Translations of spherical harmonics expansion coefficients for a sound field using plane wave expansions

An accurate description of the diffraction line profile from nanocrystalline powders can be obtained by a spherical harmonics expansion of the profile function. The procedure outlined in this work is found to be computationally efficient and applicable to the line profile for any crystallite shape and size. Practical examples of the diffraction pattern peak profiles resulting from cubic crystallites between 1 and 100 nm in size are shown.

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Total Electron Content (TEC) estimation over Pakistan from local GPS network using spherical harmonics

Annals of Geophysics ◽

10.4401/ag-8433 ◽

2021 ◽

Vol 64 (1) ◽

Author(s):

Maria Mehmood ◽

Sajid Saleem ◽

Renato Filjar ◽

Najam Naqvi ◽

Arslan Ahmed

Keyword(s):

Spherical Harmonics ◽

Orbit Determination ◽

Region Of Interest ◽

Local Model ◽

Small Scale ◽

Electron Content ◽

Total Electron ◽

Gps Network ◽

Spherical Harmonics Expansion ◽

The Impact

Many organizations allow GNSS users to access Global Ionosphere Maps (GIMS). However, the TEC estimates derived from GIMs are of insufficient quality to describe small-scale TEC variations over Pakistan. In this paper, the first local TEC map over Pakistan for the year 2019, derived from a regional GPS network, is presented. Spherical harmonics expansion is employed to estimate TEC with the spatial resolution of latitude 0.2° x longitude 0.2° and temporal resolution of 5 minutes. The impact of changing the degree/order of harmonics is assessed and it is determined that harmonic expansion up to 6 degrees is sufficient for estimating accurate TEC map for the region of interest. We have demonstrated that the TEC maps of Pakistan generated by local model conform better to the GIM by Center of Orbit Determination (CODE) (RMS = 5.83) as compared to International Reference Ionosphere (IRI-2016) (RMS = 7.18). We found that the TEC estimated by the local model shows a better correlation to measured TEC; CODE-GIM overestimated TEC, while IRI-2016 underestimates it. Moreover, it was observed that TEC peaks during noon (1100-0100 LT) and Equinox (April). The residuals of local TEC estimates with respect to TEC obtained from CODE- GIM indicate the inaccuracy of CODE-GIM over the region of Pakistan: highest deviation of TEC from local model with respect to CODE –GIM was observed in April (RMS = 8.73) and minimum in October (RMS = 2.78). We have also analyzed the performance of our maps in geomagnetically disturbed days. The research presented in this paper will contribute towards the ionosphere study over Pakistan, where limited research is available currently.

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Radiation modes of propeller tonal noise

Journal of Vibration and Acoustics ◽

10.1115/1.4051864 ◽

2021 ◽

pp. 1-25

Author(s):

Hanbo Jiang ◽

Siyang Zhong ◽

Han Wu ◽

Xin Zhang ◽

Xun Huang ◽

...

Keyword(s):

Spherical Harmonics ◽

Sound Field ◽

Low Noise ◽

Noise Model ◽

Sound Waves ◽

Tonal Noise ◽

Noise Sources ◽

Separate Source ◽

Radial Forces ◽

Flow Variables

Abstract This paper focuses on the radiation modes and efficiency of propeller tonal noise. The thickness noise and loading noise model of propellers has been formulated in spherical coordinates, thereby simplifying numerical evaluation of the integral noise source. More importantly, the radiation field can be decomposed and projected to spherical harmonics, which can separate source-observer positions and enable an analysis of sound field structures. Thanks to the parity of spherical harmonics, the proposed model can mathematically explain the fact that thrusts only produce antisymmetric sound waves with respect to the rotating plane. In addition, the symmetric components of the noise field can be attributed to the thickness, as well as drags and radial forces acting on the propeller surface. The radiation efficiency of each mode decays rapidly as noise sources approach the rotating centre, suggesting the radial distribution of aerodynamic loadings should be carefully designed for low-noise propellers. The noise prediction model has been successfully applied to a drone propeller and achieved a reliable agreement with experimental measurements. The flow variables employed as an input of the noise computation were obtained with computational fluid dynamics (CFD), and the experimental data were measured in an anechoic chamber.

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Carrier Transport in Silicon Dioxide using the Spherical-Harmonics Expansion of the BTE

Progress in Industrial Mathematics at ECMI 2000 - Mathematics in Industry ◽

10.1007/978-3-662-04784-2_25 ◽

2002 ◽

pp. 190-194

Author(s):

S. Reggiani ◽

M. Marsella ◽

A. Gnudi ◽

M. Rudan

Keyword(s):

Silicon Dioxide ◽

Spherical Harmonics ◽

Carrier Transport ◽

Spherical Harmonics Expansion

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A Monte Carlo Transport Model Based on Spherical Harmonics Expansion of the Valence Bands

Simulation of Semiconductor Devices and Processes ◽

10.1007/978-3-7091-6619-2_96 ◽

1995 ◽

pp. 396-399 ◽

Cited By ~ 7

Author(s):

H. Kosina ◽

M. Harrer ◽

P. Vogl ◽

S. Selberherr

Keyword(s):

Monte Carlo ◽

Spherical Harmonics ◽

Transport Model ◽

Model Based ◽

Spherical Harmonics Expansion ◽

Valence Bands ◽

Monte Carlo Transport

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FISSION DYNAMICS IN THE FOUR-DIMENSIONAL DEFORMATION SPACE

International Journal of Modern Physics E ◽

10.1142/s0218301306004296 ◽

2006 ◽

Vol 15 (02) ◽

pp. 417-425 ◽

Cited By ~ 28

Author(s):

KRZYSZTOF POMORSKI ◽

JOHANN BARTEL

Keyword(s):

Spherical Harmonics ◽

Deformation Space ◽

Neck Formation ◽

Deformation Parameters ◽

Fission Barriers ◽

Spherical Harmonics Expansion ◽

Left Right Asymmetry ◽

Rotating Nuclei

A four-dimensional deformation space adapted to describe the fission dynamics of hot, rotating nuclei is proposed. The deformation coordinates consisting of the elongation, neck formation, left-right asymmetry and nonaxiality result in fission barriers much lower and thiner than those obtained in the spherical-harmonics expansion using the same number of deformation parameters.

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