scholarly journals Image Theory for Neumann Functions in the Prolate Spheroidal Geometry

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Changfeng Xue ◽  
Robert Edmiston ◽  
Shaozhong Deng
Keyword(s):  
Prolate Spheroid ◽  
Radial Coordinate ◽  
Uniform Density ◽  
Prolate Spheroidal ◽  
Image System ◽  
Focal Line ◽  
Line Image ◽  
Surface Image ◽  
Point Image ◽  
Symmetric Surface

Interior and exterior Neumann functions for the Laplace operator are derived in terms of prolate spheroidal harmonics with the homogeneous, constant, and nonconstant inhomogeneous boundary conditions. For the interior Neumann functions, an image system is developed to consist of a point image, a line image extending from the point image to infinity along the radial coordinate curve, and a symmetric surface image on the confocal prolate spheroid that passes through the point image. On the other hand, for the exterior Neumann functions, an image system is developed to consist of a point image, a focal line image of uniform density, another line image extending from the point image to the focal line along the radial coordinate curve, and also a symmetric surface image on the confocal prolate spheroid that passes through the point image.

On the Inverse Problem of Scattering from a Perfectly Conducting Prolate Spheroid

1972 ◽  
Vol 50 (8) ◽  
pp. 754-759 ◽  
Author(s):  
F. H. Vandenberghe ◽  
W. M. Boerner
Keyword(s):  
Inverse Problem ◽  
Electromagnetic Scattering ◽  
Scattered Field ◽  
Spherical Wave ◽  
Prolate Spheroid ◽  
Wave Functions ◽  
Prolate Spheroidal ◽  
Spheroidal Wave Functions ◽  
Prolate Spheroidal Wave Functions ◽  
Model Technique

The inverse problem of electromagnetic scattering from a prolate spheroidal scatterer is considered. The approach is based on the model technique presented in Boerner and Vandenberghe, conjecturing that the salient features of the scatterer can be determined from the far scattered field via matrix inversion. An expansion in spherical wave functions for the scattered field based on the formulation of Senior is employed instead of an expansion in prolate spheroidal wave functions. It is then shown that the characteristic parameters of the ellipse generating the prolate spheroid (the interfocal distance d and the eccentricity ε) can be directly recovered from Senior's expansion coefficients.

Radiation characteristics of a slot antenna on a conducting prolate spheroid

1995 ◽  
Vol 73 (5-6) ◽  
pp. 376-385 ◽  
Author(s):  
M. Zhang ◽  
A. A. Sebak
Keyword(s):  
Prolate Spheroid ◽  
Wave Functions ◽  
Slot Antenna ◽  
Published Data ◽  
System Of Equations ◽  
Prolate Spheroidal ◽  
Radiation Characteristics ◽  
Vector Wave ◽  
Slot Length ◽  
Expansion Coefficients

In this paper, the radiation characteristics of an asymmetrical slot antenna on a conducting prolate spheroid are considered. The radiated fields are expanded in terms of prolate-spheroidal vector wave functions. The unknown expansion coefficients are determined by a system of equations derived from the boundary conditions. Numerical results for radiation patterns and conductance are obtained and compare well with published data for a slotted sphere. The effect of the slot length and the shape of the spheroid on the magnitude of the radiated field and radiation conductance is also presented.

Force on a Prolate Spheroid in an Axisymmetric Potential Flow

1964 ◽  
Vol 8 (03) ◽  
pp. 24-37
Author(s):  
L. Landweber
Keyword(s):  
Unsteady Flow ◽  
Potential Flow ◽  
Axisymmetric Flow ◽  
Prolate Spheroid ◽  
External Potential ◽  
Image System ◽  
Axis Of Symmetry ◽  
Asymmetric Flows

The present work is the first of a two-part contribution to the development of hydrodynamic procedures for determining forces on ship forms immersed in an external potential flow. In this first part, the case of a prolate spheroid in an axisymmetric flow is considered, and exact and linearized expressions for the image system of sources and doublets, valid under certain conditions, have been obtained. By means of the Lagally theorem, these yield the values of the forces acting on the spheroid for both steady and unsteady flow. The case of an external potential flow due to a source on the axis of symmetry is considered in detail. In the second part the results for a prolate spheroid in asymmetric flows will be presented.

Mathematical model of geometry and fibrous structure of the heart

1991 ◽  
Vol 260 (4) ◽  
pp. H1365-H1378 ◽  
Author(s):  
P. M. Nielsen ◽  
I. J. Le Grice ◽  
B. H. Smaill ◽  
P. J. Hunter
Keyword(s):  
Three Dimensional ◽  
Prolate Spheroid ◽  
Basis Functions ◽  
Mathematical Representation ◽  
Radial Coordinate ◽  
Canine Heart ◽  
Element Mesh ◽  
Ventricular Geometry ◽  
Realistic Description ◽  
Rms Error

