Polar Liquid Crystalline Polymers In Steady Shear, M. Gregory Forest, Panon Phuworawong, Qi Wang, Ruhai Zhou

Mathematics & Statistics Faculty Publications

We consider the dilute regime of active suspensions of liquid crystalline polymers (LCPs), addressing issues motivated by our kinetic model and simulations in Forest et al. (Forest et al. 2013 Soft Matter 9, 5207-5222 (doi:10.1039/c3sm27736d)). In particular, we report unsteady two-dimensional heterogeneous flow-orientation attractors for pusher nanorod swimmers at dilute concentrations where passive LCP equilibria are isotropic. These numerical limit cycles are analogous to longwave (homogeneous) tumbling and kayaking limit cycles and two-dimensional heterogeneous unsteady attractors of passive LCPs in weak imposed shear, yet these states arise exclusively at semi-dilute concentrations where stable equilibria are nematic. The results in Forest …

Length Effects Of A Built-In Flapping Flat Plate On The Flow Over A Traveling Wavy Foil, Nansheng Liu, Yan Peng, Xiyun Lu

Mathematics & Statistics Faculty Publications

Flow over the traveling wavy foil with a built-in rigid flapping plate at its trailing edge has been numerically studied using the multi-relaxation-time Lattice Boltzmann method and immersed boundary method. The effect of the plate length on the propulsive performance such as the thrust force, energy consumption, and propeller efficiency has been investigated. Three modes (body force dominated, body and tail force competing and tail force dominated modes) have been identified that are associated with different hydrodynamics and flow structures. It is revealed that there exists a better performance plate length region and, within this region, a high propeller efficiency …

Network-Based Assessments Of Percolation-Induced Current Distributions In Sheared Rod Macromolecular Dispersions, Feng Shi, Simi Wang, M. Gregory Forest, Peter J. Mucha, Ruhai Zhou

Mathematics & Statistics Faculty Publications

Conducting high-aspect-ratio rods with 1-10 nm-scale diameters dispersed in poorly conducting matrices at extremely low, O(1%), volume fractions induce dramatic gains in bulk conductivity at rod percolation threshold. Experimentally [Nan, Shen, and Ma, Annu. Rev. Mater. Res., 40 (2010), pp. 131-151], bulk conductivity abandons the prepercolation, linear scaling with volume fraction that follows from homogenization theory [Zheng et al., Adv. Funct. Mater., 15 (2005), pp. 627-638], and then postpercolation jumps orders of magnitude to approach that of the pure rod macromolecular phase as predicted by classical percolation theory [Stauffer and Aharony, Introduction to Percolation Theory, CRC …

Robust Calibration Of Cameras With Telephoto Lens Using Regularized Least Squares, Mingpei Liang, Xinyu Huang, Chung-Hao Chen, Gaolin Zheng, Alade Tokuta

Electrical & Computer Engineering Faculty Publications

Cameras with telephoto lens are usually used to recover details of an object that is either small or located far away from the cameras. However, the calibration of this kind of cameras is not as accurate as the one of cameras with short focal lengths that are commonly used in many vision applications. This paper has two contributions. First, we present a first-order error analysis that shows the relation between focal length and estimation uncertainties of camera parameters. To our knowledge, this error analysis with respect to focal length has not been studied in the area of camera calibration. Second, …

Generator Polynomial Formulation For Parallel Counters With Applications, Lee A. Belfore Ii

Electrical & Computer Engineering Faculty Publications

Parallel counters have been studied for several decades as a component in high speed multipliers and multi-operand adder circuits. Using a generator polynomial as a formalism for describing parallel counters in the general case, parallel counter properties can be derived and inferred. Furthermore, the structure and decomposition of the generator polynomial can suggest different implementation strategies. These include simple implementations of (7,3) and (15,4) parallel counters. By grouping factors, the design of a fast (7,3) parallel counter is presented. Finally, the generator polynomial is extended to permit factors of different weights. This extension provides a means for describing the design …

Mathematical Methods Applied To Digital Image Processing, Yi-Hung Liu, Chung Hao Chen, Paul C.P. Chao

