A NOTE ON DIFFRACTION BY AN INFINITE SLIT

1960 ◽  
Vol 38 (1) ◽  
pp. 38-47 ◽  
Author(s):  
R. F. Millar
Keyword(s):  
Integral Equation ◽  
Normal Derivative ◽  
Cylindrical Wave ◽  
Narrow Slit ◽  
Angle Of Incidence ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Boundary Values ◽  
Transmission Coefficients ◽  
Differential Integral Equation

The two-dimensional problem of diffraction of a plane wave by a narrow slit is considered. The assumed boundary values on the screen are the vanishing of either the total wave function or its normal derivative. In the former case, a differential–integral equation is obtained for the unknown function in the slit; in the latter, a pure integral equation is found. Solutions to these equations are given in the form of series in powers of ε (where ε/π is the ratio of slit width to wavelength), the coefficients of which depend on log ε. Expressions are found for the transmission coefficients as functions of ε and the angle of incidence; these are compared with previous determinations of other authors.A brief outline is given for the treatment of diffraction of a cylindrical wave by the slit.

DIFFRACTION BY A NARROW SLIT IN THE INTERFACE BETWEEN TWO DIFFERENT MEDIA

1967 ◽  
Vol 45 (1) ◽  
pp. 57-81 ◽  
Author(s):  
Karen Houlberg
Keyword(s):  
Integral Equation ◽  
Plane Electromagnetic Wave ◽  
Perturbation Technique ◽  
Narrow Slit ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Special Values ◽  
Differential Integral Equation ◽  
Conducting Screen ◽  
Formal Solutions

The two-dimensional problem of diffraction of a plane electromagnetic wave by a narrow slit in an infinitely thin, perfectly conducting screen between two different media is studied. The cases of both E and H polarization are considered. In the case of E polarization, a differential-integral equation is obtained for the unknown function in the slit; in the H polarized case, a pure integral equation is obtained for the unknown. These integral equations are solved by a perturbation technique and formal solutions are given in the form of series in powers of the ratio of slit width to wavelength, the coefficients of which depend on the logarithm of this ratio. Expressions are found for the transmission and back-scatter coefficients and some numerical results are given for special values of the parameters. Errors in earlier work (Barakat 1963; Stöckel 1964) are noted.

Integral equation methods in potential theory. II

1963 ◽  
Vol 275 (1360) ◽  
pp. 33-46 ◽  
Keyword(s):  
Integral Equation ◽  
Potential Theory ◽  
Digital Computer ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Integral Equation Methods ◽  
Representative Selection ◽  
Selection Of

The boundary integral equations of potential theory can be solved to a tolerable accuracy without undue labour by digital computer techniques, and the computed datagenerate numerical values of the potential field wherever required. Tests have been made with a representative selection of two-dimensional problem s, some of which would not be amenable to any other treatment.

Scattering of surface waves obliquely incident on a fixed half immersed circular cylinder

1984 ◽  
Vol 96 (2) ◽  
pp. 359-369 ◽  
Author(s):  
B. N. Mandal ◽  
S. K. Goswami
Keyword(s):  
Integral Equation ◽  
Surface Water ◽  
Circular Cylinder ◽  
Water Waves ◽  
Wave Number ◽  
Angle Of Incidence ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Obliquely Incident ◽  
Surface Water Waves

AbstractThe problem of scattering of surface water waves obliquely incident on a fixed half immersed circular cylinder is solved approximately by reducing it to the solution of an integral equation and also by the method of multipoles. For different values of the angle of incidence and the wave number the reflection and transmission coefficients obtained by both methods are evaluated numerically and represented graphically to compare the results obtained by the respective methods.

ON AXIALLY SYMMETRIC ELECTRIC CURRENT INDUCED IN A CYLINDER UNDER A LINE SOURCE

Geophysics ◽  
1973 ◽  
Vol 38 (5) ◽  
pp. 971-974 ◽  
Author(s):  
Shri Krishna Singh
Keyword(s):  
Magnetic Field ◽  
Electric Current ◽  
Short Note ◽  
Cylindrical Wave ◽  
Wave Functions ◽  
Static Case ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Axially Symmetric ◽  
Infinite Line

An infinite conducting cylinder excited by an infinite line current located outside the cylinder is a useful model in the interpretation of electromagnetic prospecting data. Several authors, with geophysical applications in mind, have considered the problem of the source being parallel to the axis of the cylinder (Wait, 1952; Negi et al., 1972). In the latter paper, the cylinder is surrounded by a shell; conductivity of both the cylinder and the shell is a function of radius. The secondary fields are written in the form of an infinite series of cylindrical wave functions. This solution is then specialized to the quasi‐static case. For reasons not explained, the authors neglect the n = 0 term. In this short note, computed results are presented which show that the contribution from the n = 0 term (corresponding to an axially symmetric electric current induced in the cylinder causing a transverse secondary magnetic field outside) is significant and must be taken into account for the two‐dimensional problem.

