Exterior caustics produced in scattering of a diagonally incident plane wave by a circular cylinder: semiclassical scattering theory analysis

We use the semiclassical limit of electromagnetic wave scattering theory to determine the properties of the exterior caustics of a diagonally incident plane wave scattered by an infinitely long homogeneous dielectric circular cylinder in both the near zone and the far zone. The transmission caustic has an exterior/interior cusp transition as the tilt angle of the incident beam is increased, and each of the rainbow caustics has a farzone rainbow/exterior cusp transition and an exterior/interior cusp transition as the incident beam tilt angle is increased. We experimentally observe and analyze both transitions of the first-order rainbow. We also compare the predictions of the semiclassical approximation with those of ray theory and exact electromagnetic wave scattering theory.     

Diffraction of a plane wave by a two-layer dielectric cylinder

We have investigated the characteristic features of diffraction of a plane wave by extended two-layer dielectric cylinders with complex indices of refraction. Translated from Izmeritel'naya Tekhnika, No. 4, pp. 30–31, April, 1996.     

Wave scattering by a circular cylinder half-immersed in water with an ice-cover

The problem of scattering of water waves obliquely incident on a fixed long circular cylinder half-immersed in deep water with an ice-cover is investigated here. The ice-cover is modelled as an elastic plate of very small thickness. The problem is formulated using the method of multipoles. This leads to an infinite system of linear equations which are solved numerically by truncation. The reflection and transmission coefficients are obtained and depicted graphically against the wave number for various values of the angle of incidence and flexural rigidity of the ice-cover to show the effect of the presence of ice-cover on these quantities. The effect of ice-cover is seen to increase the reflection coefficient and to decrease the transmission coefficient.     

Wave scattering by a horizontal circular cylinder in a two-layer fluid with an ice-cover

In a two-layer fluid wherein the upper layer is of finite depth and bounded above by a thin but uniform layer of ice-cover modelled as a thin elastic sheet and the lower layer is infinitely deep below the interface, time-harmonic waves with a given frequency can propagate with two different wavenumbers. The wave of smaller wavenumber propagates along the ice-cover while wave of higher wavenumber propagates along the interface. In this paper problems of wave scattering by a horizontal circular cylinder submerged in either the lower or in the upper layer due to obliquely as well as normally incident wave trains of both the wave numbers are investigated by using the method of multipole expansions. The effect of the presence of ice-cover on the various reflection and transmission coefficients due to incident waves at the ice-cover and the interface is depicted graphically in a number of figures.     

Oblique wave scattering by a circular cylinder submerged beneath an ice-cover

When a train of small-amplitude surface water waves is normally incident on a very long horizontal circular cylinder fully submerged in deep water with a free surface, it is well known that it passes over and below the cylinder with a change of phase without experiencing any reflection. However the cylinder does experience reflection for oblique incidence of the surface wave train. It is shown here that the same phenomenon also holds good when the deep water has an ice-cover instead of a free surface, the ice-cover being modelled as a thin elastic plate. Here, for oblique incidence, the reflection and transmission coefficients are obtained approximately and depicted graphically against the wave number in a number of figures.     

Determining complex permittivity by measuring the scatteredwaveform from a dielectric circular cylinder

The author describes a method of measuring complex permittivity by making use of a two-dimensional scattered wave from a dielectric circular cylinder. The far-field pattern in the plane perpendicular to the cylinder axis is examined when the dielectric is illuminated by a line-source antenna that is parallel to the axis of the cylinder. An automated measurement of the complex permittivity is compared with a computed result based on theory. When the loss factor is high, this method becomes competitive with other techniques. The complex permittivity can be determined by this method over a wide range except for the case where the dielectric loss is very small     

Electromagnetic scattering by an infinite cylinder of material or metamaterial coating eccentrically a dielectric cylinder

