scholarly journals A Fast-Converging Scheme for the Electromagnetic Scattering from a Thin Dielectric Disk

Electronics ◽  
2020 ◽  
Vol 9 (9) ◽  
pp. 1451
Author(s):  
Mario Lucido ◽  
Mykhaylo V. Balaban ◽  
Sergii Dukhopelnykov ◽  
Alexander I. Nosich
Keyword(s):  
Integral Equations ◽  
Electromagnetic Scattering ◽  
Disk Surface ◽  
Hankel Transform ◽  
Transform Domain ◽  
One Dimensional ◽  
Analytical Technique ◽  
Generalized Boundary Conditions ◽  
Dielectric Disk ◽  
Dimensional Integral

In this paper, the analysis of the electromagnetic scattering from a thin dielectric disk is formulated as two sets of one-dimensional integral equations in the vector Hankel transform domain by taking advantage of the revolution symmetry of the problem and by imposing the generalized boundary conditions on the disk surface. The problem is further simplified by means of Helmholtz decomposition, which allows to introduce new scalar unknows in the spectral domain. Galerkin method with complete sets of orthogonal eigenfunctions of the static parts of the integral operators, reconstructing the physical behavior of the fields, as expansion bases, is applied to discretize the integral equations. The obtained matrix equations are Fredholm second-kind equations whose coefficients are efficiently numerically evaluated by means of a suitable analytical technique. Numerical results and comparisons with the commercial software CST Microwave Studio are provided showing the accuracy and efficiency of the proposed technique.

scholarly journals An Explicit Inverse Design Formulation for Compressible Flow

1986 ◽  
Author(s):  
D. E. Wilson
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Integral Equation Method ◽  
The Body ◽  
Inverse Design ◽  
Surface Geometry ◽  
One Dimensional ◽  
Integral Methods ◽  
Nonlinear Potential ◽  
Dimensional Integral

A new singular integral equation method has been developed for solving the full nonlinear potential flow about an arbitrary body. The method bears some resemblance to conventional integral methods, however it is inherently different in that the surface geometry is contained explicitly in the resulting integral equations. Several analytical results are exploited to reduce the two-dimensional integral equations to a one-dimensional problem on the body surface. The integral equation is inverted so that the airfoil geometry is given as an explicit function of the velocity field. The resulting one-dimensional integral equations are solved numerically and the results are compared with existing theoretical methods for both analysis and inverse design problems.

scholarly journals Integral equations of a rectilinear ribbon vibrator near a perfectly conducting infinite screen

2021 ◽  
Vol 2052 (1) ◽  
pp. 012040
Author(s):  
A V Sochilin ◽  
S I Eminov
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Current Density ◽  
General Equation ◽  
Numerical Calculations ◽  
Two Dimensional ◽  
One Dimensional ◽  
Dimensional Integral

Abstract The problem of excitation of a rectilinear ribbon vibrator near a perfectly conducting infinite screen is considered. A general equation, a two-dimensional integral equation, and a one-dimensional integral equation with respect to the current density are obtained. The results of numerical calculations are presented.

State-of-the-Art of Modeling Surface Water Impoundments

1982 ◽  
Vol 14 (1-2) ◽  
pp. 241-261 ◽  
Author(s):  
P A Krenkel ◽  
R H French
Keyword(s):  
Water Quality ◽  
Surface Water ◽  
State Of The Art ◽  
Rate Coefficients ◽  
Two Dimensional ◽  
One Dimensional ◽  
Integral Energy ◽  
Range Of Values ◽  
Dimensional Integral ◽  
Water Impoundment

The state-of-the-art of surface water impoundment modeling is examined from the viewpoints of both hydrodynamics and water quality. In the area of hydrodynamics current one dimensional integral energy and two dimensional models are discussed. In the area of water quality, the formulations used for various parameters are presented with a range of values for the associated rate coefficients.

scholarly journals The on-axis magnetic well and Mercier's criterion for arbitrary stellarator geometries

2021 ◽  
Vol 87 (2) ◽  
Author(s):  
P. Kim ◽  
R. Jorge ◽  
W. Dorland
Keyword(s):  
Magnetic Field ◽  
Original Work ◽  
Three Dimensional ◽  
Radial Distance ◽  
Analytical Form ◽  
One Dimensional ◽  
Modern Notation ◽  
Magnetic Well ◽  
First Time ◽  
Dimensional Integral

A simplified analytical form of the on-axis magnetic well and Mercier's criterion for interchange instabilities for arbitrary three-dimensional magnetic field geometries is derived. For this purpose, a near-axis expansion based on a direct coordinate approach is used by expressing the toroidal magnetic flux in terms of powers of the radial distance to the magnetic axis. For the first time, the magnetic well and Mercier's criterion are then written as a one-dimensional integral with respect to the axis arclength. When compared with the original work of Mercier, the derivation here is presented using modern notation and in a more streamlined manner that highlights essential steps. Finally, these expressions are verified numerically using several quasisymmetric and non-quasisymmetric stellarator configurations including Wendelstein 7-X.

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