Using cylindrical coordinates we examine some of the practical limits introduced by the use of an illuminating spherical lens of finite aperture in the implementation of the SOFT. By deriving simple rules of th
A formalism and the corresponding numerical procedures that calculate the Fourier transform of a single-particle wave function defined on a grid of cylindrical ( \\\(ho\\\) , z ) coordinates is presented. Single-particle states in spherical and deformed nuclei have been chosen in view of futur...
5.7). All electrode shapes were calculated so that a pure quadro-logarithmic potential exists inside the trapping cell, as expressed in the following equation: (5.7)Vrz=k2z2−r22+k2Rm2lnrRm+C, where r and z are cylindrical coordinates, Rm is termed as the characteristic radius, k the ...
In cylindrical coordinates (z, r, φ) this Poisson equation takes the form (7.2)∂2V∂z2+∂2V∂r2+1r⋅∂V∂r+1r2⋅∂2V∂φ2=−S(z,r,φ) Both functions V and S are periodic with respect to the azimuth φ, the period being 2π, which suggests that we should...
High performance computational platform in Python for the spectral Galerkin method python hpc spectral fourier turbulence fenics mobius galerkin laguerre chebyshev legendre spectral-methods spherical-coordinates cylindrical-coordinates hermite curvilinear-coordinates polar-coordinates ultraspherical Updated Dec 3, ...
While these functions are useful for problems in cylindrical or polar coordinates, they do not apply to this discussion. The definition of orthogonality for a function φ is that it must satisfy the following condition: Using the above definition, it is possible to solve for the coefficients (...
The principles underlying Brillouin microscopy, as well as our particular approach, are outlined in Fig.1. Fourier-transform spectroscopy is an established technique for spectral characterization, and relies on measuring the optical power at the output of an interferometer as a function of the optical...
If, however, completely irregular meshes are in use, such a transform is not absolutely necessary, though it might still be useful. In cartesian coordinates (x, y) or cylindrical coordinates (z, r) the material properties are usually isotropic, and the driving term is often quadratic. We ...
(Eq. 4)ωz=2qVtrapαma2wherein “Vtrap” is the trapping potential in the axial direction, “α” is a value characteristic of the trap geometry (2.77 for a cubic (9), 2.84 for a cylindrical (10, 11), and 3.87 for an open trap (12)) and “a” is the trapping electrode ...
1. A method of calculating an estimated basis function coefficient for a two dimensional surface, the method comprising: inputting a Fourier transform of the two dimensional surface; inputting a conjugate Fourier transform of a basis function surface; determining a Fourier domain sum of the Fourier...