Interaction Between a Rigid Indenter and a Near-Surface Void or Inclusion

1983 ◽  
Vol 50 (3) ◽  
pp. 615-620 ◽  
Author(s):  
G. R. Miller ◽  
L. M. Keer
Keyword(s):  
Integral Equation ◽  
Stress Field ◽  
Size Effects ◽  
Maximum Shear Stress ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Near Surface ◽  
Subsurface Maximum ◽  
Contact Stress Distribution ◽  
Shear Stress Field

A solution is presented to the two-dimensional problem of a rigid indenter sliding with friction on a half plane containing a near-surface imperfection in the form of a circular void or rigid inclusion. The complex variable formulation of Muskhelishivili is used to reduce the problem to a Fredholm integral equation of the second kind. This integral equation is solved numerically thus enabling the numerical calculation of the stress field. The behavior of the stress field is depicted in plots of the contact stress distribution and the subsurface maximum shear stress field. Results are presented showing location and size effects in the case of an inclusion, and finally, comparisons are made between the disturbances due to inclusions and voids.

scholarly journals INTERACTIONS OF WAVES WITH SUBMARINE TRENCHES

1980 ◽  
Vol 1 (17) ◽  
pp. 49
Author(s):  
Jiin-Jen Lee ◽  
Robert M. Ayer ◽  
Wen-Li Chiang
Keyword(s):  
Infinite Number ◽  
Water Waves ◽  
Laboratory Experiments ◽  
Normal Derivative ◽  
Two Dimensional ◽  
Final Solution ◽  
Reflection And Transmission ◽  
Common Boundary ◽  
Flow Configuration ◽  
Transmission Coefficients

An analysis is presented for the propagation of water waves past a submarine trench of irregular shape. Two dimensional, linearized potential flow is assumed. The fluid domain is divided into two regions along the mouth of the trench. Solutions in each region are expressed in terms of the unknown normal derivative of the potential function along this common boundary with the final solution obtained by matching. Reflection and transmission coefficients are found for various submarine geometries. The accuracy of the technique employed is demonstrated by comparing with previously published results for a rectangular trench. In addition, results from limited laboratory experiments were included for comparison. The result shows that for a particular flow configuration, there exists an infinite number of discrete wave frequencies at which waves are completely transmitted.

On Elastodynamic Diffraction of Waves From a Line-Load by a Crack

1984 ◽  
Vol 51 (2) ◽  
pp. 335-338 ◽  
Author(s):  
A. K. Gautesen
Keyword(s):  
Plane Wave ◽  
Simple Relation ◽  
Finite Width ◽  
Far Field ◽  
Angle Of Incidence ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Line Load ◽  
Fixed Angle ◽  
Plane Wave Incident

For the two-dimensional problem of elastodynamic diffraction of waves by a crack of finite width, we assume that the solution corresponding to incidence of a plane wave of either longitudinal or transverse motions under a fixed angle of incidence is known. We first show how to construct the solution corresponding to an in-plane line-load (the Green’s function) from this known solution. We then give a simple relation between the far field scattering patterns corresponding to a plane wave incident under any angle and the far field scattering patterns corresponding to the known solution. This relation is a generalization of the principle of reciprocity.

The pitching motion of a circular disk

1963 ◽  
Vol 17 (4) ◽  
pp. 607-629 ◽  
Author(s):  
W. D. Kim
Keyword(s):  
Integral Equation ◽  
Three Dimensional ◽  
Circular Disk ◽  
Moment Of Inertia ◽  
Damping Coefficient ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Pitching Motion ◽  
Surrounding Fluid

The interaction of a pitching circular disk with the motion induced by the disk in the surrounding fluid is investigated in this paper. MacCamy's (1961) method of simplifying the three-dimensional problem of a circular disk to the two-dimensional problem is found to apply in the present analysis. The integral equation is solved numerically to determine the dependence of pressure, added moment of inertia, and damping coefficient on the frequency of the oscillation.

Diffraction of Pulses by Cylindrical Obstacles of Arbitrary Cross Section

1962 ◽  
Vol 29 (1) ◽  
pp. 40-46 ◽  
Author(s):  
M. B. Friedman ◽  
R. Shaw
Keyword(s):  
Shock Wave ◽  
Integral Equation ◽  
Cross Section ◽  
Analytical Solutions ◽  
Arbitrary Cross Section ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Dimensional Problem ◽  
Acoustic Shock Wave ◽  
Square Box

The two-dimensional problem of the diffraction of a plane acoustic shock wave by a cylindrical obstacle of arbitrary cross section is considered. An integral equation for the surface values of the pressure is formulated. A major portion of the solution is shown to be contributed by terms in the integral equation which can be evaluated explicitly for a given cross section. The remaining contribution is approximated by a set of successive, nonsimultaneous algebraic equations which are easily solved for a given geometry. The case of a square box with rigid boundaries is solved in this manner for a period of one transit time. The accuracy achieved by the method is indicated by comparison with known analytical solutions for certain special geometries.

Modifications of the Godunov method for computing disturbance propagation in an elastic body

2016 ◽  
Vol 11 (1) ◽  
pp. 119-126 ◽  
Author(s):  
A.A. Aganin ◽  
N.A. Khismatullina
Keyword(s):  
Elastic Body ◽  
Godunov Method ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Order Accuracy ◽  
One Dimensional ◽  
Disturbance Propagation ◽  
Linear Waves ◽  
Longitudinal And Shear Waves ◽  
Contact Discontinuities

Numerical investigation of efficiency of UNO- and TVD-modifications of the Godunov method of the second order accuracy for computation of linear waves in an elastic body in comparison with the classical Godunov method is carried out. To this end, one-dimensional cylindrical Riemann problems are considered. It is shown that the both modifications are considerably more accurate in describing radially converging as well as diverging longitudinal and shear waves and contact discontinuities both in one- and two-dimensional problem statements. At that the UNO-modification is more preferable than the TVD-modification because exact implementation of the TVD property in the TVD-modification is reached at the expense of “cutting” solution extrema.

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