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.

Covariant transformations of basis differential-difference schemes in a plane

Abstract: Consistent difference approximations to differential operators in vector and tensor analysis are constructed in curvilinear coordinates in a plane by applying the basis operator method. They are obtained as a transformation of basis approximations in a Cartesian coordinate system. For the continuum mechanics equations in Lagrangian variables, this approach yields theoretically justified differential-difference schemes whose conservation laws correspond to the continuous case.

Calculation of diatomic molecules in an ellipsoidal basis with floating foci

Abstract: Basis functions expressed in elliptic coordinates with floating foci have been proposed for quantum-chemical calculations of diatomic molecules. The effectiveness of the use of such functions for the calculation of the energy and a number of nonenergetic characteristics has been demonstrated in the example case of the calculation of the H/sub 2/ and HeH/sup +/ molecules. Closed formulas for calculating the specific three-center one-electron integrals appearing in these calculations have been derived.

Three-dimensional Coordinate Transformation with Consideration of Coordinate Errors in Two Coordinate Systems

Abstract: The paper presents a new coordinate transformation model with a consideration of the coordinate errors in both coordinate systems.The computation formulae of transformation parameters are derived based on the minimization of weighted sum of coordinate corrections in two systems.In addition,the coordinate corrections of transformed points are computed according to the covariance matrix of coordinates between public and transformed points with the least-squares collocation method.The experiments show that the new model can significantly improve the precision of the coordinate transformation especially in case that the strong correlation exists between public and transformed coordinates.

On the Possibility of Generating Solutions to Electromagnetic Problems from known Solutions of Corresponding Static Problems

Abstract: This paper coordinates and formalizes previous ideas on the possibility of creating solutions to electromagnetic wave (i.e. dynamic) problems in three dimensions from the electrostatic and magnetostatic solutions for the corresponding zero-frequency (i.e. static) problems in the same geometry. Extension of the method to the conical coordinate system is shown to be possible. Previous workers had included the rectangular, circular cylindrical, elliptic cylindrical, parabolic cylindrical, and spherical coordinate systems. It is further reported that it is impossible to extend the method to the other five coordinate systems in which the Laplace and Helmholtz equations, in three dimensions, are separable.

An Improved Algorithm for Pseduo-Jacobi-Fourier Moments

Abstract: Image moments have been used in many research fields of the engineering. However, the related computation of invariant moments mostly adopted the polar coordinate system, which not only increase the computational load, but also cause large quantized error. To solve this problem, an improved algorithm to compute Pseudo-Jacobi-Fourier moments in the Cartesian coordinate system is proposed in this paper. The experimental results show that the reconstructed image with improved PJFM’s has more advantages than polar coordinate system, such as more information, fewer moments, less time consuming. And the recognition rate of the microscopic images of 8 helminth eggs was also higher than in polar coordinate system.