Investigation in thorium phosphate by NMR II-phosphorus dipolar networks

With through space and through bond experiments in two-dimensional NMR we analyze the transformation from the thorium phosphate-hydrogen phosphate hydrate (TPHPH) to the β form of the thorium phosphate diphosphate (β-TPD) in relation with the phosphorus networks. These techniques are complementary: the through space coupling gives an insight on the dipolar phosphorus networks while the through bond coupling is particularly efficient in the detection of the P₂O₇ groups. With these experiments we show that in a first step, by heating the precursor TPHPH above 250 °C, it transforms into an form of TPD. This transformation is due to the complete condensation of hydrogen phosphate groups HPO₄ into P₂O₇ entities. By heating -TPD above 950 °C it transforms into its well-known β form. The form is characterized by a hygroscopic behavior: some water molecules are present near the P₂O₇ groups that makes non-equivalent their phosphorus nuclei. PO₄ dipolar networks are always present in the form. The main effect of these PO₄ and P₂O₇ units is to give the system a channel structure and the water enters in them.     

Luminescent molecular hybrid system derived from 2-furancarboxylic acid and silylated monomer coordinated to rare earth ions

In this study, silica-based organic-inorganic hybrids were prepared by the sol-gel method. Tetraethoxysilane (abbreviated as TEOS) and a kind of monomer (abbreviated as FA-APES) derived from modified 2-furancarboxylic acid (abbreviated as FA) with (3-aminopropyl)triethoxysilane (abbreviated as APES) were used as the inorganic and organic fragments, respectively. Coordination reaction between lanthanides (europium and terbium ions) and CO group of the monomer happened simultaneously. And after days of aging process the resultant materials showed characteristic luminescence of lanthanides. The enhancement of luminescence can be seen by the comparison with simply doped lanthanide hybrid systems. And it can be explained by the coordination ability of the organic counterpart. IR, NMR, UV-vis absorption, low-temperature phosphorescence spectroscopy and fluorescence spectroscopy were applied to characterize and the above spectroscopic data revealed that the triplet state energy of organic ligand matches with the emissive energy level of lanthanides (especially of Tb³⁺).     

Density and velocity statistics in variable density turbulent mixing

We experimentally study variable–density mixing of miscible gases in an open-circuit wind tunnel using simultaneous particle image velocimetry and planar laser-induced fluorescence. Experiments of a high Atwood number (0.6) and low Atwood number (0.1) are performed to compare non-Boussinesq cases with the Boussinesq limit. The higher density gas is injected into the wind tunnel co-flow using a round jet configuration, and near-field and far-field measurements are performed to examine mixing in both momentum and buoyancy-dominated regimes. The effects of buoyancy are measurable and important in both large-scale mixing features and in turbulence quantities. The low Atwood number PDFs (probability density functions) show fast and uniform mixing. The high Atwood number PDFs of density have skewness towards the larger densities, indicating less mixing of the heavy fluid due to its inertia. The skewness in the density gradient PDFs at high Atwood number displays strong density local variations that can enhance mixing at molecular scales. Turbulent kinetic energy decreases with streamwise distance from the jet for low Atwood number but increases for high Atwood number due to larger buoyancy and density-driven shear. Over 3000 experimental realisations are used to calculate statistical characteristics of the mixing, including valuable and rarely given data such as Favre-averaged turbulent quantities: mass flux velocity, Reynolds stress, turbulent kinetic energy, and density-specific volume correlation. Buoyancy effects are observed in these quantities and the trends are compared qualitatively with direct numerical simulations.     

Zero Expectile Processes and Bayesian Spatial Regression

We introduce new classes of stationary spatial processes with asymmetric, sub-Gaussian marginal distributions using the idea of expectiles. We derive theoretical properties of the proposed processes. Moreover, we use the proposed spatial processes to formulate a spatial regression model for point-referenced data where the spatially correlated errors have skewed marginal distribution. We introduce a Bayesian computational procedure for model fitting and inference for this class of spatial regression models. We compare the performance of the proposed method with the traditional Gaussian process-based spatial regression through simulation studies and by applying it to a dataset on air pollution in California.     

