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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7 citations
01 Aug 1976
TL;DR: In this paper, the numerically generated body-fitted coordinate systems have been studied from a very basic point of view, which leads to a well structured method of coordinate system control in any region of interest and is also instrumental in obtaining the machine solutions of the field differential equations in general dependent variables on the generated coordinate systems.
Abstract: : This paper presents a study in depth on the numerically generated body-fitted coordinate systems All fundamental ideas have been developed from a very basic point of view which leads to a well structured method of coordinate system control in any region of interest It is also shown how the developed concepts are instrumental in obtaining the machine solutions of the field differential equations in general dependent variables on the generated coordinate systems (Author)
7 citations
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TL;DR: In this article, a new method of analysis of an arbitrary configuration of elliptical cylinders is presented based on a combination of the cylindrical and elliptical coordinates systems, which is applied to the formulation of the scattered field at the surface of equivalent cylinder surrounding dielectric or metal elliptical object.
Abstract: A new method of analysis of an arbitrary configuration of elliptical cylinders is presented. The treatment of such a problem is based on a combination of the cylindrical and elliptical coordinates systems. This approach is applied to the formulation of the scattered field at the surface of equivalent cylinder surrounding dielectric or metal elliptical object. To analyse the arbitrary set of elliptical cylinders, the iterative scattering procedure is used. A good agreement of the proposed method with the commercial FD simulator is achieved.
7 citations
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TL;DR: In this article, an extension of the power series in R and ln R of interaction energy k and separation constant A for the system of two protons and one electron in the Born-Oppenheimer approximation is presented.
Abstract: This work aims at the extension of the power series in R and ln R of interaction energy k and separation constant A for the system of two protons and one electron in the Born–Oppenheimer approximation. The wave equation is separated into confocal elliptic coordinates, in order to obtain two one-dimensional problems. The approach that we present here is based upon our previous calculations, where a relation between A and k for the (outer) ξ-equation was obtained in two different but substantially equivalent ways: either by an integral equation representation of the solution or by a logarithmic-perturbative expansion, in powers of the energy difference k, from the united atom state. At variance with our previous work, we make use of the (inner) η-equation of a remarkably simple determinantal equation proposed long ago by Hylleraas for which we develop a recursive method of calculation. By combining the two procedures we obtain the solution of the problem by solving for the coefficients of the R and ln R expansion. We calculate in this way coefficients up to O(R7) and show how higher order coefficients may be evaluated recursively.
7 citations
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TL;DR: In this article, a class of vector beams with elliptical symmetry where the spatial DoF is encoded in the Ince-Gaussian modes of the cylindrical elliptical coordinates is presented.
Abstract: Complex vector light modes, classically-entangled in their spatial and polarisation degrees of freedom (DoF), havebecome ubiquitous in a vast diversity of research fields. Crucially, while polarisation is limited to a bi-dimensionalspace, the spatial mode is unbounded, it can be specified by any of the sets of solutions the wave equation can supportin the different coordinate systems. Here we report on a class of vector beams with elliptical symmetry where thespatial DoF is encoded in the Ince-Gaussian modes of the cylindrical elliptical coordinates. We outline their geometricrepresentation on the Higher-Order Poincare Sphere, demonstrate their experimental generation and analyse the qualityof the generated modes via Stokes polarimetry. We anticipate that such vector modes will be of great relevance inapplications, such as, optical manipulations, laser material processing and optical communications amongst others.
7 citations