Separation of Variables for Electromagnetic Scattering by Spheroidal Particles

Author(s):  
Ioan R. Ciric ◽  
Francis R. Cooray
1973 ◽  
Vol 40 (2) ◽  
pp. 388-394 ◽  
Author(s):  
Y. K. Lou

Perturbation methods have been used for electromagnetic scattering and diffraction problems in recent years. A similar method suitable for low-frequency fluid-structure interaction problems is presented. The essence of the method lies in the fact that approximate solutions for fluid-structure interaction problems can be obtained from a set of Poisson’s equations, rather than from the reduced wave equation. The method is particularly useful for those problems where the Poisson’s equation may be solved by the method of separation of variables while the reduced wave equation cannot. As an illustrative example, the vibrations of a submerged spherical shell is studied using the perturbation method and the accuracy of the method is demonstrated.


2008 ◽  
Vol 89 (12) ◽  
pp. 1853-1862 ◽  
Author(s):  
Michael I. Mishchenko ◽  
Larry D. Travis

The year 2008 marks the centenary of the seminal paper by Gustav Mie on electromagnetic scattering by homogeneous spherical particles. Having been cited in almost 4,000 journal articles since 1955 (according to the Science Citation Index Expanded database), Mie s paper has been among the more influential scientific publications of the twentieth century. It has affected profoundly the development of a great variety of natural science disciplines including atmospheric radiation, meteorological optics, remote sensing, aerosol physics, astrophysics, and biomedical optics. Mies paper represented a fundamental advancement over the earlier publications by Ludvig Lorenz in that it was explicitly based on the Maxwell equations, gave the final solution in a convenient form suitable for practical computations, and imparted physical reality to the abstract concept of electromagnetic scattering. The Mie solution anticipated such general concepts as far-field scattering and the Sommerfeld-Silver-Müller boundary conditions at infinity as well as paved the way to such important extensions as the separation of variables method for spheroids and the T-matrix method. Key ingredients of the Mie theory are quite prominent in the superposition T-matrix method for clusters of particles and even in the recent microphysical derivation of the radiative transfer equation. Among the most illustrative uses of the Mie solution have been the explanation of the spectacular optical displays caused by cloud and rain droplets, the identification of sulfuric acid particles in the atmosphere of Venus from Earth-based polarimetry, and optical particle characterization based on measurements of morphology-dependent resonances. Yet it is clear that the full practical potential of the Mie theory is still to be revealed.


2017 ◽  
Vol 21 (2) ◽  
pp. 490-514 ◽  
Author(s):  
Kun Wang ◽  
Yau Shu Wong

AbstractThis paper presents an approach using the method of separation of variables applied to 2D Helmholtz equations in the Cartesian coordinate. The solution is then computed by a series solutions resulted from solving a sequence of 1D problems, in which the 1D solutions are computed using pollution free difference schemes. Moreover, non-polluted numerical integration formulae are constructed to handle the integration due to the forcing term in the inhomogeneous 1D problems. Consequently, the computed solution does not suffer the pollution effect. Another attractive feature of this approach is that a direct method can be effectively applied to solve the tridiagonal matrix resulted from numerical discretization of the 1D Helmholtz equation. The method has been tested to compute 2D Helmholtz solutions simulating electromagnetic scattering from an open large cavity and rectangular waveguide.


2020 ◽  
Vol 23 (3) ◽  
pp. 306-311
Author(s):  
Yu. Kurochkin ◽  
Dz. Shoukavy ◽  
I. Boyarina

The immobility of the center of mass in spaces of constant curvature is postulated based on its definition obtained in [1]. The system of two particles which interact through a potential depending only on the distance between particles on a three-dimensional sphere is considered. The Hamilton-Jacobi equation is formulated and its solutions and trajectory equations are found. It was established that the reduced mass of the system depends on the relative distance.


Sign in / Sign up

Export Citation Format

Share Document