Contraction of the G_r,s Quantum Group to its Nonstandard analogue and corresponding Coloured Quantum Groups

The quantum group G_r,s provides a realisation of the two parameter quantum GL_p,q(2) which is known to be related to the two parameter nonstandard GL_hh'(2) group via a contraction method. We apply the contraction procedure to G_r,s and obtain a new Jordanian quantum group G_m,k. Furthermore, we provide a realisation of GL_h,h'(2) in terms of G_m,k. The contraction procedure is then extended to the coloured quantum group GL_r{\lambda,\mu}(2) to yield a new Jordanian quantum group GL_m{\lambda,\mu}(2). Both G_r,s and G_m,k are then generalised to their coloured versions which inturn provide similar realisations of GL_r{\lambda,\mu}(2) and GL_m{\lambda,\mu}(2).Comment: 22 pages LaTeX, to be published in J. Math. Phy

Coloured extension of GL_q(2) and its dual algebra

We address the problem of duality between the coloured extension of the quantised algebra of functions on a group and that of its quantised universal enveloping algebra i.e. its dual. In particular, we derive explicitly the algebra dual to the coloured extension of GL_q(2) using the coloured RLL relations and exhibit its Hopf structure. This leads to a coloured generalisation of the R-matrix procedure to construct a bicovariant differential calculus on the coloured version of GL_q(2). In addition, we also propose a coloured generalisation of the geometric approach to quantum group duality given by Sudbery and Dobrev.Comment: 10 pages LaTeX. Talk given at the "XXIII International Colloquium on Group Theoretical Methods in Physics", July 31 - August 05, 2000, Dubna (Russia); to appear in the proceeding

Exact results for Casimir interactions between dielectric bodies: The weak-coupling or van der Waals Limit

In earlier papers we have applied multiple scattering techniques to calculate Casimir forces due to scalar fields between different bodies described by delta function potentials. When the coupling to the potentials became weak, closed-form results were obtained. We simplify this weak-coupling technique and apply it to the case of tenuous dielectric bodies, in which case the method involves the summation of van der Waals (Casimir-Polder) interactions. Once again exact results for finite bodies can be obtained. We present closed formulas describing the interaction between spheres and between cylinders, and between an infinite plate and a retangular slab of finite size. For such a slab, we consider the torque acting on it, and find non-trivial equilibrium points can occur.Comment: 4 pages, 3 figure

A (p,q) Deformation of the Universal Enveloping Superalgebra U(osp(2/2))

We investigate a two parameter quantum deformation of the universal enveloping orthosymplectic superalgebra U(osp(2/2)) by extending the Faddeev-Reshetikhin-Takhtajan formalism to the supersymetric case. It is shown that $U_{p,q}(osp(2/2))$ possesses a non-commutative, non-cocommutative Hopf algebra structure. All the results are expressed in the standard form using quantum Chevalley basis.Comment: 8 pages; IC/93/41

Electromagnetic semitransparent δ\delta-function plate: Casimir interaction energy between parallel infinitesimally thin plates

We derive boundary conditions for electromagnetic fields on a $\delta$-function plate. The optical properties of such a plate are shown to necessarily be anisotropic in that they only depend on the transverse properties of the plate. We unambiguously obtain the boundary conditions for a perfectly conducting $\delta$-function plate in the limit of infinite dielectric response. We show that a material does not "optically vanish" in the thin-plate limit. The thin-plate limit of a plasma slab of thickness $d$ with plasma frequency $\omega_p^2=\zeta_p/d$ reduces to a $\delta$-function plate for frequencies ($\omega=i\zeta$) satisfying $\zeta d \ll \sqrt{\zeta_p d} \ll 1$. We show that the Casimir interaction energy between two parallel perfectly conducting $\delta$-function plates is the same as that for parallel perfectly conducting slabs. Similarly, we show that the interaction energy between an atom and a perfect electrically conducting $\delta$-function plate is the usual Casimir-Polder energy, which is verified by considering the thin-plate limit of dielectric slabs. The "thick" and "thin" boundary conditions considered by Bordag are found to be identical in the sense that they lead to the same electromagnetic fields.Comment: 21 pages, 7 figures, references adde

