Extended frequency range measurements for determining the Kneser-type acoustic relaxation time

In the present paper, the authors discuss studies carried out for many years dealing particularly with two compounds: benzene and carbon disulphide and compare them with the results obtained by numerous acoustics researchers. These compounds are typical liquids in which acoustic Kneser-type relaxation occurs, caused by an irreversible vibrational and translational (VT) transition. Since magnitudes describing the relaxation process were diverse in many papers, we have undertaken an attempt to clarify these differences and to indicate how to avoid errors resulting from instrumental imperfections and the disregard of the considerable measurement errors when investigating velocity dispersion in the hypersonic (GHz) range. The results of these researches changed the interpretation of previous papers.     

测量薄凸透镜光学参量的简便方法

本文从薄凸透镜的反射成象原理出发,定性地解释了为什么物光经透镜后表面反射形成的倒立等大的实象时,其物距、象距都小于透镜焦距;介绍了逆向光路的计算方法.最后,通过薄凸透镜的反射成象原理和逆向光路的计算,推导出测量薄凸透镜的光学参量的简便方法.     

Supersonic cluster beam deposition of nanostructured titania

Nanostructured titanium dioxide films have been deposited by supersonic cluster beam deposition (CBD). Nanoparticles are produced by a pulsed microplasma cluster source (PMCS) and selected by aerodynamic separation effects. The as-deposited film is a complex mixture where amorphous material coexists, at the nanoscale, with anatase and rutile crystal phases. The nanocrystalline fraction of the film is characterized by crystal size ranging from 100 nm to less than 5 nm. We have characterized the film structure by transmission electron microscopy, Raman spectromicroscopy, X-ray diffraction, and UV-visible spectroscopy showing that correlations exist between cluster size and film properties. In particular if very small clusters are deposited, the film shows a predominant rutile phase whereas larger clusters form films with mainly anatase structure. Our observations suggest that phonon confinement effects are responsible for a significant shift and broadening observed for the Raman peaks. In addition, optical gap tuning is provided by mass selection: large clusters assembling generates a film with 3.22 eV optical gap, while smallest clusters 3.52 eV.     

Locally Scalar Graph Representations in the Category of Hilbert Spaces

The condition of being locally scalar is imposed on graph (or quiver) representations in the category of Hilbert spaces. Under this condition, reflection and Coxeter functors are constructed in categories of such representations and used to prove an analog of the Gabriel theorem.__________Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 39, No. 2, pp. 13–30, 2005Original Russian Text Copyright © by S. A. Kruglyak and A. V. Roiter     

Far infrared reflection spectra of layered semiconductors

Far infrared reflection and Raman spectra of InSe were measured at 5, 77 and 300 K. Phonon frequencies obtained by reflection spectra were well explained by two-point phonon combination. The crystal structure of-type was confirmed at low temperature. Ion blocking analysis supported also no change of phase by temperature in this semiconductor.     

Quotients of Poincaré Polynomials Evaluated at –1

For a finite reflection group W and parabolic subgroup W _J, we establish that the quotient of Poincaré polynomials \frac{W(t)}{W_J(t)}, when evaluated at t=–1, counts the number of cosets of W _J in W fixed by the longest element. Our case-by-case proof relies on the work of Stembridge (Stembridge, Duke Mathematical Journal, 73 (1994), 469–490) regarding minuscule representations and on the calculations of of Tan (Tan, Communications in Algebra, 22 (1994), 1049–1061).     

Reflection and Transmission Times Through a Linear Potential

Reflection and transmission times through a linear potential is studied by using the stationary phase method. The incident particle is described by a wave packet constructed from a momentum distribution (k – k) highly concentrated around a fixed value k. The way the reflection and transmission times are calculated is similar to the way the phase time is defined for a rectangular potential.     

Total reflection X-ray fluorescence polymer spectra: classification by taxonomy statistic tools

The aim of this work is to explore the use of chemometric tools for the classification of synthetic and natural polymers with a mean molecular weight greater than 10(6). Total Reflection X-Ray Fluorescence (TXRF) spectra were obtained and analyzed in order to retrieve matrix information and to illustrate the calibration procedure. The intensities of the coherent and incoherent scattered peaks were specially selected for this purpose. The polymers studied were aqueous solutions of scleroglucan, polyacrilamide, polyoxyethylene oxide, glucomannan, 2,3,6-tri-o-ethylamylose and xhantan, in concentrations upto 1% (m/m). matlab software was used for numerical calculations. Using a combination of principal component analysis and cluster analysis, the differences in composition of various analyzed polymers can be visualized.     

Long-Range Orders in Models of Itinerant Electrons Interacting with Heavy Quantum Fields

The Falicov–Kimball model consists of itinerant lattice fermions interacting with Ising spins by an on-site potential of strength U. Kennedy and Lieb proved that at half filling there is a low temperature phase with chessboard long range order on ^d , d2, for all non-zero values of U. Here we investigate the stability of this phase when small quantum fluctuations of the Ising spins are introduced in two different ways. The first one corresponds to replace the classical spins by quantum two level systems attached to each site of the lattice. In the second one we interpret the spins as occupation numbers of localized f-electrons or heavy ions which have a small kinetic energy. This leads to the so-called asymmetric Hubbard model. For both models we prove that for all non-zero values of U the long range order of the original Falicov–Kimball model remains stable if the additional quantum fluctuations are small enough. This result is proved by non-perturbative methods based on a chessboard estimate and the principle of exponential localisation. In order to derive the chessboard estimate the phase factors in the kinetic energy of fermions must have a flux equal to . We also investigate the models where the fermions are replaced by hard-core bosons and prove the same result for large U. For hard core bosons the kinetic term is the conventional one with zero phase factors. For small U and hard-core bosons we find that there is an off-diagonal long range order for low enough temperature and any strength of the additional quantum fluctuations. Open problems are discussed.     

Dispersion of elastic guided waves in piezoelectric infinite plates with inversion layers

In this work, we study the dispersion of elastic waves in piezoelectric infinite plates with ferroelectric inversion layers. The motivation is to analyze the effect of ferroelectric inversion layers on wave dispersion and resonant behavior under impulsive line loads. A semi-analytical finite-element (SAFE) method has been adopted to analyze the problem. Two model problems are considered for analysis. In one, the plate is composed of a layer of 36° rotated y-cut LiNbO₃ with a ferroelectric inversion layer. In the other, material is PZT-4 with a ferroelectric inversion layer. Comparison with experimental results, reported in the literature for isotropic materials, shows a very good agreement with theoretical predictions obtained using SAFE method. Furthermore, comparison of the resonance frequencies of the S₁ modes, calculated using KLM approximation (f₀ = C_d/2h) and SAFE method, are illustrated for each problem. The frequency spectra of the surface displacements show that resonant peaks occur at frequencies where the group velocity vanishes and the phase velocity remains finite, i.e., a minimum in the dispersion curve below the cut-off frequency. The effect of the ratio of the thicknesses of the inversion layer (IL) and the plate on the frequencies and strength of the resonant peaks is examined. It is observed that for PZT-4 with 50% IL to plate thickness ratio the frequency for the second resonant peak is about twice that for the first one. Results are presented showing the dependence of resonant frequencies on the material properties and anisotropy. Materials selection for single-element harmonic ultrasound transducers is a very important factor for optimum design of transducers with multiple thickness-mode resonant frequencies. The theoretical analysis presented in this study should provide a means for optimum ultrasound transducer design for harmonic imaging in medical applications.