The effect of coordinate system rotations on spherical harmonic expansions: A numerical method

1984 ◽  
Vol 89 (B6) ◽  
pp. 4413-4418 ◽  
Author(s):  
Jacob D. Goldstein
Keyword(s):  
Coordinate System ◽  
Numerical Method ◽  
Spherical Harmonic

scholarly journals BFC Method For Prediction of Transient Head on Seepage Path

2010 ◽  
Vol 1 (2) ◽  
pp. 824
Author(s):  
Sherly Hartono
Keyword(s):  
Coordinate System ◽  
Numerical Method ◽  
Water Level ◽  
Curvilinear Coordinate System ◽  
Levee Failure ◽  
Curvilinear Coordinate

Seepage causes weakening of levees and can cause levee failure or overtopping due to levee settlement. A numerical method, called the boundary fitted coordinate (BFC) method, was developed to determine seepage through a levee and the transient head on the seepage path due to the changing water level during a flood. The BFC transforms the physical coordinate system into a computational curvilinear coordinate system. The grid generated in this method accurately represents the boundary of the system regardless of its complexity. 

Cortical Cartography

Biofeedback ◽  
2010 ◽  
Vol 38 (1) ◽  
pp. 9-12 ◽  
Author(s):  
David A. Kaiser
Keyword(s):  
Light Microscopy ◽  
Coordinate System ◽  
Operant Conditioning ◽  
Spherical Harmonic ◽  
Cell Types ◽  
Spherical Harmonic Expansion ◽  
3 Dimensional ◽  
Brodmann Areas ◽  
The Brain

Abstract Architecture is one part science, one part craft, and two parts art.—David Rutten This article describes the investigation of structural-functional associations in the brain. Using light microscopy in 1909, Brodmann divided the human and primate brains into dozens of areas based on cell types and distributions, which has since been supplemented by a 3-dimensional coordinate system, an xyz system of millimeter distances. A number of electroencephalograph tomographic (volume) solutions exist, and this article explains the Brodmann montage developed by the author using the spherical harmonic expansion solution by Pascual-Marqui. The author describes his approach to training specific Brodmann areas with electroencephalograhic operant conditioning or feedback.

scholarly journals Asteroseismological Models with Rotation

1993 ◽  
Vol 137 ◽  
pp. 560-562
Author(s):  
Doru Marian Suran ◽  
Gabriela Oprescu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Method ◽  
Line Profile ◽  
Differential Rotation ◽  
Spherical Harmonic ◽  
Low Frequency ◽  
Partial Differential ◽  
Final Model ◽  
Physical Chemical

AbstractThe low frequency NRP oscillations are considered in the case of differential rotation. Partial differential equations for adiabatic oscillations are reduced to a system of ordinary equations by means of a truncated spherical-harmonic expansion. The numerical method for solving the system is described. The final model also includes line profile variations (lpv) and posttheoretical mass (pth) calculations for the complete determinations of the physical, chemical, rotational and seismological properties of the stars.

scholarly journals Dipole Near Field Analysis – A Closed Form Calculation in Cartesian Coordinates

2013 ◽  
Vol 64 (5) ◽  
pp. 327-330 ◽  
Author(s):  
René Harťanský ◽  
Jozef Slížik ◽  
Lukáš Maršálka
Keyword(s):  
Coordinate System ◽  
Closed Form ◽  
Numerical Method ◽  
Electric Dipole ◽  
Near Field ◽  
Analytical Calculation ◽  
Field Analysis ◽  
Cartesian Coordinate System ◽  
Cartesian Coordinates ◽  
Cartesian Coordinate

Abstract This article deals with analytical calculation of the near-field of an electric dipole in Cartesian coordinate system in a closed form. Results of the analytical calculation are verified by numerical method.

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