Circular Phase Research Articles

Plastic relaxation of a shear crack at a circular inclusion

The plastic relaxation of a shear crack situated normal to the interface of a second phase particle of circular cross-section is analyzed using the method of Atkinson and Kay. The ratio of applied stress to yield stress and the relative displacement of the crack faces at the tip of the crack are related to the crack parameters. The results are used to discuss the effect of the shear modulus and size of the circular second phase particle on the behaviour of the plastic zone.

Fracture of a circular inclusion in an infinite matrix

The plastic relaxation of a shear crack situated at the interface inside a second phase of circular cross-section is analyzed. The ratio of applied stress to yield stress and the relative displacement of crack faces at the tip of the crack are related to the crack length, width of the plastic zone and the size of the second phase particle. The results are used to discuss the effect of shear modulus of the matrix on the behavior of the plastic zone at the tip of the crack in the second phase. Conclusions on the fracture behavior of a circular second phase particle in an infinite matrix are made.

A NOTE ON JUPITER'S CIRCULAR POLARIZATION

ABSTRACT Observations of Jupiter were made during the 1973 postopposition period. The circular polarization of the Southern Hemisphere was monitored at phase angles between 0.5 and 10.0 degrees. Our measurements revealed a sharp-peaked feature in the circular polarization phase curve at 7.8 degrees similar to the 2.7-degree feature on Saturn.

Optimal Filter Design for Annular Imaging

Filters of the type exp(in theta)sgn J(n)(z(o)r) with theta the azimuthal angle and r the radial coordinate in the filter plane, are shown to maximize the energy content in a narrow annular image of radius z(o) with respect to incident energy. The simplest optimal filter, sgnJ(o)(z(o)r), is well approximated by the binary circular phase grating sgn cos(z(o)r - pi/4). The single lobe of the first order image of this filter contains 46% of the incident energy within the half-width 0.4lambdaf/a, centered around the image radins Nlambdaf/(2a), where N approximately z(o)/pi is the number of filter sections.

Plastic relaxation of a shear crack at a circular inclusion

Abstract The plastic relaxation of a shear crack situated normal to the interface of a second phase particle of circular cross-section is analyzed using the method of Atkinson and Kay. The ratio of applied stress to yield stress and the relative displacement of the crack faces at the tip of the crack are related to the crack parameters. The results are used to discuss the effect of the shear modulus and size of the circular second phase particle on the behaviour of the plastic zone.

VLF-ELF radiation characteristics of a 90°-phased crossed-dipole array in a cold multicomponent magnetoplasma

Linear electromagnetic theory is used to find the VLF-ELF radiation characteristics of a quadrature-phased crossed-dipole array in a cold multicomponent magnetoplasma. Each dipole is perpendicular to the static magnetic field B0, and the current on each is assumed to have a skin-triangular distribution. Formal solutions valid throughout the VLF and ELF ranges are derived for the total radiated complex power and mutual coupling power. These solutions are used to obtain both numerical results and approximate closed-form expressions for mutual input impedance ΔZ applicable to the driving terminals of either dipole of the array. Approximate closed-form expressions for the power fluxes parallel and perpendicular to B0 are also derived. When a right-circularly phased dipole array is used as a radiating source in the VLF range, the total power radiated into the whistler mode is increased, and the power flux along the field line is enhanced by a factor of 4 compared to that from a single dipole carrying the same current. In the ELF range, the effects are similar but more complicated. The mutual input reactance due to the effects of medium anisotropy and circular phasing of the dipole array are found to be negligible. It is shown that the power flux along B0 from a right-circularly phased dipole array peaks by at least 1 order of magnitude at approximately half the electron gyrofrequency. This result suggests a possible use of the proposed array as a radiating source to trigger artificially stimulated VLF emissions.

Phase Contrast Imagery of Circular Phase Objects in Partially Coherent Light

A general solution of the problem of imagery of phase discs in partially coherent phase contrast microscopy is given. The solution has been obtained in a form very much amenable to analysis of optimum phase plate characteristics.

Characteristics of dielectric loaded and covered circular waveguide phased arrays

The use of dielectric materials for the hardening and matching of phased-array antennas in recent years has shown that a more complete understanding of the effects of these materials upon the array performance is necessary. The characteristics of fully loaded, plugged, and sheath covered circular waveguide phase arrays are analyzed and discussed. Numerical solutions of the boundary-value problem are verified by experimental and convergence tests. Particular emphasis is placed on the study of (forced) surface wave resonance effects. Three different cases for surface wave resonances were obtained. These include the case in which surface wave resonances are present in the absence of dielectrics, the case in which they are trapped by the presence of dielectric plugs, as well as the case in which waves are trapped by the presence of a dielectric sheath. The surface wave resonance due to the plug is shown to vanish for certain "bandpass" ranges of plug thickness which repeat periodically for a single trapped waveguide mode. On the other hand, the surface wave trapped in the sheath exhibits no "bandpass" characteristics. Instead, multiple surface wave resonances occur with increasing sheath thickness. Finally, the surface wave resonances observed here appear at isolated points in the scan plane.

Dielectric-Lined Circular Waveguide with Increased Usable Bandwidth

This report describes how the useful (single-mode) bandwidth of circular waveguide can be significantly increased by using a smaller diameter with dielectric lining. The increased bandwidth results from an increase in the ratio of the cutoff frequency of the second, or TM-01, mode over that of the dominant, or TE-11 mode. A cavity test is described which permits the measurement of mode separation for any thickness of dielectric lining. A lining with a dielectric constant in the vicinity of 4 appears to be near optimum for maximum single-mode bandwidth. For a dielectric constant of 3.8 (fused silica), the greatest mode separation is obtained if the dielectric cross section has about 0.44 of the area of the entire cross section, in which case the useful bandwidth is about doubled (perhaps increased from 8 to 16 per cent, if the entire band is to clear the TE-11 cutoff frequency by 20 per cent). Over the useful bandwidth of such a waveguide, the guide wavelength may be calculated approximately by the simple waveguide formula in terms of the equivalent dielectric constant, as determined by the cavity measurement. Applications which would benefit from increased dominant-mode bandwidth in circular waveguide include rotary joints carrying circular polarization, rotary attenuators and phase shifters, and array radiators.

Theory and potential applications of backward waves in nonperiodic inhomogeneous waveguides

Backward waves can propagate in an inhomogeneous waveguide of circular cross-section when the geometry and the properties of the materials are suitable. The phenomenon is related to a degeneracy of the H11 and E11 modes at cutoff, and this suggests where to look for the most pronounced effect. The behaviour of the group velocity is studied in detail, in the neighbourhood of the degeneracy, for a number of values of the guide radius. A discussion is given of the possibilities of applying the phenomenon to backward-wave amplifiers, travelling-wave masers, a frequency selector, a circular polariser, switching and phase compensation.

Diffraction Images of Circular Phase Objects in Partially Coherent Light

Images of circular phase objects in partially coherent light have been studied. It has been shown that recognizable contrast is obtained in the image of phase objects formed by an ordinary microscope even when the cone of the illuminating beam is sizable and the microscope is focused perfectly.