REPRESENTATION THEOREMS FOR MULTIREGIONAL ELECTRODYNAMIC DIFFRACTION: PART II. APPLICATIONS

Geophysics ◽  
1975 ◽  
Vol 40 (1) ◽  
pp. 109-119 ◽  
Author(s):  
I. J. Won ◽  
J. T. Kuo
Keyword(s):  
Circular Cylinder ◽  
Closed Form ◽  
Line Source ◽  
Diffraction Problem ◽  
Finite Conductivity ◽  
Two Dimensional ◽  
Representation Theorems ◽  
Electric Line ◽  
Present Solution ◽  
The Difference

With the aid of the representation theorems presented in Part I of this paper, the two‐dimensional diffraction problem of a circular cylinder of finite conductivity embedded in a medium of finite‐conductivity is treated. The solution is expressed in a closed form for an arbitrary electromagnetic source. Comparison of the present solution for the case of an electric line source with the previously known solution shows that these two solutions are compatible. However, the difference between the two solutions becomes considerable as the source approaches the scatterer.

Electromagnetic diffraction of a transversal two-dimensional Gaussian beam at normal incidence on an absorbing circular cylinder

1985 ◽  
Vol 63 (2) ◽  
pp. 301-309 ◽  
Author(s):  
P. Langlois ◽  
A. Boivin ◽  
R. A. Lessard
Keyword(s):  
Circular Cylinder ◽  
Gaussian Beam ◽  
Diffraction Problem ◽  
Normal Incidence ◽  
Index Of Refraction ◽  
Two Dimensional ◽  
Edge Waves ◽  
Absorbing Materials ◽  
Electromagnetic Diffraction ◽  
Complex Index Of Refraction

We present the exact electromagnetic solution to the diffraction problem of a transversal two-dimensional Gaussian beam at normal incidence on an absorbing circular cylinder. The direction of constant amplitude for this Gaussian ribbon is perpendicular to the cylinder's axis. The results are valid in the Fresnel region as well as in the far field, and can be applied to actual values of the complex index of refraction for current-absorbing materials at optical frequencies (conductors or dielectrics). The diffracted field is expressed in terms of two cylindrical Gaussian edge waves arising from each "side" of the circular cylinder.

Diffraction of sound pulses by a fluid cylinder

1964 ◽  
Vol 60 (2) ◽  
pp. 295-312 ◽  
Author(s):  
S. K. Mishra
Keyword(s):  
Circular Cylinder ◽  
Line Source ◽  
Pulse Propagation ◽  
Surrounding Medium ◽  
Geometrical Theory ◽  
Two Dimensional ◽  
Velocity Of Sound ◽  
Homogeneous Fluid ◽  
Geometrical Theory Of Diffraction ◽  
Sound Pulses

AbstractIn this paper, we consider the problem of diffraction of two-dimensional sound pulses by a homogeneous fluid circular cylinder contained in another homogeneous fluid. The line source is situated outside the cylinder and is parallel to its axis. It is supposed that the velocity of sound inside the cylinder is less than the velocity of sound in the surrounding medium. We investigate the problem by the method of dual transformation as developed by Friedlander. The pulse propagation modes both inside and outside the cylinder are obtained, We interpret the modes as diffracted pulses in terms of Keller's Geometrical Theory of Diffraction. The results agree with Friedlander's conjecture.

scholarly journals Scattering from a Buried PEMC Cylinder due to a Line Source Excitation above a Planar Interface Between Two Isorefractive Half Spaces

2019 ◽  
Vol 8 (4) ◽  
pp. 1-6 ◽  
Author(s):  
A. K. Hamid ◽  
F. Cooray
Keyword(s):  
Circular Cylinder ◽  
Boundary Conditions ◽  
Half Space ◽  
Line Source ◽  
Planar Interface ◽  
The Other ◽  
Burial Depth ◽  
Cylinder Axis ◽  
Electric Line ◽  
Source Excitation

A solution to the problem of scattering from a perfect electromagnetic conducting (PEMC) circular cylinder   buried inside a half-space and excited by an infinite electric line source is provided. The line source is parallel to the cylinder axis, and is located in the other half-space. The two half spaces are isorefractive to each other. The source fields when incident at the planar interface separating the two half spaces, generate fields that are transmitted into the half-space where the cylinder is. These fields then become the known basic incident fields for the buried PEMC cylinder. Scattering of these incidents fields by the cylinder will consequently generate fields at the interface that get reflected back into the same half-space and transmitted frontward into the source half-space, all of which are unknown. Imposing appropriate boundary conditions at the surface of the buried cylinder and at a specified point on the interface, enables the evaluation of these unknown fields. The refection coefficient at the specified point is then computed for cylinders of different sizes, to demonstrate how it varies with the PEMC admittance of the buried cylinder, the intrinsic impedance ratio of the two isorefractive half-spaces, and the burial depth of the cylinder.