Electrical & Computer Engineering Faculty Publications

Introduction: Digital image processing (DIP) is an important research area since it spans a variety of applications. Although over the past few decades there has been a rapid rise in this field, there still remain issues to address. Examples include image coding, image restoration, 3D image processing, feature extraction and analysis, moving object detection, and face recognition. To deal with these issues, the use of sophisticated and robust mathematical algorithms plays a crucial role. The aim of this special issue is to provide an opportunity for researchers to publish their latest theoretical and technological achievements in mathematical methods and their …

Sensor Selection And Integration To Improve Video Segmentation In Complex Environments, Adam R. Reckley, Wei-Wen Hsu, Chung-Hao Chen, Gangfeng Ma, E-Wen Huang

Electrical & Computer Engineering Faculty Publications

Background subtraction is often considered to be a required stage of any video surveillance system being used to detect objects in a single frame and/or track objects across multiple frames in a video sequence. Most current state-of-the-art techniques for object detection and tracking utilize some form of background subtraction that involves developing a model of the background at a pixel, region, or frame level and designating any elements that deviate from the background model as foreground. However, most existing approaches are capable of segmenting a number of distinct components but unable to distinguish between the desired object of interest and …

Identifiability Of Additive, Time-Varying Actuator And Sensor Faults By State Augmentation, Jason M. Upchurch

Electrical & Computer Engineering Theses & Dissertations

Faults in dynamical systems can have serious safety and reliability implications. For example, actuator and sensor faults have been factors in past incidents and mishaps in many aerospace systems. A large body of research is devoted to developing methods to detect and identify actuator and sensor faults in such systems.

One fault detection and identification menthol employs state augmentation, whereby a set of time-varying faults of interest are modeled as outputs of exogenous linear, time-invariant systems and augmented to the state of the nominal system model. The resulting model represents the system dynamics due to a particular actuator-sensor fault configuration. …

Optimal Control Modeling And Simulation, With Application To Cholera Dynamics, Chairat Modnak

Mathematics & Statistics Theses & Dissertations

The theory of optimal control, a modern extension of the calculus of variations. has found many applications in a wide range of scientific fields, particularly in epidemiology with respect to disease prevention and intervention. In this dissertation. we conduct optimal control modeling, simulation and analysis to cholera dynamics. Cholera is a severe intestinal infectious disease that remains a serious public health threat in developing countries. Transmission of cholera involves complex interactions between the human host, the pathogen, and the environment. The worldwide cholera outbreaks and their increasing severity, frequency and duration in recent years underscore the gap between the complex …

Topics In Electromagnetic, Acoustic, And Potential Scattering Theory, Umaporn Nuntaplook

Mathematics & Statistics Theses & Dissertations

With recent renewed interest in the classical topics of both acoustic and electromagnetic aspects for nano-technology, transformation optics, fiber optics, metamaterials with negative refractive indices, cloaking and invisibility, the topic of time-independent scattering theory in quantum mechanics is becoming a useful field to re-examine in the above contexts. One of the key areas of electromagnetic theory scattering of plane electromagnetic waves — is based on the properties of the refractive indices in the various media. It transpires that the refractive index of a medium and the potential in quantum scattering theory are intimately related. In many cases, understanding such scattering …

Section Abstracts: Astronomy, Mathematics And Physics

Virginia Journal of Science

Abstracts of the Astronomy, Mathematics and Physics Section for the 91st Annual Virginia Journal of Science Meeting, May 2013

Study Of Spatiotemporal Signatures Between Objects To Improve Video Segmentation In Complex Environments, Adam Robert Reckley

Electrical & Computer Engineering Theses & Dissertations

Background subtraction is often considered to be a required stage of any video surveillance system being used to detect objects in a single frame and/or track objects across multiple frames in a video sequence. Most current state-of-the-art techniques for object detection and tracking utilize some form of background subtraction that involves developing a model of the background at a pixel, region or frame level and designating any elements that deviate from the background model as foreground. Most existing approaches are capable of segmenting a number of distinct components, but are unable to distinguish between the desired object of interest and …

Novel Algorithms And Instrumentation For Vibrational Spectroscopic Methods Of Analysis, Mohamed F. Abdelkader

