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.

Discretization of Macroscopic Transport Equations on Non-Cartesian Coordinate Systems

Abstract: We discuss discretization schemes for the Poisson equation, the isothermal drift-diffusion equations, and higher order moment equations derived from the Boltzmann transport equation for general coordinate systems. We briefly summarize the method of dimension reduction when the problem does not depend on one coordinate. Discretization schemes for dimension-reduced coordinate systems are introduced, which provide curvilinear coordinate systems. In addition to the reduction of the dimensionality, another benefit of these curved coordinate systems is that the domain approximation is more accurate, and therefore, the mesh point density can be kept smaller compared to the original problem. We obtain a discretization scheme for the isothermal drift-diffusion equation in closed from. For higher order transport equations, we use the approximation method of optimum artificial diffusivity and generalize it for non-Cartesian coordinate systems. For the special case of cylindrical coordinates, we can show that it is not necessary to introduce special discretization schemes apart from the standard Scharfetter-Gummel scheme.

A river-flow model based on a simplified boundary-fitted coordinate

Abstract: 河川流計算で用いる水平座標系として, デカルト座標系や直交曲線座標系のような数値モデル上の簡便さを有しつつ, 一般座標系と同程度の計算精度を兼ね備えた簡易境界適合座標系 (水平σ座標系) を新たに提案した. この水平σ座標系とは, 鉛直座標系として気象・海洋計算に用いられる一種の境界適合座標系であるσ座標系を, 河川流計算における水平座標系に応用するものである. 水平σ座標系に基づく河川流モデルの基本的な有効性を調べるために, 本モデルを直線開水路流れや実河川流場へ適用し, 他の水平座標系と計算精度や計算負荷を比較・検討した. その結果, 水平σ座標系は一般座標系と比べて計算精度に大差なく, その上, デカルト座標系と同程度の低計算負荷を保つことが示された.

How to construct a coordinate representation of a Hamiltonian operator on a torus

Abstract: The dynamical system of a point particle constrained on a torus is quantized a la Dirac with two kinds of coordinate systems respectively; the Cartesian and toric coordinate systems. In the Cartesian coordinate system, it is difficult to express momentum operators in coordinate representation owing to the complication in structure of the commutation relations between canonical variables. In the toric coordinate system, the commutation relations have a simple form and their solutions in coordinate representation are easily obtained with, furthermore, two quantum Hamiltonians turning up. A problem comes out when the coordinate system is transformed, after quantization, from the Cartesian to the toric coordinate system.

Algorithm for the storage of expansion coefficients for the product of associated Legendre functions in elliptical coordinates useful for the calculations of molecular integrals

Abstract: An algorithm is presented for the generation and storage of expansion coefficients for the product of two associated Legendre functions both with different centers introduced by the one of authors [J. Phys. B 3 (1970) 1399] for the calculation of multicenter integrals over STOs using auxiliary functions. The formulae for retrieving these coefficients in a non-sequential fashion are developed and presented. We believe that the use of formulae given in this work for the storage of expansion coefficients will have important contributions in reducing requirements for computer time in the calculation of molecular integrals with the aid of auxiliary functions.

Is Possible to Plot Matrices into a Multi-Dimensional Coordinate System?

Abstract: This paper proposes two types of multi-dimensional coordinate systems to plot matrices, these two multi-dimensional coordinate systems are the surface mapping coordinate system and the four dimensional physical space. The idea is to represent graphically a large system of simultaneous equations into the same graphical space and time.