Topic
Elliptic coordinate system
About: Elliptic coordinate system is a research topic. Over the lifetime, 670 publications have been published within this topic receiving 11135 citations. The topic is also known as: elliptical coordinate system & elliptic coordinates.
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TL;DR: In this article, an elliptical plate subjected to unaxisymmetric heating on the elliptic boundary with heat transfer on the upper and lower surfaces was considered and the authors provided analytical solutions in elliptical coordinates for both a steady-state temperature field and an associated plane thermal stress problem.
Abstract: As another example of heat conduction and plane thermal stress problems in which the solutions are expressed in Mathieu and modified Mathieu functions, analytical solutions in elliptical coordinates are given for both a steady-state temperature field and an associated plane thermal stress problem in an elliptical plate subjected to unaxisymmetric heating on the elliptic boundary with heat transfer on the upper and lower surfaces. When heat loss from the upper and lower surfaces into the surrounding media exists, the temperature function must be expressed in Mathieu and modified Mathieu functions and thermal stresses occur even in a steady-state temperature field. The associated plane thermal stress problem can be formulated in terms of Airy's stress function. Numerical calculations are carried out for the distributions of temperature and circumferential thermal stress in the elliptical plate subjected to unaxisymmetric heating expressed in the form of a fourth-order equation and Heviside step function of the η coordinate on the elliptic boundary.
1 citations
Journal Article•
TL;DR: In this paper, the authors explored the concentrating effects of both the electric current density and the stresses in the plate due to the existence of the elliptic hole and determined the stress distribution in a thin conductive plate containing an elliptic holes under the external electromagnetic loads.
Abstract: Stress distribution is determined in a thin conductive plate containing an elliptic hole under the external electromagnetic loads The aim of this study is to explore the concentrating effects of both the electric current density and the stresses in the plate due to the existence of the elliptic hole Use is made of the elliptic coordinates for the ease of treating ellipse shaped boundary, while the analytical results for the components in the Cartesian coordinates are provided for convenience of application After the distribution of the current density is derived, an anti-plane shear problem is formulated whose solution is obtained in closed form The mode Ⅲ stress intensity factor is deduced by considering the case in which the minor axis vanishes when the ellipse degenerates to a Griffith crack
1 citations
06 Jun 2013
TL;DR: In this paper, the authors used the traditional cavity model for the estimation of resonant modes of patch antennas in spherical coordinates on a spherical ground plane, where the ground plane is assumed to be planar.
Abstract: Summary form only given. The traditional cavity model has been a valuable tool for the estimation of resonant modes of patch antennas since its inception nearly 30 years ago. This model is frequently used for planar antenna structures having canonical shapes in Cartesian, cylindrical, and elliptical coordinates. However, there is no limitation on the cavity model that requires the ground plane to be planar. As such, the cavity model can be useful for determining resonant modes of patch antennas having canonical shapes in spherical coordinates on a spherical ground plane. Indeed, the resonant modes readily follow by solving for the internal fields (underneath the patch) with the presumption of fictitious magnetic walls around the perimeter of the patch and electric walls on the top and bottom. Using a classical TE/TM decomposition of the fields, the resonant modes may be found.
1 citations
12 May 2008
TL;DR: The hyperspherical elliptic ansatz for representing a stationary state wave function of a three-body system with arbitrary masses was introduced in this paper, which gives direct generalization of the Born-Oppenheimer formula.
Abstract: New approximate symmetry of the three‐body Coulomb problem is discussed The symmetry reveals itself on the level of the hyperspherical adiabatic Hamiltonian, giving two new quantum numbers nξ and nη On the basis of these quantum numbers, we introduce the hyperspherical elliptic ansatz for representing a stationary state wave function of a three‐body system with arbitrary masses, which gives direct generalization of the well‐known Born‐Oppenheimer formula Such an approach provides a simple and accurate computational scheme for study of correlation and mass‐polarization effects in a wide class of three‐body systems
1 citations
09 Jun 2008
TL;DR: In this article, Riemannian wavefield extrapolation is extended to prestack migration through the use of 2D elliptic coordinate systems, and the authors demonstrate that the RWE migration algorithm generates high-quality prestack images comparable to, or better than, the corresponding Cartesian coordinate systems.
Abstract: Riemannian wavefield extrapolation is extended to prestack migration through the use of 2D elliptic coordinate systems. The corresponding 2D elliptic coordinate extrapolation wavenumber is demonstrated to introduce only a slowness model stretch to the single-square-root operator, enabling the use of existing Cartesian implicit finite-difference extrapolators to propagate wavefields. A post-stack migration example illustrates the advantages of elliptic coordinates in imaging overturning wavefields. Imaging tests of BP Velocity Benchmark data set illustrate that the RWE migration algorithm generates high-quality prestack migration images comparable to, or better than, the corresponding Cartesian coordinate systems.
1 citations