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.

Development of hybrid analytical-numerical methods of calculating heat and mass transfer

Abstract: The expediency of using approximate numerical or analytical methods of calculation with respect to elliptical coordinates and accurate methods with respect to unidirectional parabolic variables is demonstrated.

Double-minimum potential-energy curves resulting from adiabatic effects: The 4s 3 Sigma g+ state of the hydrogen molecule.

Abstract: Born-Oppenheimer potential-energy curve and adiabatic corrections for the 4s $^{3}\mathrm{\ensuremath{\Sigma}}_{\mathit{g}}^{+}$ state of the hydrogen molecule have been computed using an explicitly correlated wave function in elliptic coordinates. It is shown that, in contrast to the Born-Oppenheimer results, the adiabatic potential-energy curve for this state is characterized by a double-minimum function. The energies of the vibrational levels and rotational constants have also been computed. Large and irregular differences have been found between thoeretical and experimental results.

Effect of an image potential on the ground-state energy of shallow-donor impurities near the surface of semi-infinite crystals.

Abstract: The effect of image potential on the ground-state energy of a shallow-donor impurity near a sharp surface of a semi-infinite crystal is studied. A simple but realistic trial function is used in the confocal elliptic coordinate system with the foci at the hydrogenic donor impurity and its image point. The groundstate energy of this system is calculated as a function of the impurity position

Thin Wire Modeling for FDTD Electromagnetic Calculations in the Two-Dimensional Cylindrical Coordinate System

Abstract: In this paper, the equivalent radius of a thin wire represented using the FDTD method in the two-dimensional (2D) cylindrical coordinate system is identified as 0.135Δr, where Δr is the lateral side length of the rectangular cells, while that of a thin wire represented in the 3D Cartesian coordinate system is known to be 0.230Δr. Furthermore, it is shown that the technique proposed by Noda and Yokoyama to represent a thin wire having an arbitrary radius in the 3D Cartesian coordinate system can be applied successfully to representing such a thin wire in the 2D cylindrical coordinate system if 0.135Δr is used for the equivalent radius instead of 0.230Δr.

Galaxy mass profiles from strong lensing II: The elliptical power-law model

Abstract: We present a systematic analysis of the constraints $\sigma_\gamma$ on the mass profile slope $\gamma$ obtainable when fitting a singular power-law ellipsoid model to a typical strong lensing observation of an extended source. These results extend our previous analysis of circular systems, Paper I. We draw our results from 676 mock observations covering a range of image configurations, each created with a fixed signal to noise ratio $S=100$ in the images. We analyse the results using a combination of theory and a simplified model which identifies the contribution to the constraints of the individual fluxes and positions in each of the lensed images. The main results are: 1. For any lens ellipticity, the constraints $\sigma_\gamma$ for two image systems are well described by the results of Paper I, transformed to elliptical coordinates; 2. We derive an analytical expression for $\sigma_\gamma$ for systems with the source aligned with the axis of the lens; 3. For both two-image systems and aligned systems, $\sigma_\gamma$ is limited by the flux uncertainties; 4. The constraints for off-axis four-image systems are a factor of two to eight better, depending on source size, than for two-image systems, and improve with increasing lens ellipticity. We show that the constraints on $\gamma$ in these systems derive from the complementary positional information of the images alone, without using flux. The complementarity improves as the offset of the source from the axis increases, such that the best constraints $\sigma_\gamma<0.01$, for $S=100$, occur when the source approaches the caustic.