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.
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01 Jan 2008
TL;DR: In this paper, a new class of three-dimensional absorbing boundary conditions is proposed to be employed on polygonal spheroid boundaries that are primary candidates for surrounding elongated scatterers.
Abstract: SUMMARYWe propose a new class of three-dimensional absorbing boundary conditions to be employed onprolate spheroid boundaries that are primary candidates for surrounding elongated scatterers. Theseconditions are constructed from a local approximation of the Dirichlet-to-Neumann (DtN) operatorcorresponding to the Helmholtz problem when expressed in elliptical coordinates. The constructionprocedureisbasedonanidentificationofcoefficientsinaRobin-typeboundaryconditionpreservingthe symmetry and the local nature of the initial problem. We also require that the considered con-dition to be an exact representation of the first modes. Consequently, we obtain one first-order andone second-order boundary condition. We analyze the effect of the wavenumber and the eccentricityvaluesontheperformanceoftheseboundaryconditionswhenappliedforsolvingacousticscatteringproblems using two different mathematical frameworks depending on the frequency regime. First,we assess the effect of low wavenumber values in the context of the on-surface radiation conditionformulation (OSRC) [2]. The performance of these conditions in the high frequency regime is in-vestigated using the exact Fourier representation of the solution of the acoustic scattering problemin the bounded computational domain [1]. The analysis reveals that the DtN2 boundary conditionretains an excellent level of accuracy for all frequency regime and eccentricity values of the artificialboundaries. In addition, guidelines for avoiding excessive computational cost for practical applica-tions are provided evaluating the effect of the localisation of the artificial boundary on the accuracyof the approached solution.Keywords: Absorbingboundaryconditions,prolatespheroidalcoordinates,Dirichlet-to-Neumannoperator, acoustic scattering problems.References[1] J. J. B
15 Sep 2019
TL;DR: In this article, the authors simulate the nonlinear quantum pendulum using non-diffracting solutions of the 2-dimensional Helmholtz equation in elliptical coordinates and show that stationary and wavepacket Mathieu spatial modes are in quantitative agreement with the quantum probabilities.
Abstract: We simulate the nonlinear quantum pendulum using non-diffracting solutions of the 2-dimensional Helmholtz equation in elliptical coordinates. Stationary and wavepacket Mathieu spatial modes are in quantitative agreement with the quantum probabilities.
31 May 2015
TL;DR: Wang et al. as mentioned in this paper presented a novel circular effect generation approach to manipulate (i,j) coordinate system easier, by transforming (i and j) coordinate systems into (ρ,θ) coordinates.
Abstract: This paper presents a novel circular effect generation approach. In general, pixel location in an image can be represented with i and j coordinate. To manipulate (i,j) coordinate system easier, we transform (i,j) coordinate system into (ρ,θ) coordinate system. Two parameters are used for generating circular effect: R and T. After applying selected R and T in (ρ,θ) coordinate system, (ρ2,θ2) are obtained. Finally, (ρ2,θ2) signals are inverse-transformed into (i,j) coordinate system and (i2,j2) is obtained. Experimental results introduce performance comparison.
TL;DR: The Ince-Gaussian modes as discussed by the authors are a complete family of exact and orthogonal solutions of the paraxial wave equation in elliptic coordinates and are natural resonating modes of stable laser resonators.
Abstract: We present the Ince-Gaussian modes that are a new complete family of exact and orthogonal solutions of the paraxial wave equation in elliptic coordinates and are natural resonating modes of stable laser resonators
Patent•
20 Oct 2009
TL;DR: In this paper, a touch panel detects a point in one of a plurality of unit areas at which an input was made, the unit areas being arranged in a matrix in an instruction plane.
Abstract: A touch panel detects a point in one of a plurality of unit areas at which an input was made, the unit areas being arranged in a matrix in an instruction plane. A game apparatus repeatedly acquires detection coordinates for locating a unit area detected by a pointing device. Also, the game apparatus repeatedly calculates, in response to the acquisition of the detection coordinates, detailed coordinates by which a point can be represented with accuracy in more detail than by the detection coordinates. The detailed coordinates indicate a point in the direction of a unit area indicated by previously acquired detection coordinates, as viewed from a predetermined reference point within a unit area indicated by currently acquired detection coordinates.