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.
Papers published on a yearly basis
Papers
More filters
TL;DR: It is shown that the Coulomb singularities at the nuclei can be successfully overcome so that both bound and continuum states can be accurately calculated by the method of separation of variables.
Abstract: We present an efficient and accurate grid method to study the strong field dynamics of planar H(2)(+) under Born-Oppenheimer approximation. After introducing the elliptical coordinates to the planar H(2)(+), we show that the Coulomb singularities at the nuclei can be successfully overcome so that both bound and continuum states can be accurately calculated by the method of separation of variables. The time-dependent Schrodinger equation (TDSE) can be accurately solved by a two-dimensional discrete variable representation (DVR) method, where the radial coordinate is discretized with the finite-element discrete variable representation for easy parallel computation and the angular coordinate with the trigonometric DVR which can describe the periodicity in this direction. The bound states energies can be accurately calculated by the imaginary time propagation of TDSE, which agree very well with those computed by the separation of variables. We apply the TDSE to study the ionization dynamics of the planar H(2)(+) by short extreme ultra-violet (xuv) pulses, in which case the differential momentum distributions from both the length and the velocity gauge agree very well with those calculated by the lowest order perturbation theory.
3 citations
01 Jun 1977
TL;DR: In this article, a generalized curvilinear orthogonal coordinate system is presented which can be used for approximating various axisymmetric and two-dimensional body shapes of interest to aerodynamicists.
Abstract: A generalized curvilinear orthogonal coordinate system is presented which can be used for approximating various axisymmetric and two-dimensional body shapes of interest to aerodynamicists. Such body shapes include spheres, ellipses, spherically capped cones, flat-faced cylinders with rounded corners, circular disks, and planetary probe vehicles. A set of transformation equations is also developed whereby a uniform velocity field approaching a body at any angle of attack can be resolved in the transformed coordinate system. The Navier-Stokes equations are written in terms of a generalized orthogonal coordinate system to show the resultant complexity of the governing equations.
3 citations
TL;DR: The qualitative investigation of the motion in the two-dimensional tori is given in this paper in order to obtain the bifurcation and the phase portrait of the Kovalevskaya problem.
Abstract: The rotation of a rigid body about a fixed point in the Kovalevskaya case, where A = B = 2C, y{sub 0} = z{sub 0} = O (A, B, C are the principal moments of inertia; x{sub 0}, y{sub 0}, z{sub 0} represent the center of mass), has been reduced to quadrature, and the system can be integrated to a Riemann 0-function of two variables. The qualitative investigation of the motion of Kovalevskaya tops has been undertaken by many authors, starting with Applort and continuing with Kozlov. Kolossoff transformed the Kovalevskaya problem into plane motion under a certain potential force. By using elliptic coordinates, Kolossoff proved the inverse problem, i.e., he converted the plane motion system into a Kovalevskaya system. The qualitative investigation of the motion in the two-dimensional tori is given in order to obtain the bifurcation and the phase portrait of the problem.
3 citations
TL;DR: In this article, the quasi-TEM modes on a planar multiconductor transmission line embedded in an elliptically stratified cross section are considered, and asymptotic solutions for the radial dependences of the terms of the series can be used under certain conditions on the profiles of stratification.
Abstract: The quasi-TEM modes on a planar multiconductor transmission line embedded in an elliptically stratified cross section are considered. Electro- and magneto-static problems are solved using separation of variables in elliptical coordinates. It is shown that asymptotic solutions for the radial dependences of the terms of the series can be used, under certain conditions, on the profiles of stratification. Results about the convergence and the usefulness of the asymptotic solution are presented.
3 citations
TL;DR: Imaging tests of the SMAART JV Pluto 1.5 data set illustrate that the RWE migration algorithm generates high-quality prestack migration 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 poststack migration example illustrates the advantages of elliptic coordinates in imaging overturning wavefields. Imaging tests of the SMAART JV Pluto 1.5 data set illustrate that the RWE migration algorithm generates high-quality prestack migration images comparable to, or better than, the corresponding Cartesian coordinate systems.
3 citations