The electromagnetic scattering by an infinite cylinder of dielectric material or metamaterial, coating eccentrically another infinite dielectric cylinder, is treated in this work. The problem is solved using classical separation of variables techniques. No use is made of the translational addition theorem. For small eccentricities h = d/a(? 1), where d is the distance between the axes of the cylinders and a the radius of the outer cylinder, we use instead the cosine and the sine laws to satisfy the boundary conditions at the surface of the outer cylinder. Keeping terms up to the order h2 we finally obtain exact, closed-form expressions for the expansion coefficients g(1) and g(2) in the relation S(h) = S(0)[1 + g(1)h + g(2)h2 + O(h3)], giving the scattered field and the scattering cross sections of the problem, where S(0) corresponds to the coaxial geometry, with h = 0 (d = 0). Both polarizations are considered for normal incidence. Numerical results are given for various values of the parameters, corresponding to materials or metamaterials. Our method is an alternative of the one using the translational addition theorem in the case of small eccentricities h.     

The transient behavior of diffraction of plane pulse by a circular cylinder

The large-time transient behavior of diffraction of a plane pulse by a circular cylinder is investigated for three different boundary conditions. In each case the behavior is found to be quite different from others. The solutions are expressed in integral forms by Laplace Transforms. The integrals are then evaluated asymptotically for large time or small transform variable. Special attention has been paid to show that the otal field vanishes in the region ahead of the incoming shock front.     

Analysis of a crack emanating from a circular hole in a loaded plane

The problem of a linear elastic loaded plane containing a circular hole with an arbitrary positioned edge crack is considered. The formulation is based on consideration of the dislocational pile-up in order to represent the crack, and on a fictious dislocation in the hole in order to satisfy single valued displacement requirement for the resulting stress potentials.The results are given in terms of the stress intensity factors at the crack tip for a variety of geometries. As the results indicate, at certain geometries there exists a critical crack length such that, below that value, the crack experiences an intensive growth, and, above this value, retardation of growth or crack arrest will take place.

---

Résumé On considère le problème d'une plaque plane linéaire élastique, mise en charge, et comportant un trou circulaire avec une fissure de bord placée de manière arbitraire. Pour la formulation, on se base sur une représentation de la fissure par un empilement de dislocations et, pour satisfaire à l'exigence de déplacement unitaire associé aux potentiels de contrainte résultants, on suppose l'existence d'une dislocation fictive dans le trou.On présente les résultats sous forme de facteurs d'intensité de contraintes correspondant à diverses géométries. Comme l'indiquent les résultats, il existe pour certaines configurations une longueur critique de fissure telle que la fissure passe par une phase de croissance intensive lorsque sa longueur en est inférieure, ou au contraire se ralentit, voire s'arrête, lorsque sa longueur est supérieure à cette longueur critique.

     

Electromagnetic plane wave scattering by arbitrarily oriented elliptical dielectric cylinders

The electromagnetic scattering by an arbitrarily oriented elliptical cylinder having different constitutive parameters than those of the background medium is treated in this work. The separation of variables method is used to solve this problem, but, due to the oblique incidence of the source fields, hybrid waves for the scattered and induced fields are generated, thus making the formulation complicated. Moreover, because of the different wavenumbers between the scatterer and the background medium, the orthogonality relations for Mathieu functions do not hold, leading to more complicated systems, compared to those of normal incidence, which should be solved in order to obtain the solution for the scattered or induced fields. The validation of the results reveals the high accuracy of the implementation, even for electrically large scatterers. Both polarizations are considered and numerical results are given for various values of the parameters. The method is exact and can be used for reference as an alternative validation for future methods involving scattering problems.     

Light scattering by an infinite circular cylinder immersed in an absorbing medium

Analytic solutions are developed for the single-scattering properties of an infinite dielectric cylinder embedded in an absorbing medium with normal incidence, which include extinction, scattering and absorption efficiencies, the scattering phase function, and the asymmetry factor. The extinction and scattering efficiencies are derived by the near-field solutions at the surface of the particle. The normalized scattering phase function is obtained by use of the far-field approximation. Computational results show that, although the absorbing medium significantly reduces the scattering efficiency, it has little effect on absorption efficiency. The absorbing medium can significantly change the conventional phase function. The absorbing medium also strongly affects the polarization of the scattered light. However, for large absorbing particles the degrees of polarization change little with the medium's absorption. This implies that, if the transmitting lights are strongly weakened inside the particle, the scattered polarized lights can be used to identify objects even when the absorption property of the host medium is unknown, which is important for both active and passive remote sensing.     

