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Mathematics

2014

Old Dominion University

Articles 1 - 14 of 14

Full-Text Articles in Physical Sciences and Mathematics

Section Abstracts: Astronomy, Mathematics, And Physics With Materials Science Apr 2014

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

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Ray- And Wave-Theoretic Approach To Electromagnetic Scattering From Radially Inhomogeneous Spheres And Cylinders, Michael A. Pohrivchak Apr 2014

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 …

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Computational Solutions Of The Forward And Adjoint Euler Equations With Application To Duct Aeroacoustics, Ibrahim Kocaogul Apr 2014

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 …

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Toward A Formalism Of Modeling And Simulation Using Model Theory, Saikou Y. Diallo, Jose Padilla, Ross Gore, Heber Herencia-Zapana, Andreas Tolk Jan 2014

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 …

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Mathematical Methods Applied To Digital Image Processing, Yi-Hung Liu, Chung Hao Chen, Paul C.P. Chao Jan 2014

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 …

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Robust Calibration Of Cameras With Telephoto Lens Using Regularized Least Squares, Mingpei Liang, Xinyu Huang, Chung-Hao Chen, Gaolin Zheng, Alade Tokuta Jan 2014

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, …

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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 Jan 2014

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 …

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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 Jan 2014

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 …

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Generator Polynomial Formulation For Parallel Counters With Applications, Lee A. Belfore Ii Jan 2014

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 …

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Graph Partitioning Using Matrix Values For Preconditioning Symmetric Positive Definite Systems, Eugenr Vecharynski, Yousef Saad, Masha Sosonkina Jan 2014

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 …

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Length Effects Of A Built-In Flapping Flat Plate On The Flow Over A Traveling Wavy Foil, Nansheng Liu, Yan Peng, Xiyun Lu Jan 2014

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 …

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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 Jan 2014

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 …

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Scalar Wave Scattering By Two-Layer Radial Inhomogeneities, Umaporn Nuntaplook, John Adam Jan 2014

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.

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Sensor Selection And Integration To Improve Video Segmentation In Complex Environments, Adam R. Reckley, Wei-Wem Hsu, Chung-Hao Chen, Gangfeng Ma, E-Wen Huang Jan 2014

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

Civil & Environmental 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 …

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