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We compare the performance of very fast simulated quenching; generalized simulated quenching, which unifies classical Boltzmann simulated quenching and Cauchy fast simulated quenching; and variable step size simulated quenching. The comparison is carried out by applying these algorithms to the design of diffractive optical elements for beam shaping of monochromatic, spatially incoherent light to a tightly focused image spot, whose central lobe should be smaller than the geometrical-optics limit. For generalized simulated quenching we choose values of visiting and acceptance shape parameters recommended by other investigators and use both a one-dimensional and a multidimensional Tsallis random number generator. We find that, under our test conditions, variable step size simulated quenching, which generates each parameter's new states based on the acceptance ratio instead of a certain theoretical probability distribution, produces the best results. Finally, we demonstrate experimentally a tightly focused image spot, with a central lobe 0.22-0.68 times the geometrical-optics limit and a relative sidelobe intensity 55%-60% that of the central maximum intensity. OCIS codes: 230.3670, 050.1970, 220.0220, 100.5090.

Fresnel-type diffractive optical elements (DOEs) for general beam shaping of monochromatic, spatially incoherent light are demonstrated. Direct and indirect methods, i.e., adding a lens' phase to the designed Fraunhofer-type DOEs, are used for the design. The indirect method can reduce the calculation time by approximately half without loss of design accuracy. Two different design examples are shown. For one design the direct method gives a maximum sidelobe intensity of 5.0% of the maximum intensity in the signal window. For the second design the indirect method gives 23.0% of this value. The generated patterns can maintain their basic shapes over a long distance. The elements have been fabricated by directly using gray-scale commercial slides as masks. Experimental results are in close agreement with numerical predictions.

This paper describes the computational fluid dynamics (CFD) approach coupled with an automated grid generation technique utilized for the numerical optimization of a modern centrifugal compressor with an inducer vaned shroud for increased operability margin. The grid generation process was automated to permit rapid optimization of the impeller and vaned shroud geometry. A three-dimensional, viscous, steady flow, mixing-plane approach was utilized to numerically analyze the impeller and vaned shroud in a coupled fashion to capture the interaction effects. The numerical technique verifies the ability of the vane shroud to extend compressor surge margin at the part-speed operating condition, while maintaining acceptable high-speed performance. CFD analyses confirm that the aerodynamics of the vaned shroud match expectation, and are consistent with the mass-averaged compressor speedline characteristics generated from the CFD results.

Most general relativity textbooks devote considerable attention to the simplest example of a black hole containing a singularity, the Schwarzschild geometry. Only a few discuss the dynamical process of gravitational collapse by which black holes and singularities form. We present two simple analytical models that describe this process. The first involves collapsing spherical shells of light and is analyzed mainly in Eddington-Finkelstein coordinates; the second involves collapsing spheres filled with a perfect fluid and is analyzed mainly in Painleve-Gullstrand coordinates. Our main goal is simplicity and algebraic completeness, but we also present a few more sophisticated results such as the collapse of a light shell in Kruskal-Szekeres coordinates. [DOI: 10.1119/1.2117187]

Polycrystalline SrBi2Ta2O9 (SBT) ferroelectric thin films were synthesized on Pt/Ti/SiO2/Si substrates employing the metalorganic decomposition technique and investigated the structure as well as the dependence of ferroelectric behavior on the applied voltage and frequency. Using x-ray diffraction, the crystalline structure of the SBT thin films was observed and the surface morphologies of the SBT films were analyzed by scanning electron microscopy. A RT6000HVS ferroelectric tester was used to measure the ferroelectric features. The results are discussed.

The microstructure and transport properties of YBa2Cu3O(sub 7-delta)/La(sub 0.67)Ca(sub 0.33)MnO3 (YBCO/LCMO) bilayers are presented. The superconductivity and ferromagnetism coexisted in the bilayer with the YBCO thickness of 12.5 nm and they are related to the interaction between spin polarized electrons in the manganites and the copper pairs in the cuprates.

The stacking faults and their effects on ferroelectric properties in stronium-bismuth-tantalate SrBi2Ta2O9 are evaluated by transmission electron microscopy (TEM) and ferroelectric hysteresis loop measurement. It was seen that with excess Bi, the density of the extrinsic stacking faults can be reduced, and with deficient Sr, the stacking faults change its form.