Finite-difference and finite-volume methods for nonlinear standing ultrasonic waves in fluid media

In the framework of the application of high-power ultrasonics in industrial processing in fluid media, the mathematical prediction of the acoustical parameters inside resonators should improve the development of practical systems. This can be achieved by the use of numerical tools able to treat the nonlinear acoustics involved in these phenomena. In particular, effects like nonlinear distortion and nonlinear attenuation are fundamental in applications. In this paper, three one-dimensional numerical models in the time domain for calculating the nonlinear acoustic field inside a one-dimensional resonant cavity are presented and compared. They are based on the finite-difference and the finite-volume methods. These different algorithms solve the differential equations, from the linear up to the strongly nonlinear case (including weak shock). Some physical results obtained from the modelling of ultrasonic waves and a comparison of the efficiency of the different algorithms are presented.     

Flow-injection determination of amine contaminants in cyclamate samples based on temperature for controlling selectivity

This paper describes a flow-injection (FI) method for the simultaneous determination of aniline and cyclohexylamine impurities in cyclamate products. The method consists of the derivatization of amines with 1,2-naphthoquinone-4-sulfonate under selective and non-selective conditions. Here, the selectivity is achieved by working at 20 degree C, at which only aniline reacts, whilst higher temperatures (80 degree C) lead to a non-selective reaction of the two analytes. The FI manifold is composed of two flow cells for the spectrophotometric detection of derivatives at 480 nm. Experimental conditions have been optimized by factorial design and multicriteria making approach. Quantification is accomplished by differential analysis of the analyte contributions in the double peaks generated when the sample reaches cell 1 and cell 2. Results obtained with the proposed method are in satisfactory agreement with those provided by the standard method for the analysis of cyclamate samples.     

A novel organic-inorganic hybrid based on a dinuclear copper complex supported on a keggin polyoxometalate

The autoassembly process of copper-oxalate dimers and Keggin type polyoxometalates leads to the first example of a new family of organic-inorganic hybrids, K(14)[(Cu(2)(bpy)(2)(mu-ox))(SiW(11)O(39)Cu(H(2)O))](2)[SiW(11)O(39)Cu(H(2)O)]. approximately 55H(2)O. This compound crystallizes in the monoclinic space group C2/m, a = 37.932(6) A, b = 21.303(3) A, c = 12.546(2) A, beta = 106.16(1) degrees, Z = 2. The crystal structure reveals the presence of a polymeric hybrid built up of alternating dimer and polyoxometalate entities.     

Symmetric and Rees algebras of Koszul cycles and their Gröbner bases

In this paper we study the symmetric algebra S(E _i ) and Rees algebra R(E _i ) of the modules E _i of i-cycles of the Koszul complex associated with the sequence of indeterminates of a polynomial ring . For i=2 and i=n–2 we show that is a d-sequence on S(E _i ) and R(E _i ) and we determine Gröbner bases and Sagbi bases related to these algebras. Mathematics Subject Classification (2000):13A30, 13D02, 13H10, 13P10The second author is grateful to the National Natural Science Foundation of China for support.Part of this work was made while the third author was visiting the Fachbereich Mathematik und Informatik der Universität Essen, to which he would like to thank for its hospitality.     

The Yamabe problem for almost Hermitian manifolds

The conformal class of a Hermitian metric g on a compact almost complex manifold (M^2m, J) consists entirely of metrics that are Hermitian with respect to J. For each one of these metrics, we may define a J-twisted version of the Ricci curvature, the J-Ricci curvature, and its corresponding trace, the J-scalar curvature s^J. We ask if the conformal class of g carries a metric with constant s^J, an almost Hermitian version of the usual Yamabe problem posed for the scalar curvature s. We answer our question in the affirmative. In fact, we show that (2m−1)s^J−s=2(2m−1)W(ω, ω), where W is the Weyl tensor and ω is the fundamental form of g. Using techniques developed for the solution of the problem for s, we construct an almost Hermitian Yamabe functional and its corresponding conformal invariant. This invariant is bounded from above by a constant that only depends on the dimension of M, and when it is strictly less than the universal bound, the problem has a solution that minimizes the almost complex Yamabe functional. By the relation above, we see that when W (ω, ω) is negative at least one point, or identically zero, our problem has a solution that minimizes the almost Hermitian Yamabe functional, and the universal bound is reached only in the case of the standard 6-sphere equipped with a suitable almost complex structure. When W(ω, ω) is non-negative and not identically zero, we prove that the conformal invariant is strictly less than the universal bound, thus solving the problem for this type of manifolds as well. We discuss some applications.     

Low Dimension Dynamics in the EPRB Experiment with Random Variable Analyzers

The Einstein–Podolsky–Rosen–Bohm (EPRB) experiment performed with random variable and spatially separated analyzers is a milestone test in the controversy between Objective Local Theories (OLT) and Quantum Mechanics (QM). Only a few OLT are still possible. Some of the surviving OLT (specifically, the so called non-ergodic theories) would be undetectable in the averaged statistical values, but they may leave their trace in the time dynamics. For, while QM predicts random processes, the OLT of this kind predict the existence of regularities that may be revealed as a low dimensional object in the phase space. We perform a numerical analysis of the time-resolved data recorded in that experiment to unveil any hypothetical low dimensional dynamics that may be present. We find no consistent indication of such dynamics except for one data file, the longest of all in the real time. The possible causes of these dynamics are discussed.      

Analysis of plume deflection in the silicon laser ablation process

Changes in target surface morphology and ablation plume direction have been experimentally observed during the initial stages of the silicon laser ablation process. A relationship between both phenomena can be observed upon analysing the temperature field induced by the laser beam in a rough surface material. Theoretical studies on the deflection of the ablation plume are presented. These analyses are based on the hypothesis that particles that reach evaporation temperature will exit normally to the target surface with a velocity that is proportional to the surface temperature and the amount of the ablated material. Numerical solutions and experimental results of laser ablation process of silicon targets are found to agree with theoretical studies. PACS 42.25.Lc; 79.20.Dc; 02.70.Dc