Modeling plane turbulent Couette flow

Among the salient features of shear-driven plane Couette flow is the constancy of the total shear stress (viscous and turbulent) across the flow. This constancy gives rise to a quasi-homogenous core region, which makes the bulk of the flow substantially different from pressure-driven Poiseuille flow. The present second-moment closure study addresses the conflicting hypotheses relating to turbulent Couette flow. The inclusion of a new wall-proximity function in the wall-reflection part of the pressure-strain model seems mandatory, and the greement with recent experimental and direct numerical simulation (DNS) results is encouraging. Analysis of model computations in the range 750 ≤ Re ≤ 35,000 and comparisons with low-Re DNS data suggest that plane Couette flow exhibits a local-equilibrium core region, in which anisotropic, homogeneous turbulence prevails. However, the associated variation of the mean velocity in the core, as obtained by the model, conflicts with the intuitively appealing assumption of homogeneous mean shear. The constancy of the velocity gradient exhibited by the DNS therefore signals a deficiency in the modeled transport equation for the energy dissipation rate.     

Towards understanding the increase in strength of thermotropic polyesters with heat treatment

Thermotropic copolyester fibers of oxynaphthoate and oxybenzoate have been subjected to conditions that promote solid-state polymerization as well as annealing. The annealing process causes the crystals to perfect with a simultaneous increase in heat of fusion and melting temperature. Solid-state polymerization, a reaction rate-controlled process, causes the polymer viscosity average molecular weight to increase by chain extension from about 14,000 g/mole to more than 87,000 g/mole with a simultaneous impressive increase in tenacity from about 10 g/d (1.2 GPa) to almost 30 g/d (3.7 GPa). To understand the changes in mechanical properties, we have modeled the fiber structure as short rod-like molecules poorly bonded to a continuous matrix of parallel molecules. Lengthening of the reinforcing molecules facilitates better transfer of load from matrix to molecules, resulting in higher tenacity fibers. © 1994 John Wiley & Sons, Inc.     

Manganese(II) complexes with diethylamine in aqueous solutions

Interaction between MnCl₂ and diethylamine (DEA) in aqueous solutions has been studied by UV, IR, and EPR spectroscopy as part of the design and research program on models of natural photosystems. The composition of the precipitate for comparable concentrations of reagents and solute oxygen has been investigated. Mn(II) was found to be oxidized with oxygen to give MnO₂·H₂O as a precipitate. In the solution over the precipitate, Mn(III) complexes with DEA are formed; the complex molecule has four and six amine molecules in the coordination sphere.     

Deactivation reactions in the modeled 2,2,6,6‐tetramethyl‐1‐piperidinyloxy‐mediated free‐radical polymerization of styrene: A comparative study with the 2,2,6,6‐tetramethyl‐1‐piperidinyloxy/acrylonitrile system

The competitiveness of the combination and disproportionation reactions between a 1‐phenylpropyl radical, standing for a growing polystyryl macroradical, and a 2,2,6,6‐tetramethyl‐1‐piperidinyloxy (TEMPO) radical in the nitroxide‐mediated free‐radical polymerization of styrene was quantitatively evaluated by the study of the transition geometry and the potential energy profiles for the competing reactions with the use of quantum‐mechanical calculations at the density functional theory (DFT) UB3‐LYP/6‐311+G(3df, 2p)//(unrestricted) Austin Model 1 level of theory. The search for transition geometries resulted in six and two transition structures for the radical combination and disproportionation reactions, respectively. The former transition structures, mainly differing in the out‐of‐plane angle of the N? O bond in the transition structure TEMPO molecule, were correlated with the activation energy, which was determined to be in the range of 8.4–19.4 kcal mol^?1 from a single‐point calculation at the DFT UB3‐LYP/6‐311+G(3df, 2p)//unrestricted Austin Model 1 level. The calculated activation energy for the disproportionation reaction was less favorable by a value of more than 30 kcal mol^?1 in comparison with that for the combination reaction. The approximate barrier difference for the TEMPO addition and disproportionation reaction was slightly smaller for the styrene polymerization system than for the acrylonitrile polymerization system, thus indicating that a β‐proton abstraction through a TEMPO radical from the polymer backbone could diminish control over the radical polymerization of styrene with the nitroxide even more than in the latter system. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 232–241, 2007     

