Besov spaces and the multifractal hypothesis

Parisi and Frisch proposed some time ago an explanation for multiscaling of turbulent velocity structure functions in terms of a multifractal hypothesis, i.e., they conjecture that the velocity field has local Hölder exponents in a range [h _min,h _max], with exponents <h occurring on a setS(h) with a fractal dimensionD(h). Heuristic reasoning led them to an expression for the scaling exponentz _p ofpth order as the Legendre transform of the codimensiond-D(h). We show here that a part of the multifractal hypothesis is correct under even weaker assumptions: namely, if the velocity field hasL ^p -mean Hölder indexs, i.e., if it lies in the Besov spaceB _p ^s, , then local Hölder regularity is satisfied. Ifs<d/p, then the hypothesis is true in a generalized sense of Hölder space with negative exponents and we discuss the proper definition of local Hölder classes of negative index. Finally, if a certain box-counting dimension exists, then the Legendre transform of its codimension gives the scaling exponentz _p , and, more generally, the maximal Besov index of order,p, ass _p =z _p /p. Our method of proof is derived from a recent paper of S. Jaffard using compactly-supported, orthonormal wavelet bases and gives an extension of his results. We discuss implications of the theorems for ensemble-average scaling and fluid turbulence.     

Glass capillary gas chromatography of amino acid enantiomers

Glass capillaries coated with Chirasil-Val, a chirally functionalised polysiloxane, are capable in principle of resolving all protein amino-acid enantiomers in a single run and within a short analysis time, thus allowing for example the quantitative amino acid determination by enantiomer labelling. The elution characteristics of the individual amino acids however are also dependent upon the chemical nature of the capillary wall surface, and a surface pretreatment is found to be necessary if all protein amino acids are to be analysed. Of the various methods of pretreatment tested, etching of borosilicate glass with gaseous HCl followed by deposition of colloidal silicic acid is considered to be the most suitable.     

Influence of mechanical properties of pectin films on charge density and charge density distribution in pectin macromolecule

The hydration and mechanical properties of citrus pectin films were examined in conditions relevant to those in the plant cell wall. The pectins used for this study varied in the degree of esterification (DE) (high or low) and charge distribution on the backbone (random or block). The hydration of the films was controlled in an osmotic pressure experiment using polyethylene glycol solutions (PEG 20000). Hysteresis tests at constant deformation rate (stress vs deformation) were used for investigating the mechanical behaviour of films. Mechanical and hydration properties of pectin films were examined as a function of charge density, charge density distribution and counterion environment—K⁺, Ca²⁺, Mg²⁺. Swelling decreased with increasing counterion concentration. The effect is stronger in the case of Ca²⁺ and Mg²⁺ for low esterified pectins and therefore crosslinks from divalent ions could be assumed. The crosslink effect is confirmed in mechanical experiments where an increase in the film tensile modulus is observed with increasing counterion concentration. It is shown for the first time that in case of highly concentrated pectin solutions Mg²⁺ cations also act as a crosslinker for pectin macromolecules.     

MoS2纳米管包覆单壁碳纳米管束的制备

MoS₂ nanotube coated SWNT (Single wall carbon nanotube) bundles have been successfully prepared by adsorbing (NH₄)₂MoS₄ onto SWNT bundles and subsequent heat treatment under H₂ at 900 ℃ in a tube furnace. The morphologies, structure and composition of the as-prepared sample were investigated by XRD, SEM, HRTEM coupled with EDS. The formation mechanism has also been preliminarily discussed.     

Sensitive Voltammetric Response of p‐Nitroaniline on Single‐Wall Carbon Nanotube‐Ionic Liquid Gel Modified Glassy Carbon Electrodes

