Melt rheology of polylactide/montmorillonite nanocomposites

In this article, the linear and nonlinear shear rheological behaviors of polylactide (PLA)/clay (organophilic‐montmorillonite) nanocomposites (PLACNs) were investigated by an Advanced Rheology Expanded System rheometer. The nanocomposites were prepared by master batch method using a twin‐screw extruder with poly(ε‐caprolactone) (PCL) as a compatibilizer. The presence of org‐MMT leads to obvious pseudo‐solid‐like behaviors of nanocomposite melts. The behaviors caused by the formation of a “percolating network” derived from the reciprocity among the strong related sheet particles. Therefore, the storage moduli, loss moduli, and dynamic viscosities of PLACNs show a monotonic increase with MMT content. Nonterminal behaviors exists in PLACNs nanocomposites. Besides the PLACNs melts show a greater shear thinning tendency than pure PLA melt because of the preferential orientation of the MMT layers. Therefore, PLACNs have higher moduli but better processibility compared with pure PLA. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 3189–3196, 2007     

2,3,4,5,6‐Penta­nitro­aniline 1,2‐dichloro­ethane disolvate: `push–pull' deformation of aromatic rings by intra­molecular charge transfer

The title compound, C₆H₂N₆O₁₀·2C₂H₄Cl₂, forms layered stacks of penta­nitro­aniline mol­ecules, which possess twofold symmetry. The voids between these stacks are occupied by dichloro­ethane mol­ecules, which reside near a 2/m symmetry element and display pseudo‐inversion symmetry. The C atoms in one of the two solvent mol­ecules are threefold disordered. In the penta­nitro­aniline mol­ecule, considerable distortion of the benzenoid ring, coupled with the short C—N(H₂) bond and out‐of‐plane NO₂ twistings, point to significant intra­molecular `push–pull' charge transfer at the amino‐ and nitro‐substituted (ortho and para) positions, as theoretically quantified by natural bond orbital analysis of the π‐electron density.     

Numerical analysis of the rotating viscous flow approaching a solid sphere

A numerical simulation is performed to investigate the flow induced by a sphere moving along the axis of a rotating cylindrical container filled with the viscous fluid. Three‐dimensional incompressible Navier–Stokes equations are solved using a finite element method. The objective of this study is to examine the feature of waves generated by the Coriolis force at moderate Rossby numbers and that to what extent the Taylor–Proudman theorem is valid for the viscous rotating flow at small Rossby number and large Reynolds number. Calculations have been undertaken at the Rossby numbers (R_o) of 1 and 0.02 and the Reynolds numbers (R_e) of 200 and 500. When R_o=O(1), inertia waves are exhibited in the rotating flow past a sphere. The effects of the Reynolds number and the ratio of the radius of the sphere and that of the rotating cylinder on the flow structure are examined. When R_o ? 1, as predicted by the Taylor–Proudman theorem for inviscid flow, the so‐called ‘Taylor column’ is also generated in the viscous fluid flow after an evolutionary course of vortical flow structures. The initial evolution and final formation of the ‘Taylor column’ are exhibited. According to the present calculation, it has been verified that major theoretical statement about the rotating flow of the inviscid fluid may still approximately predict the rotating flow structure of the viscous fluid in a certain regime of the Reynolds number. Copyright © 2004 John Wiley & Sons, Ltd.     

n维氢原子的散射态

研究了n维氢原子的散射态性质．给出了精确的按“k/2π标度”归一化的散射态的精确解波函数及相移表达式，讨论了相移的解析性质，获得了束缚-连续跃迁矩阵元的解析计算公式．普通氢原子(n=3)散射态的有关结果作为特例包含在本文的一般结论之中． 关键词： n维氢原子 散射态 精确解 相移 束缚-连续跃迁矩阵元     

Optical investigation of cavitation erosion by laser-induced bubble collapse

By means of a new force sensor based on optical beam deflection (OBD), the mechanical effects of laser-matter interaction underwater at different incident laser energy are investigated in detail. The experimental results show that a target underwater is impacted in turn by laser-plasma ablation force and high-speed liquid-jet impulse induced by bubbles collapse in the vicinity of a solid boundary. Furthermore, the amplitudes of the two forces increase monotonously with laser energy. According to the ablation force detected by the experiment and the theoretical relationship between laser intensity and ablation pressure, the value of liquid-jet impact against a solid boundary can be easily obtained. In addition, based on the model of a collapsing bubble, some characteristic parameters, such as the liquid-jet impact velocity, the maximum bubble radius, the bubble energy can also be obtained at different laser energy, which are valuable in the corresponding research fields.     

<Emphasis Type="Italic">L</Emphasis><Subscript>1</Subscript> linear interpolator for missing values in time series

We propose a minimum mean absolute error linear interpolator (MMAELI), based on theL ₁ approach. A linear functional of the observed time series due to non-normal innovations is derived. The solution equation for the coefficients of this linear functional is established in terms of the innovation series. It is found that information implied in the innovation series is useful for the interpolation of missing values. The MMAELIs of the AR(1) model with innovations following mixed normal andt distributions are studied in detail. The MMAELI also approximates the minimum mean squared error linear interpolator (MMSELI) well in mean squared error but outperforms the MMSELI in mean absolute error. An application to a real series is presented. Extensions to the general ARMA model and other time series models are discussed. This research was supported by a CityU Research Grant and Natural Science Foundation of China.     

求解非对称线性方程组的QMRGCGS方法

1 引言 求解非对称线性方程组Ax=b的双共轭梯度方法(BCG)[3]和它的变形共轭梯度平方方法(CGS)[6]都有典型的不规则收敛行为,后来Freund和Nachtigal提出一种BCG类方法,即拟极小剩余方法(QMR)[7],用来补救BCG方法的收敛性并且产生了光滑的收敛曲线。然而,象BCG方法一样,QMR方法要用到系数矩阵A及其转置A~T与向量的乘积,为了解决这一问题,Freund提出TFQMR方法,此方法具有拟极小剩余性,同时不需用到A~T与向量的乘积。     

Endpoint estimates for certain commutators of fractional and singular integrals

In this paper, the authors obtain the endpoint estimates for a class of non-standard commutators with higher order remainders and their variants. Moreover, the authors show that these operators are actually not bounded in certain cases.

     

Preparation of nanometer MgO by sol-gel auto-combustion

Nanometer MgO was prepared via a sol-gel auto-combustion technique using magnesium nitrate as raw material and citric acid as chelating agent. IR spectra of the dried gel were used to investigate the structure of the precursors. By studying the different TG curves of magnesium citrate gel prepared by different methods, we found that a combustion process occurred and the nitrate ions acted as an oxidant in the combustion process. TEM photographs of synthesized powders from the sol-gel auto-combustion showed that the crystallites were uniform in size. In addition, the XRD pattern of this sample showed that the particle size was 8.9 nm. The BET curves, in turn, showed that the specific surface of the sample was 26.34 m²/g. The mechanism of the frothing process in restraining agglomeration is discussed. __________ Translated from Journal of East China Normal University (Natural Science), 2007, (2): 52–57 [译自: 华东师范大学学报(自然科学版)]