Probabilistically induced domain decomposition methods for elliptic boundary-value problems

Monte Carlo as well as quasi-Monte Carlo methods are used to generate only few interfacial values in two-dimensional domains where boundary-value elliptic problems are formulated. This allows for a domain decomposition of the domain. A continuous approximation of the solution is obtained interpolating on such interfaces, and then used as boundary data to split the original problem into fully decoupled subproblems. The numerical treatment can then be continued, implementing any deterministic algorithm on each subdomain. Both, Monte Carlo (or quasi-Monte Carlo) simulations and the domain decomposition strategy allow for exploiting parallel architectures. Scalability and natural fault tolerance are peculiarities of the present algorithm. Examples concern Helmholtz and Poisson equations, whose probabilistic treatment presents additional complications with respect to the case of homogeneous elliptic problems without any potential term and source.     

Stress Inhomogeneity in Powder Specimens Tested in the Jenike Shear Cell: Myth or Fact?

In the mechanical characterization of powders using the direct shear testers such as the Jenike shear cell, the existence of a uniform or well‐defined stress field in a powder specimen is assumed. This assumption has not been subjected to any serious scrutiny in the literature. In this study, the normal stress variation in a silica powder was locally determined by locating a pressure‐sensitive TekScan pad at the bottom section of a Jenike shear cell. A computer simulation of the consolidation and pre‐shearing stages of the Jenike test procedure was performed using the Discrete Element Method (DEM). The paper presents both experimental and computational evidence for the existence of a complex stress field in the powder specimen, thus clearly invalidating the long‐standing stress homogeneity assumption in the direct shear testing of powders. The implications of the stress inhomogeneity in terms of the accuracy of the material properties extracted from the Jenike test are also presented.     

Synthesis of new amphiphilic and lypophilic polymer networks containing 2‐methyl‐ and 2‐nonyl‐2‐oxazoline by the macroinitiator method

New amphiphilic and lypophilic polymer networks were obtained by the copolymerization of 2‐methyl‐2‐oxazoline (MeOXA), and/or 2‐nonyl‐2‐oxazoline (NoOXA) and 2,2′‐tetramethylenebis(2‐oxazoline) (BisOXA), respectively, initiating the copolymerization by random copolymers of chloromethylstyrene and methyl methacrylate or of chloromethylstyrene and styrene (macroinitiator method). Potassium iodide was used as an activator agent and the reaction was carried out in benzonitrile at 110 °C. In general, the polymer gels were obtained with a yield of 62 to 88%. The networks were characterized by high‐resolution magic angle spinning (HRMAS) NMR spectroscopy and by its absorption of polar and nonpolar solvents. In the case of amphiphilic polymer networks, the absorption of solvents depends on the molar ratio of 2‐methyl‐ to 2‐nonyl‐2‐oxazoline inside the polymer network favoring the absorption of polar solvents with a higher content of 2‐methyl‐2‐oxazoline. These gels showed a maximal swelling degree of 13 mL of water, 20 mL of methanol, and 13 mL of chloroform, respectively, per g of polymer. The lypophilic polymer networks containing only 2‐nonyl‐2‐oxazoline showed a maximal swelling degree of 8 mL of toluene, 14 mL of chloroform, and 2 mL of methanol, respectively, per g of the lypophilic network. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 122–128, 2005     

Polyisophthalamides with heteroaromatic pendent rings: Synthesis,physical properties,and water uptake

