High frequency diffraction by a soft circular disc

1972 ◽  
Vol 71 (3) ◽  
pp. 527-543
Author(s):  
J. C. Newby
Keyword(s):  
Integral Equation ◽  
Scattered Field ◽  
High Frequency ◽  
Circular Disc ◽  
Single Function ◽  
Contour Deformation ◽  
Axis Of Symmetry

AbstractThe problem is governed by a Jones integral equation and the solution is shown to depend upon a single function which occurs naturally after a contour deformation has produced extensive cancellation in the work. The far-scattered field off the axis of symmetry is found in detail, yielding terms which are believed to be new.

A method for the exact solution of a class of two-dimensional diffraction problems

1951 ◽  
Vol 205 (1081) ◽  
pp. 286-308 ◽  
Keyword(s):  
Integral Equation ◽  
Plane Wave ◽  
Integral Equations ◽  
Scattered Field ◽  
Plane Waves ◽  
Angular Spectrum ◽  
Diffraction Theory ◽  
General Interest ◽  
Two Dimensional ◽  
Dual Integral Equations

In the last few years Copson, Schwinger and others have obtained exact solutions of a number of diffraction problems by expressing these problems in terms of an integral equation which can be solved by the method of Wiener and Hopf. A simpler approach is given, based on a representation of the scattered field as an angular spectrum of plane waves, such a representation leading directly to a pair of ‘dual’ integral equations, which replaces the single integral equation of Schwinger’s method. The unknown function in each of these dual integral equations is that defining the angular spectrum, and when this function is known the scattered field is presented in the form of a definite integral. As far as the ‘radiation’ field is concerned, this integral is of the type which may be approximately evaluated by the method of steepest descents, though it is necessary to generalize the usual procedure in certain circumstances. The method is appropriate to two-dimensional problems in which a plane wave (of arbitrary polarization) is incident on plane, perfectly conducting structures, and for certain configurations the dual integral equations can be solved by the application of Cauchy’s residue theorem. The technique was originally developed in connexion with the theory of radio propagation over a non-homogeneous earth, but this aspect is not discussed. The three problems considered are those for which the diffracting plates, situated in free space, are, respectively, a half-plane, two parallel half-planes and an infinite set of parallel half-planes; the second of these is illustrated by a numerical example. Several points of general interest in diffraction theory are discussed, including the question of the nature of the singularity at a sharp edge, and it is shown that the solution for an arbitrary (three-dimensional) incident field can be derived from the corresponding solution for a two-dimensional incident plane wave.

The alignment of form and function

2007 ◽  
Vol 12 (4) ◽  
pp. 511-534 ◽  
Author(s):  
Dunstan Brown ◽  
Carole Tiberius ◽  
Greville G. Corbett
Keyword(s):  
High Frequency ◽  
The Other ◽  
Frequency Information ◽  
Form And Function ◽  
Frequent Form ◽  
Single Function ◽  
The One ◽  
Default Rules ◽  
And Function

This paper analyses constraints on inflectional syncretism and inflectional allomorphy using frequency information. Syncretism arises where one form is associated with more than one function, whereas inflectional allomorphy occurs where there is more than one inflectional class, and a single function is associated with two or more forms. If high frequency is associated with more differentiation on both sides, we expect, on the one hand, that a frequent function will have a high number of forms and, on the other, that a frequent form will have a high number of functions. Our study focuses on Russian nominals, in particular nouns, which exhibit both syncretism and inflectional allomorphy. We find that there is a relationship between frequency and differentiation, but that it is not exceptionless, and that the exceptions can be understood in terms of the use of referrals as default rules.

Correlation analysis of radio-auroral scatter signals

1970 ◽  
Vol 48 (14) ◽  
pp. 1716-1723 ◽  
Author(s):  
F. H. Palmer ◽  
D. R. Moorcroft
Keyword(s):  
Correlation Analysis ◽  
Drift Velocity ◽  
Scattered Field ◽  
High Frequency ◽  
Very High Frequency ◽  
Drift Speed ◽  
Scale Size ◽  
Spaced Antennas ◽  
Very High ◽  
East West

Very high frequency radio-auroral scatter signals are regularly observed on an Ottawa–London (Ontario) backscatter circuit operating at 40.35 MHz. For three of these events the scale size and drift velocity of the scattered field at the receiving site were determined by a correlation analysis of the signals received at spaced antennas. The overall east–west extent of the scattering regions was determined from the scale-size measurements. At least two types of event were observed. One type results from scattering by extended regions with horizontal dimensions greater than 200 km and having minimum drift velocities of a few hundred m/s. The second type of event results from simultaneous scattering by a number of independent regions, each having its own drift speed and direction. These regions have drift velocities in excess of 1 km/s and horizontal dimensions often less than 30 km.

A preliminary numerical study of a swirling jet behind a circular disc

2008 ◽  
Vol 223 (5) ◽  
pp. 1127-1139
Author(s):  
H T Toh ◽  
R F Huang ◽  
M J Chern
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Saddle Points ◽  
Three Dimensional ◽  
Second Order ◽  
Circular Disc ◽  
Mean Velocity ◽  
Swirling Jet ◽  
First Case ◽  
Axis Of Symmetry

The three-dimensional flow fields behind a circular disc produced by an annular swirling jet alone and by an annular swirling jet with a central jet issuing from the disc centre are studied by solving the three-dimensional incompressible Navier—Stokes equations numerically using the solution algorithm of Hirt et al. ( Los Alamos Scientific Lab. Rept. LA-5852 (1970)). The swirl number and the Reynolds number based on the disc diameter and the volumetric mean axial velocity of the annular swirling jet are S=0.194 and Re=656, respectively. The convective and diffusive terms in the governing equations are discretized using the second-order central difference scheme. The resulting discretized equations are advanced in time using the second-order Runge—Kutta scheme. The simulation shows that the flow field behind the circular disc exhibit periodic oscillating behaviour, with the second case having a higher frequency due to the presence of the central jet. The mechanism responsible for this oscillating behaviour is identified and discussed. An analysis of the mean velocity fields in the mid-plane shows the existence of a stagnation point on the axis of symmetry in the first case and two saddle points off the axis of symmetry in the second case.

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