Chemistry & Biochemistry Theses & Dissertations

Raman spectroscopy is a form of vibrational spectroscopy that has been increasingly applied to qualitative analysis of chemicals, explosives, pharmaceuticals, and fuels due to its non-invasive and non-destructive nature; its ease of sampling; and its high molecular specificity. These characteristics of Raman spectroscopy also facilitate its use for both in-line and at-line analysis. The principle limitation of Raman spectroscopy is optical interference arising from both analyte and non-analyte fluorescence. In this dissertation, a solution to this problem is presented in the form of a novel spectrometer design which operates in a sequentially shifted excitation mode to eliminate fluorescence backgrounds, fixed …

Identifying Requirements For The Invasion Of A Tick Species And Tick-Borne Pathogen Through Ticksim, Holly Gaff, Robyn Nadolny

Biological Sciences Faculty Publications

Ticks and tick-borne diseases have been on the move throughout the United State over the past twenty years. We use an agent-based model, TICKSIM, to identify the key parameters that determine the success of invasion of the tick and if that is successful, the success of the tick-borne pathogen. We find that if an area has competent hosts, an initial population of ten ticks is predicted to always establish a new population. The establishment of the tick-borne pathogen depends on three parameters: the initial prevalence in the ten founding ticks, the probability that a tick infects the longer-lived hosts and …

Convergence Analysis Of Markov Chain Monte Carlo Linear Solvers Using Ulam--Von Neumann Algorithm, Hao Ji, Michael Mascagni, Yaohang Li

Computer Science Faculty Publications

The convergence of Markov chain--based Monte Carlo linear solvers using the Ulam--von Neumann algorithm for a linear system of the form x = Hx + b is investigated in this paper. We analyze the convergence of the Monte Carlo solver based on the original Ulam--von Neumann algorithm under the conditions that ||H|| < 1 as well as ρ(H) < 1, where ρ(H) is the spectral radius of H. We find that although the Monte Carlo solver is based on sampling the Neumann series, the convergence of Neumann series is not a sufficient condition for the convergence of the Monte Carlo solver. Actually, properties of H are not the only factors determining the convergence of the Monte Carlo solver; the underlying transition probability matrix plays an important role. An improper selection of the transition matrix may result in divergence even though the condition ||H|| <1 holds. However, if the condition ||H|| < 1 is satisfied, we show that there always exist certain transition matrices that guarantee convergence of the Monte Carlo solver. On the other hand, if ρ(H) <1 but ||H|| ≥ 1, the Monte Carlo linear solver may or may not converge. In particular, if the row sum ∑ n/j= 1|H_ij > 1 for every row in H or, more generally, ρ(H⁺) >1, where H⁺ is the nonnegative matrix where H+_ij = |H_ij|, we show that transition matrices leading to convergence of the Monte Carlo solver do not exist. Finally, given …

Intensity-Based Skeletonization Of Cryoem Gray-Scale Images Using A True Segmentation-Free Algorithm, Kamal Al Nasr, Chunmei Liu, Mugizi Rwebangira, Legand Burge, Jing He

Computer Science Faculty Publications

Cryo-electron microscopy is an experimental technique that is able to produce 3D gray-scale images of protein molecules. In contrast to other experimental techniques, cryo-electron microscopy is capable of visualizing large molecular complexes such as viruses and ribosomes. At medium resolution, the positions of the atoms are not visible and the process cannot proceed. The medium-resolution images produced by cryo-electron microscopy are used to derive the atomic structure of the proteins in de novo modeling. The skeletons of the 3D gray-scale images are used to interpret important information that is helpful in de novo modeling. Unfortunately, not all features of the …

Analysis And Simulation Of Kinetic Model For Active Suspensions, Panon Phuworawong

Mathematics & Statistics Theses & Dissertations

In this research, we study the recently proposed kinetic model for active suspensions, where the active particles are assumed to be rigid rod and are driven in the suspension either by their own biological/chemical forces or external electric/magnetic fields. We first study the stability of the isotropic suspension in quiescent flow. Then we investigate the weak shear perturbation of the isotropic state and study some rheological properties of the suspension by explicit analytic formulas derived directly from the model. For imposed shear, we give some bifurcation diagrams of the stable states in some parametric spaces through numerical simulations. Some rheological …