A set of novel aromatic polyamides containing pyridine pendent groups was prepared from aromatic diamines and new monomers that are 5‐substituted derivatives of isophthalic acid bearing nicotinamide, isonicotinamide, or picolinamide groups. The polymers were obtained in high yield and high molecular weight by the phosphorylation method of polycondensation. They were characterized by spectroscopic and chromatographic methods and several of their properties were investigated. All of the polymers were soluble in polar aprotic solvents and gave films of good mechanical properties. Glass transition temperatures were higher than that of the reference polymer, poly(m‐phenyleneisophthalamide) (IP‐MPD), while the thermal resistance, defined by the initial decomposition temperature observed by thermogravimetry, was in the range 370–420 °C, lower by 30–70 °C than that of IP‐MPD. The presence of a pendent pyridine group and an additional amide side group per repeat unit made the polymers essentially amorphous and greatly improved their abilities to absorb water in comparison with nonsubstituted polyamides. Water uptake values up to 15% were observed at 65% relative humidity. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 5300–5311, 2005     

四元Heisenberg群上次拉普拉斯算子的m幂次的基本解

本文研究了四元Heisenberg群上次拉普拉斯算子的m幂次的基本解，该结论是Heisenberg群上结果的推广.本文利用了四元Heisenberg群上的Fourier变换理论构造了该群上次拉普拉斯算子的m幂次的基本解，并且给出了基本解的积分表示.     

Correlation analysis of chaotic trajectories from Chua’s system

Chaotic systems exhibit an erratic behavior reflected by a strong divergence of trajectories with arbitrarily close initial condition. In this way, similar to trajectories from pseudorandom number generators, chaotic trajectories can be seen as noise with some degree of correlation. This work focuses on the study of some correlation properties (i.e., scaling) of chaotic trajectories from the Chua’s system. This is done by using detrended fluctuation analysis, which is a method designed for the detection of correlations in stochastic time series. It is found that, in general, Chua’s trajectories behave as a Brownian motion for small time scales, while they can display a white noise-like behavior or be dominated by harmonic oscillations for large time scales.     

Kinetics and mechanism of the chromic oxidation of 3-O-methyl-d-glucopyranose

The oxidation of 3-O-methyl-d-glucopyranose (Glc3Me) by Cr^VI in acid medium yields Cr^III, formic acid and 2-O-methyl-d-arabinose as final products when a 50-times or higher excess of Glc3Me over Cr^VI is used. The redox reaction takes place through the combination of Cr^VI → Cr^IV → Cr^II and Cr^VI → Cr^IV → Cr^III pathways. Intermediacy of free radicals and Cr^II in the reaction was demonstrated by the observation of induced polymerization of acrylamide and detection of CrO₂²⁺ formed by reaction of Cr^II with O₂. Intermediate oxo-Cr^V–Glc3Me species were detected by EPR spectroscopy. In 0.3–0.5 mol/L HClO₄, intermediate Cr^V rapidly decompose to the reaction products, while, at pH 5.5–7.5, where the redox processes are very slow, five-coordinate Cr^V bis-chelates of the pyranose and furanose forms of Glc3Me remain more than 15 h in solution. The C1–C2 bond cleavage of Glc3Me upon reaction with Cr^VI distinguishes this derivative from glucose, which is oxidized to gluconic acid.     

Modelling the effects of emergent vegetation on an open‐channel flow using a lattice model

A two‐dimensional lattice model has been developed to describe the influence of vegetation on the turbulent flow structure in an open channel. The model includes the influence of vegetation density on the frictional effect of the channel bed and walls. For the walls, a semi‐slip boundary condition has been considered as an alternative to overcome the no‐slip boundary condition limitations in turbulent flows. The drag stress exerted by the flow on the vegetation as well as the gravity effect has also been taken into account. The proposed lattice model has been used to simulate the experimental results reported from the study of the influence of alternate vegetated zones on the open‐channel flow. The results show that the lattice model approach is a valid tool for describing these kinds of flows. Copyright © 2007 John Wiley & Sons, Ltd.     

顶端受集中力偶的双材料平面界面接合楔体的对数奇异应力场

应用复变函数方法,通过构造复函数形式的特解序列,从理论上研究了顶端受集中力偶的双材料平面界面接合楔体的应力场,给出了相应的经典解,发现其存在一次和二次佯谬,相应的应力具有(Inr)／r2和(In2r)／r2的奇异性。