Search results for "Spherical Harmonic"
showing 10 items of 28 documents
Photoionization of adsorbates on sites with non-axial local symmetry. An example of the symmetry group
1996
We present an analysis of the influence of the local adsorption site symmetry on the angular distribution of photoelectrons ejected from adsorbed atoms or molecules. This analysis applies to photoelectron spectra obtained with photons of any energy in the VUV (photoelectron spectroscopy) or x-ray (XPS) regions, provided that the associated wave of the electron `sees' the neighbouring surface atoms. The adsorbate - substrate system is modelled by a cluster of symmetry group consisting of an adsorbate and several atoms of the substrate. The analysis applies also to clean surfaces of symmetry and to molecules of the symmetry group fixed in space. This local symmetry analysis is an alternative …
A star product on the spherical harmonics
1996
We explicitly define a star product on the spherical harmonics using the Moyal star product on ℝ6, and a polarization equation allowing its restriction on S2.
Spherical Harmonics Expansion of Fundamental Solutions and Their Derivatives for Homogeneous Elliptic Operators
2017
In this work, a unified scheme for computing the fundamental solutions of a three-dimensional homogeneous elliptic partial differential operator is presented. The scheme is based on the Rayleigh expansion and on the Fourier representation of a homogeneous function. The scheme has the advantage of expressing the fundamental solutions and their derivatives up to the desired order without any term-by-term differentiation. Moreover, the coefficients of the series need to be computed only once, thus making the presented scheme attractive for numerical implementation. The scheme is employed to compute the fundamental solution of isotropic elasticity showing that the spherical harmonics expansion…
Low angle neutron scattering of ferritin studied by contrast variation.
1976
Ferritins containing different amounts of iron have been studied by neutron small angle scattering in H 2 O/D 2 O mixtures. Apoferritin has also been studied in solutions of small organic molecules. There is a larger contrast variation in the solutions of small organic molecules than in the corresponding H 2 O/D 2 O experiments from which it may be calculated that I g of apoferritin contains 0·3 g of H 2 O. The solvent composition at zero contrast varies regularly with the iron content of the protein: there is evidence for polydispersity in the iron content of the ferritin used. From analysis of the scattering curves it is concluded that the iron is probably not homogeneously distributed in…
Study of the partial wave structure of π0η photoproduction on protons
2013
Abstract Analysis of the partial wave structure of γ p → π 0 η p reaction is presented in the energy region from threshold up to the total center-of-mass energy W = 1.9 GeV . Angular distributions measured with the Crystal Ball/TAPS hermetic detector system at the Mainz Microtron MAMI are expanded in terms of spherical harmonics. The relation of the extracted moments to the partial wave structure of the reaction amplitude is discussed and compared with predictions from model calculations.
A fully automated method for accurate measurement of geometrical distortion in magnetic resonance imaging of a 3D-lattice phantom
2019
Abstract This paper describes an automated method for extracting the apparent positions of fiducial points from 2D or 3D images of a phantom. We consider a 3D-lattice phantom for two main reasons: first, ease of manufacture and isotropy of its structure with respect to coordinate projections; second, a connected structure allowing to uniquely assess the adjacency relationship between fiducial points even if geometric distortions arising from main magnet inhomogeneity and gradient fields non-linearity is severe as observed in open-bore systems. In order to validate our proposed method and compare different choices for the parameters of our phantom (i.e. number and distance between grids and …
The infancy of core-collapse supernova remnants
2020
We present 3D hydrodynamic simulations of neutrino-driven supernovae (SNe) with the PROMETHEUS-HOTB code, evolving the asymmetrically expanding ejecta from shock breakout until they reach the homologous expansion phase after roughly one year. Our calculations continue the simulations for two red supergiant (RSG) and two blue supergiant (BSG) progenitors by Wongwathanarat et al., who investigated the growth of explosion asymmetries produced by hydrodynamic instabilities during the first second of the explosion and their later fragmentation by Rayleigh-Taylor instabilities. We focus on the late time acceleration and inflation of the ejecta caused by the heating due to the radioactive decay of…
Small Angular Scale Simulations of the Microwave Sky
1996
We describe and compare two types of microwave sky simulations which are good for small angular scales. The first type uses expansions in spherical harmonics, and the second one is based on plane waves and the Fast Fourier Transform. The angular power spectrum is extracted from maps corresponding to both types of simulations, and the resulting spectra are appropriately compared. In this way, the features and usefulness of Fourier simulations are pointed out. For $\ell \geq 100$, all the simulations lead to similar accuracies; however, the CPU cost of Fourier simulations is $\sim 10$ times smaller than that for spherical harmonic simulations. For $\ell \leq 100$, the simulations based on sph…
Comments on “Four-Stream Spherical Harmonic Expansion Approximation for Solar Radiative Transfer”
1998
Comments on : four-stream spherical harmonic expansion approximation for solar radiative transfer.
Comparison of cartesian and lobe function Gaussian basis sets
1970
The lobe function and cartesian (spherical harmonic) gaussian are compared with reference to calculations for second-row atoms. Single and grouped gaussian basis sets which have been reported for cartesian functions are taken over directly to construct corresponding lobe function bases with identical sets of exponents and with lobe separations chosen by a scaling procedure. Total and orbital energies and SCF coefficients resulting from calculations on the second-row atoms using the two types of functions for both primitive and grouped gaussian basis sets are seen to be in excellent agreement, thereby emphasizing the essential equivalence of lobe functions and cartesian gaussians, at the ver…