Convex Cylinders Research Articles

Incremental length diffraction coefficients for the shadow boundary of a convex cylinder

Incremental length diffraction coefficients (ILDCs) are obtained for the shadow boundaries of perfectly electrically conducting (PEC) convex cylinders of general cross section. A two-step procedure is used. First, the nonuniform (NU) current in the vicinity of the shadow boundary is approximated using Fock (1965) functions. The product of the approximated current and the free-space Green's function is then integrated on a differential strip of the cylinder surface transverse to the shadow boundary to obtain the ILDCs. This integration is performed in closed form by employing quadratic polynomial approximations for the amplitude and unwrapped phase of the integrand. Examples are given of both the current approximations and the integration procedure. Finally, as an example, the scattered far field of a PEC sphere is obtained by adding the integral of the NU ILDCs of a circular cylinder along the shadow boundary of the sphere to the physical optics (PO) far field of the sphere. This correction to the PO field is shown to significantly improve upon the accuracy of the PO far-field approximation to the total scattered field of the sphere.

An experimental study on natural convective heat transfer from a vertical wavy surface heated at convex/concave elements

Natural convective heat transfer from a vertical wavy surface has been studied experimentally. The wavy surface has isothermally heated convex or concave semicircular cylinders. Such a problem involves the effect of complex geometries and heat conduction in unheated elements on natural convection flow. In this problem, the clarification of the interaction between the fields of fluid convection and heat conduction in the unheated elements is the most important part of explaining the heat transfer behavior. Therefore, a new proposed parameter S (= BR/Gr D 1 4 ) was introduced through a vectorial dimensional analysis, taking into account the thermal properties of the material of the unheated elements. Heat transfer characteristics for cases of both convex and concave heating surface are discussed on the basis of the parameter S and visual observations of the velocity and temperature fields. Empirical formulas for the cases of convex and concave heating have been derived to correlate the heat transfer characteristic Nu/Gr D 1 4 and the parameter S.

On the inverse conductivity problem with one measurement

The authors are looking for an open set D entering the coefficient of the elliptic equation div((1+chi (D)) Del u)=0 in a domain Omega when for one given non-zero Neumann data on delta Omega they know the Dirichlet data on a part of delta Omega (a single boundary measurement). Here chi (D) is the indicator function of D. They prove uniqueness for sets D which are convex cylinders or unions of discs whose centres are extreme points of the convex hull of those centres.

Geometric Inequalities for Poisson Processes of Convex Bodies and Cylinders

Geometric Inequalities for Poisson Processes of Convex Bodies and Cylinders

A new formulation of electromagnetic wave scattering using an on-surface radiation boundary condition approach

A new formulation of electromagnetic wave scattering by convex, two-dimensional conducting bodies is reported. This formulation, called the on-surface radiation condition (OSRC) approach, is based upon an expansion of the radiation condition applied directly on the surface of a scatterer. Past approaches involved applying a radiation condition at some distance from the scatterer in order to achieve a nearly reflection-free truncation of a finite-difference time-domain lattice. However, it is now shown that application of a suitable radiation condition directly on the surface of a convex conducting scatterer can lead to substantial simplification of the frequency-domain integral equation for the scattered field, which is reduced to just a line integral. For the transverse magnetic (TM) case, the integrand is known explicitly. For the transverse electric (TE) case, the integrand can be easily constructed by solving an ordinary differential equation around the scatterer surface contour. Examples are provided which show that OSRC yields computed near and far fields which approach the exact results for canonical shapes such as the circular cylinder, square cylinder, and strip. Electrical sizes for the examples are ka = 5 and ka = 10 . The new OSRC formulation of scattering may present a useful alternative to present integral equation and uniform high-frequency approaches for convex cylinders larger than ka = 1 . Structures with edges or corners can also be analyzed, although more work is needed to incorporate the physics of singular currents at these discontinuities. Convex dielectric structures can also be treated using OSRC. These will be the subject of a forthcoming paper.

Self-consistent GTD formulation for conducting cylinders with arbitrary convex cross section

A user-oriented computer program has been developed for high frequency radiation and scattering from infinitely-long perfectly. conducting convex cylinders. The analysis is based on the self-consistent geometrical theory of diffraction (GTD). The cylinder is modeled as an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> -sided polygon. Two cylindrical waves with unknown amplitudes are assumed to travel in opposite directions on each face of the polygon. The boundary conditions for the corners are applied to set up a matrix equation for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2N</tex> unknowns (the amplitudes associated with the traveling cylindrical waves). Crout's method is used to solve the matrix equation. Once the amplitudes for the traveling waves are determined, the radiation or scattered field is readily obtained via the usual GTD techniques. Numerical results are presented for radiation and scattering from rectangular, semi-circular, circular, and elliptic cylinders for both principal polarizations. The results show excellent agreement with GTD, moment, and eigenfunction solutions.

Scattering of Inertial Waves by Smooth Convex Cylinders

A general method of solution of the hyperbolic partial differential equation governing the scattering of inertial waves in a rotating fluid is presented for the case of cylindrical scatterers with smooth convex cross‐sections. The specific case of a parabolic cylinder is discussed in some detail.

On the validity of the geometrical theory of diffraction by convex cylinders

In this paper we consider the scattering of a wave from an infinite line source by an infinitely long cylinder C. The line source is parallel to the axis of C, and the cross section C of this cylinder is smooth, closed and convex. C is formed by joining a pair of smooth convex arcs to a circle C0, one on the illuminated side, and one on the dark side, so that C is circular near the points of diffraction. By a rigorous argument we establish the asymptotic behavior of the field at high frequencies, in a certain portion of the shadow S that is determined by the geometry of C in S. The leading term of our asymptotic expansion is the field predicted by the geometrical theory of diffraction.Previous authors have derived asymptotic expansions in the shadow regions of convex bodies in special cases where separation of variables is possible. Others, who have considered more general shapes, have only been able to obtain bounds on the field in the shadow. In contrast our result is believed to be the first rigorous asymptotic solution in the shadow of a nonseparable boundary, whose shape is frequency independent.

On the asymptotic behavior of electromagnetic fields scattered from convex cylinders near grazing incidence

On the asymptotic behavior of electromagnetic fields scattered from convex cylinders near grazing incidence

Diffraction of plane elastic waves by smooth convex cylinders

Diffraction of plane elastic waves by smooth convex cylinders