Radar systems for the water resources mission, volume 2

The application of synthetic aperture radar (SAR) in monitoring and managing earth resources was examined. The function of spaceborne radar is to provide maps and map imagery to be used for earth resource and oceanographic applications. Spaceborne radar has the capability of mapping the entire United States regardless of inclement weather; however, the imagery must have a high degree of resolution to be meaningful. Attaining this resolution is possible with the SAR system. Imagery of the required quality must first meet mission parameters in the following areas: antenna patterns, azimuth and range ambiguities, coverage, and angle of incidence

Radar systems for the water resources mission, volume 1

The state of the art determination was made for radar measurement of: soil moisture, snow, standing and flowing water, lake and river ice, determination of required spacecraft radar parameters, study of synthetic-aperture radar systems to meet these parametric requirements, and study of techniques for on-board processing of the radar data. Significant new concepts developed include the following: scanning synthetic-aperture radar to achieve wide-swath coverage; single-sideband radar; and comb-filter range-sequential, range-offset SAR processing. The state of the art in radar measurement of water resources parameters is outlined. The feasibility for immediate development of a spacecraft water resources SAR was established. Numerous candidates for the on-board processor were examined

Radar systems for the water resources mission. Volume 4: Appendices E-I

The use of a scanning antenna beam for a synthetic aperture system was examined. When the resolution required was modest, the radar did not use all the time the beam was passing a given point on the ground to build a synthetic aperture, so time was available to scan the beam to other positions and build several images at different ranges. The scanning synthetic-aperture radar (SCANSAR) could achieve swathwidths of well over 100 km with modest antenna size. Design considerations for a SCANSAR for hydrologic parameter observation are presented. Because of the high sensitivity to soil moisture at angles of incidence near vertical, a 7 to 22 deg swath was considered for that application. For snow and ice monitoring, a 22 to 37 deg scan was used. Frequencies from X-band to L-band were used in the design studies, but the proposed system operated in C-band at 4.75 GHz. It achieved an azimuth resolution of about 50 meters at all angles, with a range resolution varying from 150 meters at 7 deg to 31 meters at 37 deg. The antenna required an aperture of 3 x 4.16 meters, and the average transmitter power was under 2 watts

Radar systems for a polar mission, volume 3, appendices A-D, S, T

Success is reported in the radar monitoring of such features of sea ice as concentration, floe size, leads and other water openings, drift, topographic features such as pressure ridges and hummocks, fractures, and a qualitative indication of age and thickness. Scatterometer measurements made north of Alaska show a good correlation with a scattering coefficient with apparent thickness as deduced from ice type analysis of stereo aerial photography. Indications are that frequencies from 9 GHz upward seem to be better for sea ice radar purposes than the information gathered at 0.4 GHz by a scatterometer. Some information indicates that 1 GHz is useful, but not as useful as higher frequencies. Either form of like-polarization can be used and it appears that cross-polarization may be more useful for thickness measurement. Resolution requirements have not been fully established, but most of the systems in use have had poorer resolution than 20 meters. The radar return from sea ice is found to be much different than that from lake ice. Methods to decrease side lobe levels of the Fresnel zone-plate processor and to decrease the memory requirements of a synthetic radar processor are discussed

Binary Neutron Stars in General Relativity: Quasi-Equilibrium Models

We perform fully relativistic calculations of binary neutron stars in quasi-equilibrium circular orbits. We integrate Einstein's equations together with the relativistic equation of hydrostatic equilibrium to solve the initial value problem for equal-mass binaries of arbitrary separation. We construct sequences of constant rest mass and identify the innermost stable circular orbit and its angular velocity. We find that the quasi-equilibrium maximum allowed mass of a neutron star in a close binary is slightly larger than in isolation.Comment: 4 pages, 3 figures, RevTe