The dyadic diffraction coefficient for a curved edge

A compact dyadic diffraction coefficient for electromagnetic waves obliquely incident on a curved edge formed by perfectly conducting curved or plane surfaces is obtained. This diffraction coefficent remains valid in the transition regions adjacent to shadow and reflection boundaries, where the diffraction coefficients of Keller's original theory fail. The method is on Keller's method of the canonical problem, which in this case is the perfectly conducting wedge illuminated by plane, cylindrical, conical, and spherical waves. When the proper ray fixed coordinate system is introduced, the dyadic diffraction coefficient for the wedge is found to be the sum of only two dyads, and it is shown that this is also true for the dyadic diffraction coefficients of higher order edges. One dyad contains the acoustic soft diffraction coefficient; the other dyad contains the acoustic hard diffraction coefficient. The expressions for the acoustic wedge diffraction coefficients contain Fresnel integrals, which ensure that the total field is continuous at shadow and reflection boundaries. The diffraction coefficients have the same form for the different types of edge illumination; only the arguments of the Fresnel integrals are different. Since diffraction is a local phenomenon, and locally the curved edge structure is wedge shaped, this result is readily extended to the curved edge

Analysis of the EM scattering from arbitrary open-ended waveguide cavities using axial Gaussian Beam tracking

The electromagnetic (EM) scattering from a planar termination located inside relatively arbitrarily shaped open-ended waveguide cavities with smoothly curved interior walls is analyzed using a Gaussian Beam (GB) expansion of the incident plane wave fields in the open end. The cavities under consideration may contain perfectly-conducting interior walls with or without a thin layer of material coating, or the walls may be characterized by an impedance boundary condition. In the present approach, the GB's are tracked only to the termination of the waveguide cavity via beam reflections from interior waveguide cavity walls. The Gaussian beams are tracked approximately only along their beam axes; this approximation which remains valid for relatively well focussed beams assumes that an incident GB gives rise to a reflected GB with parameters related to the incident beam and the radius of curvature of the wall. It is found that this approximation breaks down for GB's which come close to grazing a convex surface and when the width of the incident beam is comparable to the radius of curvature of the surface. The expansion of the fields at the open end depend on the incidence angle only through the expansion coefficients, so the GB's need to be tracked through the waveguide cavity only once for a wide range of incidence angles. At the termination, the sum of all the GB's are integrated using a result developed from a generalized reciprocity principle, to give the fields scattered from the interior of the cavity. The rim edge at the open end of the cavity is assumed to be sharp and the external scattering from the rim is added separately using Geometrical Theory of Diffraction. The results based on the present approach are compared with solutions based on the hybrid asymptotic modal method. The agreement is found to be very good for cavities made up of planar surfaces, and also for cavities with curved surfaces which are not too long with respect to their width

Non-destructive Orthonormal State Discrimination

We provide explicit quantum circuits for the non-destructive deterministic discrimination of Bell states in the Hilbert space $C^{d^{n}}$, where $d$ is qudit dimension. We discuss a method for generalizing this to non-destructive measurements on any set of orthogonal states distributed among $n$ parties. From the practical viewpoint, we show that such non-destructive measurements can help lower quantum communication complexity under certain conditions.Comment: 11 pages, 6 fugure

A hybrid asymptotic-modal analysis of the EM scattering by an open-ended S-shaped rectangular waveguide cavity

The electromagnetic fields (EM) backscatter from a 3-dimensional perfectly conducting S-shaped open-ended cavity with a planar interior termination is analyzed when it is illuminated by an external plane wave. The analysis is based on a self-consistent multiple scattering method which accounts for the multiple wave interactions between the open end and the interior termination. The scattering matrices which described the reflection and transmission coefficients of the waveguide modes reflected and transmitted at each junction between the different waveguide sections, as well at the scattering from the edges at the open end are found via asymptotic high frequency methods such as the geometrical and physical theories of diffraction used in conjunction with the equivalent current method. The numerical results for an S-shaped inlet cavity are compared with the backscatter from a straight inlet cavity; the backscattered patterns are different because the curvature of an S-shaped inlet cavity redistributes the energy reflected from the interior termination in a way that is different from a straight inlet cavity

