Spherical growth and surface-quasifree vibrations of Si nanocrystallites in Er-doped Si nanostructures

Si-based Er-doped Si nanostructures were fabricated for exploring efficient light emission from Er ions and Si nanocrystallites. High-resolution transmission electron microscopy observations reveal that Si nanocrystallites are spherically embedded in the SiO2 matrix. Energy-dispersive x-ray analysis indicates that the Er centers are distributed at the surfaces of nanocrystallites surrounded by the SiO2 matrix. Low-frequency Raman scattering investigation shows that Lamb's theory can be adopted to exactly calculate the surface vibration frequencies from acoustic phonons confined in spherical Si nanocrystallites and the matrix effects are negligible.     

A new processing method of CaZn2(OH)6·2H2O powders: Photoluminescence and growth mechanism

In this communication, we report on the formation of calcium hexahydroxodizincate dehydrate, CaZn₂(OH)₆·2H₂O (CZO) powders under microwave-hydrothermal (MH) conditions. These powders were analyzed by X-ray diffraction (XRD), Field-emission gum scanning electron microscopy (FEG-SEM), ultraviolet-visible (UV-vis) absorption spectroscopy and photoluminescence (PL) measurements. XRD patterns confirmed that the pure CZO phase was obtained after MH processing performed at 130 °C for 2 h. FEG-SEM micrographs indicated that the morphological modifications as well as the growth of CZO microparticles are governed by Ostwald-ripening and coalescence mechanisms. UV-vis spectra showed that this material have an indirect optical band gap. The pure CZO powders exhibited an yellow PL emission when excited by 350 nm wavelength at room temperature.     

Finite generation of canonical ring by analytic method

An overview of the analytic proof of the theorem on the finite generation of the canonical ring for the projective algebraic manifold of general type is given.     

Dynamics of Finger Formation in Laplacian Growth Without Surface Tension

We study the dynamics of “finger” formation in Laplacian growth without surface tension in a channel geometry (the Saffman–Taylor problem). We present a pedagogical derivation of the dynamics of the conformal map from a strip in the complex plane to the physical channel. In doing so we pay attention to the boundary conditions (no flux rather than periodic) and derive a field equation of motion for the conformal map. We first consider an explicit analytic class of conformal maps that form a basis for solutions in infinitely long channels, characterized by meromorphic derivatives. The great bulk of these solutions can lose conformality due to finite time singularities. By considerations of the nature of the analyticity of these solutions, we show that those solutions which are free of such singularities inevitably result in a single asymptotic “finger” whose width is determined by initial conditions. This is in contradiction with the experimental results that indicate selection of a finger of width 1/2. In the last part of this paper we show that such a solution might be determined by the boundary conditions of a finite body of fluid, e.g. finiteness can lead to pattern selection.     

Optically induced rotation of an exciton spin in a semiconductor quantum dot

We demonstrate control over the spin state of a semiconductor quantum dot exciton using a polarized picosecond laser pulse slightly detuned from a biexciton resonance. The control pulse follows an earlier pulse, which generates an exciton and initializes its spin state as a coherent superposition of its two nondegenerate eigenstates. The control pulse preferentially couples one component of the exciton state to the biexciton state, thereby rotating the exciton's spin direction. We detect the rotation by measuring the polarization of the exciton spectral line as a function of the time difference between the two pulses. We show experimentally and theoretically how the angle of rotation depends on the detuning of the second pulse from the biexciton resonance.     

Quantitative x-ray phase-contrast imaging using a single grating of comparable pitch to sample feature size

The ability to quantitatively retrieve transverse phase maps during imaging by using coherent x rays often requires a precise grating or analyzer-crystal-based setup. Imaging of live animals presents further challenges when these methods require multiple exposures for image reconstruction. We present a simple method of single-exposure, single-grating quantitative phase contrast for a regime in which the grating period is much greater than the effective pixel size. A grating is used to create a high-visibility reference pattern incident on the sample, which is distorted according to the complex refractive index and thickness of the sample. The resolution, along a line parallel to the grating, is not restricted by the grating spacing, and the detector resolution becomes the primary determinant of the spatial resolution. We present a method of analysis that maps the displacement of interrogation windows in order to retrieve a quantitative phase map. Application of this analysis to the imaging of known phantoms shows excellent correspondence.     

A Construction of Almost Steiner Systems

Let n, k, and t be integers satisfying . A Steiner system with parameters t, k, and n is a k‐uniform hypergraph on n vertices in which every set of t distinct vertices is contained in exactly one edge. An outstanding problem in Design Theory is to determine whether a nontrivial Steiner system exists for . In this note we prove that for every and sufficiently large n, there exists an almost Steiner system with parameters t, k, and n; that is, there exists a k‐uniform hypergraph on n vertices such that every set of t distinct vertices is covered by either one or two edges.     

Correlations of image quality metrics studied using systematically distorted videos

Several frequently used image quality metrics were selected to systematically study the correlations between them using many distorted videos, which were revised by gradual changes of usual types of distortion. A modified power-law equation was found as a general relation between the metrics. The parameters obtained by data fittings on the experimental results can be approximated as additions of independent components, which are functions of average, distortion and video. Hence, a metrics can be written as a product of the power-law functions of another metrics with individual coefficients corresponding to distortion, video, and the minor terms.