纳秒脉冲等离子体合成射流激励器的流场特性分析

采用一台高重频、快上升沿纳秒脉冲电源作为激励源,对典型的双电极合成射流激励器进行放电,通过粒子图像测速法（particle image velocimetry,PIV）测量放电实验中激励器稳定流场特性以及发展速度.分析实验结果发现,随着重复频率的提高,合成射流的平均发展速度也随之增大,1 kHz时的平均速度最高达到28.28 m/s,并在单脉冲能量远低于微秒脉冲的情况下,实现了更快的稳态流场控制,表明高重复频率下,更多次数的脉冲放电可提高激励总能量,有效地弥补纳秒脉冲单脉冲输出能量不足的缺点.而且频率越高,流场发展速度越快,说明高重频工作模式会对输出总能量有补偿作用.      

High-speed imaging of ultrasonic emulsification using a water-gallium system

Aiming at elucidating ultrasonic emulsification mechanisms, the interaction between a single or multiple acoustic cavitation bubbles and gallium droplet interface was investigated using an high-speed imaging technique. To our best knowledge, the moment of emulsification and formation of fine droplets during ultrasound irradiation were observed for the first time. It was found that the detachment of fine gallium droplets occurs from the water-gallium interface during collapse of big cavitation bubbles. The results suggest that the maximum size of cavitation bubble before collapsing is of prime importance for emulsification phenomena. Previous numerical simulation revealed that the collapse of big cavitation bubble is followed by generation of high-velocity liquid jet directed toward the water-gallium interface. Such a jet is assumed to be the prime cause of liquid emulsification. The distance between cavitation bubbles and water-gallium interface was found to slightly affect the emulsification onset. The droplet fragmentation conditions are also discussed in terms of the balance between (1) interfacial and kinetic energies and (2) dynamic and Laplace pressure during droplet formation.     

椭圆方程双侧障碍问题解的局部有界性

研究非齐次椭圆方程divA(x,u,■u)=f(x)的双侧障碍问题,获得了解的局部有界性结果,这可以认为是经典结果的推广.     

C imaging by double resonance scalar-coupling editing

The two-dimensional FT Imaging of ¹³C-glucose obtained with twin spin-echo double resonance sequence is presented. The images have been obtained by a doubly tuned surface coil on samples containing water and ¹³C-enriched glucose in water. It is shown, both theoretically and experimentally, that the whole editing capability of the twin spin-echo double resonance imaging sequence is also preserved in the presence of the radiofrequency field inhomogeneity produced by the surface coil. As in an efficient selective irradiation method, the enhancement in the signal-to-noise ratio with respect to the direct ¹³C detection, depends on the number of protons J-coupled to ¹³C.     

On a double degenerate fourth-order parabolic equation

The existence of solutions to a fourth-order p-Laplacian equation with boundary degeneracy is studied. For the purpose of solving the corresponding non-degenerate (with respect to the coefficient of fourth-order term) regularized problem, a fourth-order semi-discrete elliptic problem with homogeneous boundary conditions is established and its existence and uniqueness are obtained by the functional minimization method. It follows that the approximate solutions of the non-degenerate parabolic problem are constructed and the corresponding existence and uniqueness are discovered by a limit procedure from the energy estimation method and a compactness argument. Finally, the existence and regularity of solutions for the problem with boundary degeneracy is obtained by using a regularization parameter vanishing limit.     

Comparison Theorems for Four Dimensional Regular Matrices

A four dimensional summability matrix is stronger than convergence in the Pringsheim sense if it sums a divergent double sequence. Presented in this paper are sufficient conditions on a four dimensional matrix transformation which ensure that the summability matrix is stronger than convergence in the Pringsheim sense. Also other sufficient conditions will be presented to ensure the failure of inclusion between two summability matrices.AMS Subject Classification (2000): Primary 40B05.