Shock propagation in locally driven granular systems

We study shock propagation in a system of initially stationary hard-spheres that is driven by a continuous injection of particles at the origin. The disturbance created by the injection of energy spreads radially outwards through collision between particles. Using scaling arguments, we determine the exponent characterizing the power law growth of this disturbance in all dimensions. The scaling functions describing the various physical quantities are determined using large scale event driven simulations in two and three dimensions for both the elastic and the inelastic system. The results are shown to describe well the data from two different experiments on granular systems that are similarly driven.Comment: 8 pages, 9 figure

The radiation from slots in truncated dielectric-covered surfaces

A theoretical approach based on the geometrical theory of diffraction is used to study the electromagnetic radiation from a narrow slot in a dielectric-covered perfectly-conducting surface terminated at an edge. The total far-zone field is composed of a geometrical optics field and a diffracted field. The geometrical optics field is the direct radiation from the slot to the field point. The slot also generates surface waves which are incident at the termination of the dielectric cover, where singly-diffracted rays and reflected surface waves are excited. The diffraction and reflection coefficients are obtained from the canonical problem of the diffraction of a surface wave by a right-angle wedge where the dielectric-covered surface is approximated by an impedance surface. This approximation is satisfactory for a very thin cover; however, the radiation from its vertical and faces cannot be neglected in treating the thicker dielectric cover. This is taken into account by using a Kirchhoff-type approximation, which contributes a second term to the diffraction coefficient previously obtained. The contributions from the geometrical optics field, the singly-diffracted rays and all significant multiply-diffracted rays are summed to give the total radiation. Calculated and measured patterns are found to be in good agreement

Cosmic ray intensity distribution perpendicular to solar equatorial plane at 1 A.U. during 1978-83

The distribution of cosmic ray intensity perpendicular to solar equatorial plane, was investigated by using its yearly variation with respect to the heliolatitudinal position of the Earth, for the two intervals 1978 to 1980 and 1981 to 1983. The monthly mean values of two high latitude stations along with the solar and geomagnetic indices are used to derive the cosmic ray intensity distribution free from the changes due to variation in solar activity. The correction is found to be significant only during the interval 1976 to 1980. The results indicate a significant linear increase in cosmic ray intensity from north to south of solar equator, contrary to that observed during 1973 to 1975. No symmetrical gradients are found during the period of study, in agreement with earlier results

A Compact Instrument for the Measurement of Surface Tension of Liquids

An Instrument for the measurement of surface tension of liquids by a null method is described. The method of balancing the downward force of surface tension on the edge of a thin gloss plate by the upward hydrostatic pressure of the liquid is used. The instrument is quite compact, handy and sensitive and can be used for rapid measurement on a number of samples

High-frequency asymptotic methods for analyzing the EM scattering by open-ended waveguide cavities

Four high-frequency methods are described for analyzing the electromagnetic (EM) scattering by electrically large open-ended cavities. They are: (1) a hybrid combination of waveguide modal analysis and high-frequency asymptotics, (2) geometrical optics (GO) ray shooting, (3) Gaussian beam (GB) shooting, and (4) the generalized ray expansion (GRE) method. The hybrid modal method gives very accurate results but is limited to cavities which are made up of sections of uniform waveguides for which the modal fields are known. The GO ray shooting method can be applied to much more arbitrary cavity geometries and can handle absorber treated interior walls, but it generally only predicts the major trends of the RCS pattern and not the details. Also, a very large number of rays need to be tracked for each new incidence angle. Like the GO ray shooting method, the GB shooting method can handle more arbitrary cavities, but it is much more efficient and generally more accurate than the GO method because it includes the fields diffracted by the rim at the open end which enter the cavity. However, due to beam divergence effects the GB method is limited to cavities which are not very long compared to their width. The GRE method overcomes the length-to-width limitation of the GB method by replacing the GB's with GO ray tubes which are launched in the same manner as the GB's to include the interior rim diffracted field. This method gives good accuracy and is generally more efficient than the GO method, but a large number of ray tubes needs to be tracked

Current correlation functions of ideal fermi gas at finite temperature

Expressions for transverse and longitudinal current-current correlation functions of an ideal Fermi gas describing the current fluctuations induced in the electron system by external probe perpendicular and parallel to the propagation of electron wave, have been obtained at finite temperature. The results obtained for transverse and longitudinal functions are presented for different values of wavelength and frequency at different temperatures. The diamagnetic susceptibility as a function of temperature has also been obtained from transverse current correlation function as its long wavelength and static limit, which smoothly cross over from known quantum values to the classical limit with increase in temperature