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Showing papers on "Elliptic coordinate system published in 1994"


Journal ArticleDOI
TL;DR: In this article, the authors studied three-dimensional volume preserving vector fields that are invariant under the action of a one-parameter symmetry group whose infinitesimal generator is autonomous and volume-preserving.
Abstract: The purpose of this paper is to develop analytical methods for studyingparticle paths in a class of three-dimensional incompressible fluid flows. In this paper we study three-dimensionalvolume preserving vector fields that are invariant under the action of a one-parameter symmetry group whose infinitesimal generator is autonomous and volume-preserving. We show that there exists a coordinate system in which the vector field assumes a simple form. In particular, the evolution of two of the coordinates is governed by a time-dependent, one-degree-of-freedom Hamiltonian system with the evolution of the remaining coordinate being governed by a first-order differential equation that depends only on the other two coordinates and time. The new coordinates depend only on the symmetry group of the vector field. Therefore they arefield-independent. The coordinate transformation is constructive. If the vector field is time-independent, then it possesses an integral of motion. Moreover, we show that the system can be further reduced toaction-angle-angle coordinates. These are analogous to the familiar action-angle variables from Hamiltonian mechanics and are quite useful for perturbative studies of the class of systems we consider. In fact, we show how our coordinate transformation puts us in a position to apply recent extensions of the Kolmogorov-Arnold-Moser (KAM) theorem for three-dimensional, volume-preserving maps as well as three-dimensional versions of Melnikov's method. We discuss the integrability of the class of flows considered, and draw an analogy with Clebsch variables in fluid mechanics.

142 citations


Journal ArticleDOI
TL;DR: The representation of electromagnetic quantities by differential forms allows the use of nonorthogonal coordinate systems as mentioned in this paper, and a judicious choice of coordinate system facilitates the finite element modeling of infinite or very thin domains.
Abstract: The representation of electromagnetic quantities by differential forms allows the use of nonorthogonal coordinate systems. A judicious choice of coordinate system facilitates the finite element modeling of infinite or very thin domains.

73 citations


Patent
14 Sep 1994
TL;DR: In this paper, a line detection method using line neighborhoods and a parallel coordinate transformation is proposed to accommodate the uncertainty in line detection arising from image noise, where line neighborhoods are used to transform Cartesian coordinate image plane line segments to points in a bounded and nonambiguous region of the parallel coordinate transform plane.
Abstract: A system for detecting lines in images using line neighborhoods and a parallel coordinate transformation. The process introduces the concept of line neighborhoods to accommodate the uncertainty in line detection arising from image noise. Because line neighborhoods in Cartesian coordinates have ambiguous and unbounded regions and always overlap one another, a parallel coordinate transform is used to transform Cartesian coordinate image plane line segments to points in a bounded and nonambiguous region of the parallel coordinate transform plane. Line detection then becomes a simple problem of detecting point clusters in the parallel coordinate transform plane.

18 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that only one of the two sets gives the conventional interpretation of quantum field theory, based on a Fock space, and discarding the other set, one can still keep the Milne coordinate system.
Abstract: The upper and lower quadrants of flat space-time can be described using the Milne coordinate system. The Klein-Gordon equation of a scalar field in such a coordinate system admits at least two sets of solutions. Based on the Feynman propagator behavior it is shown that only one of the two sets gives the conventional interpretation of quantum field theory, based on a Fock space. Therefore, discarding the other set, one can still keep the Milne coordinate system.

3 citations


Journal ArticleDOI
TL;DR: In this article, a systematic error in the numerical solution for the spherical and cylindrical coordinate systems was examined by a material balance for the system, and the systematic error was found to decrease rapidly as the dimensionless time increased and the grid spacing decreased.
Abstract: Spherulitic crystallization presents an inverse Stefan problem, which is solved by numerical methods using the DuFort-Frankel scheme and Lagrangian coordinate systems. The numerical solution shows excellent agreement with the analytical solution in the Cartesian coordinate system. A systematic error in the numerical solution for the spherical and cylindrical coordinate systems is examined by a material balance for the system. The systematic error was found to decrease rapidly as the dimensionless time increased and the grid spacing decreased.

2 citations


Book ChapterDOI
01 Jan 1994
TL;DR: In this article, a family of confocal quadrics in a projective space and the elliptic coordinates associated with these quadrics are known to be a powerful tool for explicit solving various integrable systems in terms of the Abelian integrals.
Abstract: A family of confocal quadrics in a projective space and the elliptic coordinates associated with these quadrics are known to be a powerful tool for explicit solving various integrable systems in terms of the Abelian integrals. Using the elliptic coordinates associated with such quadrics K. Jacobi solved the problem on the geodesics on an ellipsoid and K. Neumann [9] did the same for the problem of a mass point motion on a sphere in a force field with a quadratic potential.

Journal ArticleDOI
TL;DR: In this paper, an analysis of the integrand occurring in current density functional calculations is presented, concentrating attention on correlation energy functionals and the atomic regions, i.e., the regions of space surrounding atomic centers.
Abstract: An analysis of the integrand occurring in current density functional calculations is presented, concentrating attention on correlation energy functionals and the atomic regions, i.e., the regions of space surrounding atomic centers. The analysis follows the structure of a previously proposed numerical integration scheme for three-dimensional integrals occurring in electronic structure calculations. The scheme is based on the choice of density-based weight functions that naturally partition the space into «atomic» volumes (in which the integration is performed in terms of spherical coordinates) and «diatomic» volumes (in which the integration is performed in terms of confocal elliptical coordinates). From this analysis, a simplified procedure for the atomic «internal» integrations is developed, whereas preliminary results are discussed for the atomic and diatomic «external» integrations. The numerical tests are performed on the C60 molecule in the symmetrical configuration. © John Wiley & Sons, Inc.