An ionic liquid (i.e., 1‐butyl‐3‐methylimidazolium hexafluorophosphate, BMIMPF₆)‐single‐walled carbon nanotube (SWNT) gel modified glassy carbon electrode (BMIMPF₆‐SWNT/GCE) is fabricated. At it the voltammetric behavior and determination of p‐nitroaniline (PNA) is explored. PNA can exhibit a sensitive cathodic peak at ?0.70 V (vs. SCE) in pH 7.0 phosphate buffer solution on the electrode, resulting from the irreversible reduction of PNA. Under the optimized conditions, the peak current is linear to PNA concentration over the range of 1.0×10^?8–7.0×10^?6 M, and the detection limit is 8.0×10^?9 M. The electrode can be regenerated by successive potential scan in a blank solution for about 5 times and exhibits good reproducibility. Meanwhile, the feasibility to determine other nitroaromatic compounds (NACs) with the modified electrode is also tested. It is found that the NACs studied (i.e., p‐nitroaniline, p‐nitrophenol, o‐nitrophenol, m‐nitrophenol, p‐nitrobenzoic acid, and nitrobenzene) can all cause sensitive cathodic peaks under the conditions, but their peak potentials and peak currents are different to some extent. Their peak currents and concentrations show linear relationships in concentration ranges with about 3 orders of magnitude. The detection limits are 8.0×10^?9 M for p‐nitroaniline, 2.0×10^?9 M for p‐nitrophenol, 5.0×10^?9 M for o‐nitrophenol, 5.0×10^?9 M for m‐nitrophenol, 2.0×10^?8 M for p‐nitrobenzoic acid and 8.0×10^?9 M for nitrobenzene respectively. The BMIMPF₆‐SWNT/GCE is applied to the determination of NACs in lake water.     

单壁碳纳米管的结构修饰

由于单壁碳纳米管具有独特的结构、电学及机械等性能，可望在许多新领域得 到应用，已引起广泛的关注。但由于单壁碳纳米管不溶于水和常见的有机溶剂，极 大地制约了其应用性能的研究。随着单壁碳纳米管制备技术的不断完善，其研究方 向已开始转向结构修饰及应用性能的研究。主要介绍近年来单壁碳纳米管结构修饰 方面的最新发展状况，重点讨论化学功能化及物理吸附。     

Preparation and Characterization of Three-dimensionally Ordered Crystalline Macroporous CeO2

Three-dimensional ordered macroporous (3DOM) materials are of great potential importance in catalysis, selective separation, sensor arrays and communications with optical band gaps1. Many results in the synthesis of 3DOM materials have been reported, such as closed-packed silica spheres or polystyrenes (PS) templating routes for silica2, metal oxides1-6 and metals7. Recently, poly(methyl methacrylate) (PMMA) colloidal crystal templates have been used to prepare 3DOM materials of metals8,…     

Modeling of plasma jets with superimposed vortex flow

This work is concerned with analytical studies of thermal plasma jets, which are finding increasing interest for thermal plasma processing. A two-dimensional model for turbulent plasma jets with superimposed vortex flow has been developed, incorporating multiple time scales for velocity and temperature fluctuations and a density-weighted averaging for the density fluctuation effect. Results show that adding swirl to the flow field for confined and free jets induces strong axial and radial pressure gradients near the nozzle exit, causing a rapid decay of the axial velocity with increasing distance from the nozzle. Comparisons with cold flow show similar trends close to the nozzle exit, but further downstream, the axial velocities increase again, especially for larges swirl numbers. Comparisons of theoretical predictions based on the present model with available experimental data are, in general, in reasonable agreement.     

The effect of a coriolis force on Taylor-Couette flow

Taylor-Couette flow subject to a Coriolis force is studied experimentally and numerically. In the experiment, the Couette apparatus is mounted on a turntable with the axis of the cylinders orthogonal to the rotation vector of the turntable. The Coriolis force stabilizes the fluid against the onset of Taylor vortices and alters the velocity fields, both above and below the transition from the initial flow. At small dimensionless turntable frequencies, the transition yields time-independent Taylor vortices which are tilted with respect to the cylinder axis. At larger there is a direct transition to turbulence. We determine the first-order correction to the classical Couette initial flow, to account for the effects of the Coriolis force, by expanding in powers of. We present numerical results for the axial velocity (the only nonvanishing correction term to order) in the infinite-cylinder approximation.     

Modelling of the pressure-velocity correlation in turbulence diffusion

Most current computations of trubulent flows with second-moment closure adopt the diffusion models which neglect the effect of pressure-velocity correlation. In the present paper the importance of this correlation effect is elucidated the neglect of this effect accounts for some major defects in the wide application of the second-moment closures. Through the relation between and , established by Lumley, we propose here a new turbulence diffusion model which takes into consideration the pressure effect. Applications of this new model in the computation of shearless turbulence mixing layer and plane and round-jet flows show that the spreading rate of these flows can be satisfactorily captured.