Extension of the Circle Theorems by Surface Source Distribution

1989 ◽  
Vol 111 (3) ◽  
pp. 243-247 ◽  
Author(s):  
O. Rand
Keyword(s):  
Circular Cylinder ◽  
Closed Form ◽  
Closed Form Solution ◽  
Strength Distribution ◽  
Form Solution ◽  
Source Distribution ◽  
Arbitrary Distribution ◽  
Normal Velocity ◽  
Two Dimensional ◽  
Surface Source

The paper presents a closed-form analytical solution for the source strength distribution along the circumference of a two-dimensional circular cylinder that is required for producing an arbitrary distribution of normal velocity. Being suitable to be used with flows having arbitrary vorticity distribution, the present formulation can be considered as an alternative and extensive form of the circle theorems. Using the conformal transformation technique, the formulation also serves as a closed-form solution of Laplace’s equation in any two-dimensional flow domain that is reducible to the outer or inner region of a circular cylinder having arbitrary prescribed normal velocity over its boundary.

Extended two-dimensional belief function based on divergence measurement

2020 ◽  
pp. 1-8
Author(s):  
Jianping Fan ◽  
Jing Wang ◽  
Meiqin Wu
Keyword(s):  
Belief Function ◽  
Distribution Functions ◽  
Divergence Measure ◽  
Uncertain Information ◽  
Belief Functions ◽  
Two Dimensional ◽  
Probability Distribution Functions ◽  
Basic Probability ◽  
The Difference ◽  
Supporting Degree

The two-dimensional belief function (TDBF = (mA, mB)) uses a pair of ordered basic probability distribution functions to describe and process uncertain information. Among them, mB includes support degree, non-support degree and reliability unmeasured degree of mA. So it is more abundant and reasonable than the traditional discount coefficient and expresses the evaluation value of experts. However, only considering that the expert’s assessment is single and one-sided, we also need to consider the influence between the belief function itself. The difference in belief function can measure the difference between two belief functions, based on which the supporting degree, non-supporting degree and unmeasured degree of reliability of the evidence are calculated. Based on the divergence measure of belief function, this paper proposes an extended two-dimensional belief function, which can solve some evidence conflict problems and is more objective and better solve a class of problems that TDBF cannot handle. Finally, numerical examples illustrate its effectiveness and rationality.

scholarly journals Colored HOMFLY-PT for hybrid weaving knot $$ {\hat{\mathrm{W}}}_3 $$(m, n)

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Vivek Kumar Singh ◽  
Rama Mishra ◽  
P. Ramadevi
Keyword(s):  
Closed Form ◽  
Topological Strings ◽  
Chebyshev Polynomials ◽  
Fibonacci Numbers ◽  
Infinite Family ◽  
Closed Form Expression ◽  
Two Dimensional ◽  
Laurent Polynomials ◽  
Form Expression ◽  
Torus Knots

Abstract Weaving knots W(p, n) of type (p, n) denote an infinite family of hyperbolic knots which have not been addressed by the knot theorists as yet. Unlike the well known (p, n) torus knots, we do not have a closed-form expression for HOMFLY-PT and the colored HOMFLY-PT for W(p, n). In this paper, we confine to a hybrid generalization of W(3, n) which we denote as $$ {\hat{W}}_3 $$ W ̂ 3 (m, n) and obtain closed form expression for HOMFLY-PT using the Reshitikhin and Turaev method involving $$ \mathrm{\mathcal{R}} $$ ℛ -matrices. Further, we also compute [r]-colored HOMFLY-PT for W(3, n). Surprisingly, we observe that trace of the product of two dimensional $$ \hat{\mathrm{\mathcal{R}}} $$ ℛ ̂ -matrices can be written in terms of infinite family of Laurent polynomials $$ {\mathcal{V}}_{n,t}\left[q\right] $$ V n , t q whose absolute coefficients has interesting relation to the Fibonacci numbers $$ {\mathrm{\mathcal{F}}}_n $$ ℱ n . We also computed reformulated invariants and the BPS integers in the context of topological strings. From our analysis, we propose that certain refined BPS integers for weaving knot W(3, n) can be explicitly derived from the coefficients of Chebyshev polynomials of first kind.

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