Geolocation of Pulses Using Bispherical Coordinates and Multiple Omnidirectional Receivers

2019 ◽  
Author(s):  
George N. Gilliam ◽  
Tracie A. Severson
Keyword(s):  
Bispherical Coordinates

Scattering by Two Impenetrable Spheres

1973 ◽  
Vol 51 (17) ◽  
pp. 1850-1860
Author(s):  
M. Razavy
Keyword(s):  
Wave Function ◽  
Scattering Amplitude ◽  
Hard Spheres ◽  
Scattering Length ◽  
Separation Of Variables ◽  
Scattered Wave ◽  
Simple Expression ◽  
Rigid Spheres ◽  
Low Energies ◽  
Bispherical Coordinates

The problem of multiple scattering by two rigid spheres is studied in the context of an effective range theory. At low energies, by expanding the total wave function in powers of the momentum of the incident particle, it is observed that the coefficients of different terms of the expansion are solutions of either Laplace or Poisson equations. These equations are separable in bispherical coordinates. Using the method of separation of variables, one can determine the scattering amplitude and its first and second derivatives with respect to momentum, at zero energy. In particular, a simple expression is obtained for the scattering length of two hard spheres. With the help of the Green's function in bispherical coordinates, it is shown that for any wavenumber, the scattered wave satisfies an inhomogeneous integral equation in two variables. Hence, the exact wave function and the scattering amplitude can be found numerically for all energies.

Electromagnetic Scattering of a Small Spherical Obstacle Near the Ground

1972 ◽  
Vol 50 (3) ◽  
pp. 237-243 ◽  
Author(s):  
David A. Hill ◽  
James R. Wait
Keyword(s):  
Approximate Solution ◽  
Electromagnetic Scattering ◽  
Ground Plane ◽  
Low Frequency ◽  
Static Solution ◽  
Conducting Sphere ◽  
Small Obstacle ◽  
Bispherical Coordinates ◽  
Ground Wave

The field scattered by an ungrounded conducting sphere above a ground plane is considered. The quasi-static solution is facilitated by the use of bispherical coordinates. The approximate solution obtained by considering only the interaction of dipole modes with the interface is presented for comparison. The general results are used to calculate the backscatter of a low frequency ground wave by a small obstacle.

The Accuracy of Doubly Asymptotic Approximations for an Acoustic Half-Space

1992 ◽  
Vol 114 (4) ◽  
pp. 555-563 ◽  
Author(s):  
M. Hasheminejad ◽  
T. L. Geers
Keyword(s):  
Half Space ◽  
Acoustic Impedance ◽  
Spherical Surface ◽  
Broad Band ◽  
Asymptotic Approximations ◽  
Rigid Surface ◽  
Planar Boundary ◽  
First Order ◽  
Pressure Surface ◽  
Bispherical Coordinates

The accuracy of doubly asymptotic approximations (DAAs) for acoustic half-space problems is assessed by examining their performance for a canonical problem in bispherical coordinates. Exact specific acoustic impedance curves for axisymmetric modal vibrations of a spherical surface near a planar boundary are generated, and corresponding curves based on the first-order DAA and the curvature-corrected DAA are compared with their exact counterparts. The comparisons show that the curvature-corrected DAA is substantially more accurate than the first-order DAA. Also, the curvature-corrected DAA is found to be satisfactory for broad-band excitations regardless of the sphere’s proximity to a compliant (zero-pressure) surface; for a rigid surface, the approximation is satisfactory only if the sphere is located at least one diameter away from the boundary.

scholarly journals The application bispherical coordinate in Schrödinger equation for Mobius square plus modified Yukawa potential using Nikiforov Uvarov Functional Analysis (NUFA) method

2020 ◽  
Vol 4 (2) ◽  
pp. 48
Author(s):  
Briant Sabathino Harya Wibawa ◽  
A Suparmi ◽  
C Cari
Keyword(s):  
Functional Analysis ◽  
Wave Function ◽  
Energy Spectrum ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Yukawa Potential ◽  
Radial Part ◽  
Angular Part ◽  
Variable Separation Method ◽  
Bispherical Coordinates

<p class="Abstract">The application bispherical coordinates in Schrödinger equation for the Mobius square plus modified Yukawa potential have been obtained. The Schrödinger equation in bispherical coordinates for the separable Mobius square plus modified Yukawa potential consisting of the radial part and the angular part for the Mobius square plus modified Yukawa potential is solved using the variable separation method to reduce it to the radial part and angular part Schrödinger equation. The aim of this study was to solve the Schrödinger's equation of radial in bispherical coordinates for the Mobius square plus modified Yukawa potential using the Nikiforov Uvarov Functional Analysis (NUFA) method. Nikiforov Uvarov Functional Analysis (NUFA) method used to obtained energy spectrum equation and wave function for the Mobius square plus modified Yukawa potential. The result of energy spectrum equation for Mobius square plus modified Yukawa potential can be shown in Equation (50). The result of un-normalized wave function equation for Mobius square plus modified Yukawa potential can be shown in Table 1.</p>

The Axisymmetric Thermoelastic Problem in Bispherical Coordinates

1967 ◽  
Vol 34 (1) ◽  
pp. 146-152
Author(s):  
W. E. Warren ◽  
J. A. Weese
Keyword(s):  
Half Space ◽  
Spherical Cavity ◽  
Thermal Conditions ◽  
Separation Distance ◽  
The Body ◽  
Graphical Form ◽  
Zero Temperature ◽  
Spherical Cavities ◽  
Thermoelastic Problems ◽  
Bispherical Coordinates

Analytical methods are developed for treating steady-state axisymmetric thermoelastic problems defined in bispherical coordinates. Possible geometrical configurations include the infinite space with two spherical cavities of arbitrary radii and separation distance, the half-space with a spherical cavity, and the thick-walled shell having eccentric spherical boundaries. Thermal conditions must be prescribed at the surface of the body such that the temperature distribution is uniquely determined. The surfaces of the body are traction free. Numerical results for a half-space containing a spherical cavity heated to constant temperature with zero temperature on the plane and at infinity are presented in graphical form for representative geometrical variations.

Transport phenomena in bispherical coordinates

2019 ◽  
Vol 31 (2) ◽  
pp. 021208 ◽  
Author(s):  
P. H. Gilbert ◽  
A. J. Giacomin
Keyword(s):  
Transport Phenomena ◽  
Bispherical Coordinates
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