Homogenization of a spherical harmonics expansion model

2018 ◽  
Vol 28 (03) ◽  
pp. 453-485 ◽  
Author(s):  
Nader Masmoudi ◽  
Mohamed Lazhar Tayeb ◽  
Abderraouf Tlili
Keyword(s):  
Spherical Harmonics ◽  
Electrostatic Potential ◽  
Spherical Harmonics Expansion ◽  
Expansion Model

This paper deals with the analysis of the behavior of a Spherical Harmonics Expansion (SHE) model associated with an oscillating electrostatic potential.

ANALYSIS OF A SPHERICAL HARMONICS EXPANSION MODEL OF PLASMA PHYSICS

2004 ◽  
Vol 14 (05) ◽  
pp. 759-774 ◽  
Author(s):  
OLAF HANSEN ◽  
ANSGAR JÜNGEL
Keyword(s):  
Spherical Harmonics ◽  
Semigroup Theory ◽  
Dirichlet Boundary Conditions ◽  
Degenerate Equation ◽  
Zero Energy ◽  
Semiconductor Physics ◽  
One Dimensional ◽  
Long Time ◽  
Spherical Harmonics Expansion ◽  
Expansion Model

A spherical harmonics expansion model arising in plasma and semiconductor physics is analyzed. The model describes the distribution of particles in the position-energy space subject to a (given) electric potential and consists of a parabolic degenerate equation. The existence and uniqueness of global-in-time solutions is shown by semigroup theory if the particles are moving in a one-dimensional interval with Dirichlet boundary conditions. The degeneracy allows to show that there is no transport of particles across the boundary corresponding to zero energy. Furthermore, under certain conditions on the potential, it is proved that the solution converges in the long-time limit exponentially fast to some steady state.

A COUPLED SPHERICAL HARMONICS EXPANSION MODEL FOR CONFINED PARTICLES

2004 ◽  
Vol 14 (08) ◽  
pp. 1133-1165
Author(s):  
JEAN-PIERRE BOURGADE
Keyword(s):  
Kinetic Equation ◽  
Diffusion Model ◽  
Spherical Harmonics ◽  
Diffusion Approximation ◽  
Charged Particles ◽  
Collision Operator ◽  
Energy Collision ◽  
Macroscopic Scale ◽  
Spherical Harmonics Expansion ◽  
Expansion Model

Our goal in this paper is to derive from a kinetic setting a diffusion model for the transport of charged particles trapped in a surface potential. The so-obtained model is derived through a diffusion approximation, as we assume the thermalization to be governed by particle-wall collisions. In order to take into account the possible inelasticity of such collisions, we introduce a nonlocal (in energy) collision operator on the boundary. At the macroscopic scale, this results in a coupled (in energy) Spherical Harmonics Expansion (SHE) model. The model is both formally and rigorously derived from the kinetic equation, and existence is obtained as a by-product of the derivation.

scholarly journals High field approximations of the spherical harmonics expansion model for semiconductors

2001 ◽  
Vol 52 (2) ◽  
pp. 201-230 ◽  
Author(s):  
N. Ben Abdallah ◽  
P. Degond ◽  
P. Markowich ◽  
C. Schmeiser
Keyword(s):  
Spherical Harmonics ◽  
High Field ◽  
Spherical Harmonics Expansion ◽  
Expansion Model

scholarly journals The Spherical Harmonics Expansion model coupled to the Poisson equation

2011 ◽  
Vol 4 (4) ◽  
pp. 1063-1079 ◽  
Author(s):  
Jan Haskovec ◽  
◽  
Nader Masmoudi ◽  
Christian Schmeiser ◽  
Mohamed Lazhar Tayeb ◽  
...  
Keyword(s):  
Poisson Equation ◽  
Spherical Harmonics ◽  
The Poisson Equation ◽  
Spherical Harmonics Expansion ◽  
Expansion Model

Simulating the diffraction line profile from nanocrystalline powders using a spherical harmonics expansion

2018 ◽  
Vol 74 (6) ◽  
pp. 640-646
Author(s):  
K. R. Beyerlein ◽  
P. Scardi
Keyword(s):  
Line Profile ◽  
Spherical Harmonics ◽  
Diffraction Line ◽  
Nanocrystalline Powders ◽  
Computationally Efficient ◽  
Profile Function ◽  
Diffraction Line Profile ◽  
Cubic Crystallites ◽  
Crystallite Shape ◽  
Spherical Harmonics Expansion

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.

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

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.

FISSION DYNAMICS IN THE FOUR-DIMENSIONAL DEFORMATION SPACE

2006 ◽  
Vol 15 (02) ◽  
pp. 417-425 ◽  
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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