Implementation and experimental study on fast object modeling based on multiple structured stripes

In this paper, a practical structured light-based system for fast object modeling and reconstruction is reported. The system consists of an off-the-shelf digital projector, a video camera and a turntable. The system calibration is implemented accurately and automatically by taking a single image of an illuminated calibration template. The multiple color light stripes emitted by the projector adopt only three colors and the color can be modified easily according to the surface texture of the object. This makes the system widely applicable in many situations, and the assumption about color neutrality, which is a limitation to other similar systems, can be largely relaxed. The registration and merging algorithm is greatly simplified by employing a turntable. The validity and high accuracy of the method are demonstrated by extensive real experiments.     

Material-Adapted Design of Textile-Reinforced Composite Structures with Optimized Vibro-Acoustic and Damping Properties Including Shear Effects

Advanced analytical models have been developed at the ILK, which offer a possibility of calculating the vibro-acoustic and damping behavior of textile-reinforced composite shells and plates with account of shear effects. The simulation models elaborated have been verified on selected examples, and the analytical results were fully corroborated by accompanying numerical calculations for typical lay-ups.__________Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 3, pp. 289–302, May–June, 2005.     

数学建模与素质教育

面对二十一世纪知识经济的挑战 ,我国高等教育模式应由应试教育 ,专业教育向素质教育转变 ,培养学生自主意识 ,效率意识 ,竞争意识 ,创新意识和民主意识 ,即高校教育应重视大学生的创新能力、实践能力和创业精神 ,普遍提高大学生的人文素质和科学素质 .本文拟就提高大学生素质的有效层面 ,对开展数学建模教学与实践进行深入分析 ,以窥探数学建模与素质教育之关系 .在深入把握数学建模教学与实践内涵的同时 ,分析得出这种以不打扰现行正常秩序的教育是提高大学生素质的有效途径之一     

紧急输送策略的线性规划模型

以美国南弗洛里达州递避飓风袭击为例建立了紧急输送情况下的线性规划模型。其中具体建立了以SCEPD(美国南弗洛里达州紧急情况预防部门)提出的公路反向，地区分块撤离，使用小路等三个最受人们关注的策略的模型。模型的灵敏度分析能很好地解释建立更多的临时避难所、限制车辆等策略对撤离的影响。在相近的环境下，中模型解得的结果很接近官方预测的结果，并且本的模型能对更广泛的情况进行分析．可给SCEPD提供一定参考。     

优化灰导数白化值的无偏灰色GM(1,1)模型

通过优化灰导数白化值 ,建立了无偏的 GM(1,1)模型 ,给出了估计模型参数的方法 ,证明了无偏GM(1,1)模型具有白指数律重合性 ,提出了新的预测公式 .实例分析表明 ,新方法提高了模型的精度 ,扩大了模型的适用范围 .     

Simplified and complex modeling of self-sustained discharge-pumped,Ne-buffered XeCl laser kinetics

Two simple kinetic models of a Ne-buffered XeCl laser discharge are presented based on different simplifications of the chemical kinetics of a complex model that recently appeared in the literature. When applied to the study of a small-volume XeCl laser, the results of both simple and complex models are in satisfactory agreement with the experiments. Shifting to a larger-volume laser, both models show problems due to loss of stability of the discharge. A one-dimensional modelling is performed, and it is found that different assumptions on the kinetics of the NeXe⁺ ion in the discharge lead to completely different results as regards the effect of a preionization-triggered instability.