Modeling of the scattering of electromagnetic waves by a thin dielectric coating on a cylinder

Double-sided boundary conditions containing only tangential components of a diffracted field are used to model the interaction of electromagnetic waves with a cylinder of arbitrary cross section covered with a thin dielectric layer. The obtained boundary-value problem is reduced to a system of two singular integral equations of the second kind with kernels whose structure is similar to the kernels of integral equations of the first kind for a perfectly conducting scatterer. The numerical solution of the integral equations of the problem is obtained by the method of mechanical quadratures. The scattering properties of an elliptic cylinder with different dielectric coatings are studied in the superhigh-frequency band. It is shown that the coating strongly affects the diffraction properties of the cylinder. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 42, No. 1, pp. 96–104, January–February, 2006.     

Acoustic scattering of an incident cylindrical wave by an infinite circular cylinder

Exact scattered acoustic fields generated by an infinite circular cylinder in the presence of an incident cylindrical wave are derived for fluid media. Equations are given for the scattered field outside the cylinder and for the total field within.     

Two-dimensional scattering of a plane wave from a periodic array of dielectric cylinders with arbitrary shape

A two-dimensional scattering of a plane wave from a periodic array of dielectric cylinders with arbitrary shape using the multigrid-moment method is examined. The scattered field is expressed in terms of the integral form by an infinite summation of the surface integral over the cross section of the reference cylinder. The integral form is converted into the matrix equation by using the moment method. The integration in the elements of the matrix equation is evaluated by the lattice-sums technique to obtain a precise solution. The multigrid method is applied to the matrix equation to improve the CPU time. The CPU time and the residual norm are examined numerically for a given number of iterations and cycle indices. Then the effects of shape and material of the periodic structure on the power reflection coefficient of the fundamental Floquet mode are shown. In addition, the results indicate the effect of changing the relative permittivity of the dielectric coated body and the reflection coefficient.     

Rainbow scattering by a cylinder with a nearly elliptical cross section

We both theoretically and experimentally examine the behavior of the first- and the second-order rainbows produced by a normally illuminated glass rod, which has a nearly elliptical cross section, as it is rotated about its major axis. We decompose the measured rainbow angle, taken as a function of the rod's rotation angle, into a Fourier series and find that the rod's refractive index, average ellipticity, and deviation from ellipticity are encoded primarily in the m = 0, 2, 3 Fourier coefficients, respectively. We determine these parameters for our glass rod and, where possible, compare them with independent measurements. We find that the average ellipticity of the rod agrees well with direct measurements, but that the rod's diameter inferred from the spacing of the supernumeraries of the first-order rainbow is significantly larger than that obtained by direct measurement. We also determine the conditions under which the deviation of falling water droplets from an oblate spheroidal shape permits the first few supernumeraries of the second-order rainbow to be observed in a rain shower.     

Transverse magnetic plane-wave scattering equations for infinite and semi-infinite rectangular grooves in a conducting plane

The transverse magnetic plane-wave scattering equations for infinite and semi-infinite rectangular grooves (RGs) in a conducting plane are proposed in terms of the overlapping T-block method and Floquet theorem. By utilising the Floquet theorem and taking the limit of multiple RGs as the number of RGs becomes infinity, the simultaneous solutions of infinite RG are then analytically obtained. Combining the analyses of infinite and large number of RGs yields approximate yet numerically efficient scattering equations for semi-infinite RG. Numerical computations are performed to verify that the solutions converge fast and agree with the mode-matching method.     

Double-diffusive convection in a circular cylinder

Summary A theoretical study is made of the onset of steady double-diffusive convection in a circular cylinder of small to moderate aspect ratio. An eigenfunction expansion method is used to derive systems of amplitude equations for weakly nonlinear evolution of critical disturbances. It is shown that the nature of the convective solution near criticality depends strongly on the cylinder's aspect ratio; this is particularly the case at or near aspect ratios where two modes become unstable at the same Rayleigh number. There is also a strong dependence on Prandtl number, which is discussed.With 7 Figure