Response Surface Optimization Of Electron Beam Freeform Fabrication Depositions Using Design Of Experiments, Patricia A. Quigley

Engineering Management & Systems Engineering Theses & Dissertations

The Electron Beam Freeform Fabrication (EBF³ ) System is a material depositing, layer additive technique that produces three dimensional (3D) parts out of a wide range of metals in high vacuum, using an electron beam and wire feedstock. Screening deposition trials on a titanium alloy, Ti-6Al-4V, at the National Aeronautics Space Administration (NASA) revealed selective vaporization of the aluminum content of linear prototypes when subjected to chemical analysis. In this study, the aluminum content, bead height and bead width output responses were analyzed from a systematic study of the effects that the interactions of the EBF³ processing parameters …

Numerical Analysis And Design Optimization Of Organic Bulk Hetero-Junction Solar Cells Using The Mixed Finite Element And Arc-Length Methods, James L. Dean

Mechanical & Aerospace Engineering Theses & Dissertations

Due to the high coupling and non-linear nature of the semiconductor equations, numerical stability becomes a major problem when using a purely Newtonian numerical method in solving these equations. Presented is a robust mixed finite element formulation with application for organic solar cell devices that incorporates the arc-length predictor-corrector method to bypass such stability issues. The simulated device represents a multilayered solar cell using organic bulk hetero-junction materials including donor materials Poly[2,1,3-benzothiadiazole-4,7-diyl[4,4-bis(2-ethylhexyl)-4H-cyclopenta[2,1-b:3,4- b']dithiophene-2,6-diyl]] (PCPDTBT) and poly 3-hexylthiophene (P3HT) with acceptor fullerene materials [6,6]-phenyl C61 butyric acid methyl ester (PC61BM) or [6,6]-phenyl C71 butyric acid methyl ester (PC71BM) as the photoactive …

Section Abstracts: Astronomy, Mathematics And Physics With Materials Science

Virginia Journal of Science

Abstracts of the Astronomy, Mathematics, and Physics with Material Science Section for the 90th Annual Meeting of the Virginia Academy of Science, May 23-25, 2012, Norfolk State University, Norfolk, Virginia

A Generalized Cholera Model And Epidemic-Endemic Analysis, Jin Wang, Shu Liao

Mathematics & Statistics Faculty Publications

The transmission of cholera involves both human-to-human and environment-to-human pathways that complicate its dynamics. In this paper, we present a new and unified deterministic model that incorporates a general incidence rate and a general formulation of the pathogen concentration to analyse the dynamics of cholera. Particularly, this work unifies many existing cholera models proposed by different authors. We conduct equilibrium analysis to carefully study the complex epidemic and endemic behaviour of the disease. Our results show that despite the incorporation of the environmental component, there exists a forward transcritical bifurcation at R₀ = 1 for the combined human-environment epidemiological …

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

Flow Over A Traveling Wavy Foil With A Passively Flapping Flat Plate, Nansheng Liu, Yan Peng, Youwen Liang, Xiyun Lu

Mathematics & Statistics Faculty Publications

Flow over a traveling wavy foil with a passively flapping flat plate has been investigated using a multiblock lattice Boltzmann equation and the immersed boundary method. The foil undergoes prescribed undulations in the lateral direction and the rigid flat plate has passive motion determined by the fluid structure interaction. This simplified model is used to study the effect of the fish caudal fin and its flexibility on the locomotion of swimming animals. The flexibility of the caudal fin is modeled by a torsion spring acting about the pivot at the conjuncture of the wavy foil and the flat plate. The …

Question 1: Google And Pac-Man; Question 2: Magnetic Levitation, Larry Weinstein

Physics Faculty Publications

On the 30th anniversary of the introduction of the video game Pac-Man, Google created a miniature version of the game and placed it as its logo on its home page. How much total time was wasted in the United States playing this game?

(Thanks to Daniel Drill of Old Dominion University for suggesting the question.)

Animal tissue is diamagnetic. How large a magnetic field gradient is needed to levitate frogs or people?