We developed a mathematical representation of ventricular geometry and muscle fiber organization using three-dimensional finite elements referred to a prolate spheroid coordinate system. Within elements, fields are approximated using basis functions with associated parameters defined at the element nodes. Four parameters per node are used to describe ventricular geometry. The radial coordinate is interpolated using cubic Hermite basis functions that preserve slope continuity, while the angular coordinates are interpolated linearly. Two further nodal parameters describe the orientation of myocardial fibers. The orientation of fibers within coordinate planes bounded by epicardial and endocardial surfaces is interpolated linearly, with transmural variation given by cubic Hermite basis functions. Left and right ventricular geometry and myocardial fiber orientations were characterized for a canine heart arrested in diastole and fixed at zero transmural pressure. The geometry was represented by a 24-element ensemble with 41 nodes. Nodal parameters fitted using least squares provided a realistic description of ventricular epicardial [root mean square (RMS) error less than 0.9 mm] and endocardial (RMS error less than 2.6 mm) surfaces. Measured fiber fields were also fitted (RMS error less than 17 degrees) with a 60-element, 99-node mesh obtained by subdividing the 24-element mesh. These methods provide a compact and accurate anatomic description of the ventricles suitable for use in finite element stress analysis, simulation of cardiac electrical activation, and other cardiac field modeling problems.

The effects of surface absorbed monolayer microdiffraction patterns

1988 ◽  
Vol 46 ◽  
pp. 680-681
Author(s):  
M. Pan ◽  
J.M. Cowley
Keyword(s):  
Surface Potential ◽  
Electron Probe ◽  
Potential Distribution ◽  
Crystal Surface ◽  
Normal Direction ◽  
Surface Image ◽  
Extended Surface ◽  
Gas Molecules ◽  
Surface Nature ◽  
Electron Microdiffraction

Electron microdiffraction patterns, obtained when a small electron probe with diameter of 10-15 Å is directed to run parallel to and outside a flat crystal surface, are sensitive to the surface nature of the crystals. Dynamical diffraction calculations have shown that most of the experimental observations for a flat (100) face of a MgO crystal, such as the streaking of the central spot in the surface normal direction and (100)-type forbidden reflections etc., could be explained satisfactorily by assuming a modified image potential field outside the crystal surface. However the origin of this extended surface potential remains uncertain. A theoretical analysis by Howie et al suggests that the surface image potential should have a form different from above-mentioned image potential and also be smaller by several orders of magnitude. Nevertheless the surface potential distribution may in practice be modified in various ways, such as by the adsorption of a monolayer of gas molecules.

Flux-pinning-related defect structures in melt-processed YBa2Cu3O7-x

1993 ◽  
Vol 51 ◽  
pp. 936-937
Author(s):  
Z. L. Wang ◽  
R. Kontra ◽  
A. Goyal ◽  
D. M. Kroeger ◽  
L.F. Allard
Keyword(s):  
Volume Fraction ◽  
Local Density ◽  
Stacking Faults ◽  
Image Resolution ◽  
Defect Structures ◽  
Atomic Structures ◽  
Transmission Electron ◽  
Point Image ◽  
Related Defect ◽  
Point To Point

Previous studies of Y2BaCuO5/YBa2Cu3O7-δ(Y211/Y123) interfaces in melt-processed and quench-melt-growth processed YBa2Cu3O7-δ using high resolution transmission electron microscopy (HRTEM) and energy dispersive X-ray spectroscopy (EDS) have revealed a high local density of stacking faults in Y123, near the Y211/Y123 interfaces. Calculations made using simple energy considerations suggested that these stacking faults may act as effective flux-pinners and may explain the observations of increased Jc with increasing volume fraction of Y211. The present paper is intended to determine the atomic structures of the observed defects. HRTEM imaging was performed using a Philips CM30 (300 kV) TEM with a point-to-point image resolution of 2.3 Å. Nano-probe EDS analysis was performed using a Philips EM400 TEM/STEM (100 kV) equipped with a field emission gun (FEG), which generated an electron probe of less than 20 Å in diameter.Stacking faults produced by excess single Cu-O layers: Figure 1 shows a HRTEM image of a Y123 film viewed along [100] (or [010]).

An Adaptive Binarization Method for Cost-efficient Document Image System in Wavelet Domain

2020 ◽  
Vol 64 (3) ◽  
pp. 30401-1-30401-14 ◽  
Author(s):  
Chih-Hsien Hsia ◽  
Ting-Yu Lin ◽  
Jen-Shiun Chiang
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Document Image ◽  
Background Information ◽  
Raspberry Pi ◽  
Discrete Wavelet ◽  
Image System ◽  
Low Frequencies ◽  
Cost Efficient ◽  
Binarization Method

Abstract In recent years, the preservation of handwritten historical documents and scripts archived by digitized images has been gradually emphasized. However, the selection of different thicknesses of the paper for printing or writing is likely to make the content of the back page seep into the front page. In order to solve this, a cost-efficient document image system is proposed. In this system, the authors use Adaptive Directional Lifting-Based Discrete Wavelet Transform to transform image data from spatial domain to frequency domain and perform on high and low frequencies, respectively. For low frequencies, the authors use local threshold to remove most background information. For high frequencies, they use modified Least Mean Square training algorithm to produce a unique weighted mask and perform convolution on original frequency, respectively. Afterward, Inverse Adaptive Directional Lifting-Based Discrete Wavelet Transform is performed to reconstruct the four subband images to a resulting image with original size. Finally, a global binarization method, Otsu’s method, is applied to transform a gray scale image to a binary image as the output result. The results show that the difference in operation time of this work between a personal computer (PC) and Raspberry Pi is little. Therefore, the proposed cost-efficient document image system which performed on Raspberry Pi embedded platform has the same performance and obtains the same results as those performed on a PC.

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