Analytical and Numerical Modeling of Microelectrode Voltammetry in Oblate Spheroidal Coordinates

2021 ◽  
Vol MA2021-01 (45) ◽  
pp. 1803-1803
Author(s):  
Alexis Maguin Fenton, Jr. ◽  
Bertrand J. Neyhouse ◽  
Kevin M. Tenny ◽  
Yet-Ming Chiang ◽  
Fikile R. Brushett
Keyword(s):  
Numerical Modeling ◽  
Oblate Spheroidal ◽  
Spheroidal Coordinates

Torsional oscillation of a homogeneous elastic spheroid

1962 ◽  
Vol 52 (3) ◽  
pp. 469-484 ◽  
Author(s):  
Tatsuo Usami ◽  
Yasuo Satô
Keyword(s):  
Fundamental Mode ◽  
Free Oscillation ◽  
Torsional Oscillation ◽  
Numerical Calculations ◽  
Higher Harmonics ◽  
Oblate Spheroidal ◽  
The Earth ◽  
Spectral Peaks ◽  
The Difference ◽  
Spheroidal Coordinates

abstract There are several causes for the observations of splitting of the spectral peaks determined from the free oscillation of the earth. In this paper, the splitting due to the ellipticity is studied assuming a homogeneous earth described by oblate spheroidal coordinates. Ellipticity causes the iTn mode to split into (n + 1) modes, while the earth's rotation causes it to split into (2n + 1) modes. 1/297.0 is adopted as the ellipticity of the earth. Numerical calculations are carried out for the fundamental mode (n = 2, 3, 4) and for the first higher harmonics (n = 1). The difference between the extreme frequencies for each value of n is 0.7% (n = 2), 0.5% (n = 3), and 0.4% (n = 4).

Surface plasmon dispersion on a single-sheeted hyperboloid

1981 ◽  
Vol 59 (4) ◽  
pp. 521-529 ◽  
Author(s):  
R. S. Becker ◽  
V. E. Anderson ◽  
R. D. Birkhoff ◽  
T. L. Ferrell ◽  
R. H. Ritchie
Keyword(s):  
Dispersion Relation ◽  
Dielectric Function ◽  
Surface Plasmon ◽  
Electric Potential ◽  
Laplace’S Equation ◽  
Laplace's Equation ◽  
Oblate Spheroidal ◽  
Spheroidal Coordinates ◽  
Plasmon Dispersion

The surface-plasmon dispersion relation is obtained for a single-sheeted hyperboloid of revolution. The effects of retardation are neglected, and the electric potential is obtained from Laplace's equation in oblate spheroidal coordinates. Our results are applicable to the description of eigenmodes for a submicron hole in a material which may be supposed to have a local dielectric function.

‘Ring-current’ and ‘pseudo-contact’ magnetic shielding by non-spherical molecules

1975 ◽  
Vol 346 (1645) ◽  
pp. 209-225 ◽  
Keyword(s):  
Axial Symmetry ◽  
Ring Current ◽  
Cylindrical Symmetry ◽  
Static Field ◽  
Magnetic Shielding ◽  
Resonance Spectroscopy ◽  
Axially Symmetric ◽  
Oblate Spheroidal ◽  
Spectroscopy Experiment ◽  
Spheroidal Coordinates

A multipolar susceptibility formalism for interpreting and mapping the isotropic magnetic shielding outside axially symmetric molecules is con¬structed. The method involves spheroidal harmonic expansions of the local magnetic fields outside molecules magnetized by the uniform magneto¬ static field of the nuclear magnetic resonance spectroscopy experiment. For ‘disk-shaped’ molecules with infinite axial symmetry the shielding at field points with oblate spheroidal coordinates (U, V, Ø) reduces to where the coefficient a L0 measure anisotropy in the molecular susceptibilities and the P L (V) and Q L (iU) are Legendre polynomials of the first and second kind. A similar result holds for prolate molecules like acetylene with cylindrical symmetry but additional terms appear for molecules like benzene with finite axial symmetry. The spheroidal expansions lead to more accurate descriptions of magnetic shielding outside non-spherical molecules than methods already available and are designed for interpreting experimental shieldings by both paramagnetic and diamagnetic molecules.

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