scispace - formally typeset
Search or ask a question
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
More filters
Journal ArticleDOI
TL;DR: In this paper, the scattering of antiplane shear waves induced by a deep semielliptic canyon with a horizontal edge was studied, and the region-point-matching technique was employed to cope with the problem.
Abstract: We study scattering of antiplane shear waves induced by a deep semielliptic canyon with a horizontal edge We employ the region-point-matching technique to cope with the problem considered Through an auxiliary boundary, a part of the circumference of a semiellipse, the whole analyzed region is divided into two subregions We express the displacement fields in terms of Mathieu functions We unify two distinct elliptic coordinates via a simple coordinate transformation relation Integration of the coordinate transformation relation into the region-point-matching technique simplifies the procedure for constructing simultaneous equations Imposing the continuity conditions and traction-free ones, we obtain the expansion coefficients Frequency-domain results demonstrate ground motion variability based on several key factors Ground surface responses under seismic shaking are also simulated in the time domain

14 citations

Journal ArticleDOI
TL;DR: In this article, the Stackel potential in elliptic coordinates and momenta is studied and the forms of the orbits are found numerically and analytically, in the nonrotating case the orbits fill either an ellipse around both foci, or a region around one focus.
Abstract: A rotating potential, which has a second integral, besides the Hamiltonian, quadratic in the momenta, is studied. This can be expressed as a Stackel potential in elliptic coordinates, but it is nonseparable, unless its rotation is zero. The canonical momenta corresponding to the elliptic coordinates and the forms of the Hamiltonian and of the new integral in elliptic coordinates and momenta are found. The forms of the orbits are found numerically and analytically. In the nonrotating case the orbits fill either an ellipse around both foci, or a region around one focus limited by an ellipse and a hyperbola

14 citations

Posted Content
TL;DR: In this article, the formulas for some of the most frequently used expressions and operations in dipole coordinates are presented. But they do not cover the most common operations in a coordinate system aligned with magnetic field lines.
Abstract: A strong magnetic field can make it advantageous to work in a coordinate system aligned with dipolar field lines. This monograph collect the formulas for some of the most frequently used expressions and operations in dipole coordinates.

14 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that the Hamilton-Jacobi equation for massless geodesics can only separate in elliptic or spherical coordinates, and all known integrable backgrounds are covered by this separation.
Abstract: Motivated by the search for new backgrounds with integrable string theories, we classify the D-brane geometries leading to integrable geodesics. Our analysis demonstrates that the Hamilton-Jacobi equation for massless geodesics can only separate in elliptic or spherical coordinates, and all known integrable backgrounds are covered by this separation. In particular, we identify the standard parameterization of AdS_p X S^q with elliptic coordinates on a flat base. We also find new geometries admitting separation of the Hamilton-Jacobi equation in the elliptic coordinates. Since separability of this equation is a necessary condition for integrability of strings, our analysis gives severe restrictions on the potential candidates for integrable string theories.

13 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that a subset of the multidimensional Euler equations can be diagonalized, but not the entire set, and the authors extended the formulation of the conservation equations into the local stream-wise coordinate system to the time-dependent, 2D and 3D conservation equations.
Abstract: In dealing with multidimensional simulations, many authors have shown that a major cause of numerical dispersion errors is due to the flow being skewed to the coordinate axes. Crane and Blunt [1] have shown that the stream-wise transformations can reduce the numerical errors associated with the multidimensional transport equations. However, it has been proven that no transformation can completely diagonalize the multidimension conservation equations. It shall be demonstrated that a subset of the multidimensional Euler equations can be diagonalized, but not the entire set. The formulation of the conservation equations into the local stream-wise coordinate system is extended to the time-dependent, two- and three-dimensional (2D and 3D) conservation equations. At any point in space, there exists a set of local rotations that aligns the fluid velocity vector coincident with the stream-wise coordinate; hence, the fluid velocity components orthogonal to the stream-wise coordinate are identically zero. Such transformations result in a subset of PDEs that are diagonalized, namely, the mass, total energy, and principal momentum density PDEs. However, the orthogonal momentum component conservation PDEs are not diagonalized and are multidimensional; these PDEs are responsible for streamline bending.

13 citations


Network Information
Related Topics (5)
Boundary value problem
145.3K papers, 2.7M citations
75% related
Differential equation
88K papers, 2M citations
73% related
Numerical analysis
52.2K papers, 1.2M citations
72% related
Field (physics)
95K papers, 1.5M citations
72% related
Partial differential equation
70.8K papers, 1.6M citations
71% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20237
202211
202111
202010
201913
201810