Ground-plane-backed hemispherical Luneberg-lens reflector

A spherical Luneberg-lens reflector provides excellent passive wideband and wide-angular radar-signature augmentation, and has been widely used. Much of its signature-enhancement performance over half of its angular coverage can potentially be achieved by using a corresponding low-profile, hemispherical Luneberg-lens reflector, mounted on a reflective ground plane. This paper presents a quantitative study of a practical design of an off-the-shelf hemispherical Luneberg-lens reflector to gain insight and to fully explore its performance limits. Extensive wideband and wide-angle measurements were carried out for this lens configuration, and a comprehensive numerical analysis was also conducted, using the finite-element method combined with a boundary integral equation to complement the test data. The effect, in practice, of a finite-sized ground plane, and the resulting vertically polarized traveling-wave interference to the direct lens reflector's return, were demonstrated. Key design issues are discussed, and potential solutions are suggested.     

Corrections to Fluid Dynamics

We show that a Galilean invariant version of fluid dynamics can be derived by the methods of statistical dynamics using Maxwell's balance equations. The basic equation is non-local, and might replace the Boltzmann equation if the latter turns out not to have global smooth solutions in general. As an approximation, a local form of the equations of motion is derived. It turns out to be a version of the Navier-Stokes system, obeying the Stokes relation, and with the viscosity coefficient rising as ^1/2 with temperature . The new feature is the presence of the Dufour effect for a gas of a single component. This ensures that the principal symbol of the parabolic system is non-singular.     

A quantitative study of Luneberg-lens reflectors

Luneberg-lens reflectors, which provide passive wideband and wide-angle radar-signature augmentation, have been widely used in small military target drones, decoys, and marine vessels. Due to the difficulty of fabricating inhomogeneous dielectrics with a continuously varying index, Luneberg lenses are usually constructed with multilayered step-index dielectrics. This paper presents a quantitative study of a practical design of a three-layer Luneberg-lens reflector for C- and X-band operations. Extensive wideband and wide-angle measurements were carried out for this lens with three different cap reflectors, as well as for the lens alone without any reflector. A comprehensive numerical analysis, using the finite-element method combined with boundary integral equations, was also conducted. This was done to support the measured data and to provide additional insight for a better understanding of the performance and the limitations of the Luneberg-lens reflector than could be achieved with the traditional ray-optics method. The effect of reflector size is discussed, and the limitation of three-layer design is demonstrated. It has also been shown that very accurate material parameters must be ascertained so as to achieve the level of accuracy commonly desired in the computational electromagnetic codes applied to inhomogeneous dielectrics. The excellent agreement between the numerical and measured data indicates that this full-wave Maxwell solver can be used to explore the design limits and optimize designs for this type of lens reflector.     

Quantum Orlicz Spaces in Information Geometry

Let H₀ be a selfadjoint operator such that Tr is of trace class for some , and let denote the set of ε-bounded forms, i.e., for some 0 $$" align="middle" border="0"> . Let χ := Span . Let denote the underlying set of the quantum information manifold of states of the form . We show that if Tr ,