Generation of Nonlinear Evolution Equations by Reductions of the Self-Dual Yang–Mills Equations

With the help of some reductions of the self-dual Yang Mills （briefly written as sdYM） equations, we introduce a Lax pair whose compatibility condition leads to a set of （2 ＋ 1）-dimensional equations. Its first reduction gives rise to a generalized variable-coefficient Burgers equation with a forced term. Furthermore, the Burgers equation again reduces to a forced Burgers equation with constant coefficients, the standard Burgers equation, the heat equation, the Fisher equation, and the Huxley equation, respectively. The second reduction generates a few new （2 ＋ 1）-dimensional nonlinear integrable systems, in particular, obtains a kind of （2 ＋ 1）-dimensional integrable couplings of a new （2 ＋ 1）- dimensional integrable nonlinear equation.     

von Neumann群代数

设G是带左正则表示λ的一个离散群, VN（G）是λ（g）生成的von Neumann群代数。我们刻画了von Neu-mann群代数上的Hardy空间。     

考虑湍流模型的板片空间结构风荷载下流固耦合模拟

大跨空间结构凭借其新颖的外形和较大的内部空间,已经成为常用的建筑结构.由于大跨结构刚度、质量较小,受到风荷载作用时力学响应较一般结构大,同时大跨结构附近极易出现湍流影响.本文基于显式大涡模拟(ILES)和S-A (Spalart-Allmaras)湍流模型,使用ABAQUS软件对矢跨比为1:2的空间板片结构在不同风速下的风压系数进行流固耦合(FSI)模拟.风速以及不同湍流模型对大跨板片风压系数分布的影响得到了考察,并与相关的风洞实验比较.同时对板片结构受风载的力学响应进行了分析.结果显示选用大涡模拟湍流模型和雷诺时均方程方法湍流模型的流固耦合板片空间结构模型得到的风压系数及其分布和风洞试验实测数据吻合均较好.     

Embedding copper nanoparticle-anchored conductive nano-blocks in polyelectrolyte

Conductive carbon nanotubes （CNTs） or alternatively polyaniline （PANI） nano-blocks was introduced into aqueous solutions of polyvinyl alcohol （PVA） and copper （II） salt, to assist the reduction of copper （II） ions and the anchoring of the resulting copper nanoparticles onto the conductive blocks. The mixture solutions of nano-blocks, copper （lI） salts and PVA were spin-coated onto the cathode surface, forming swollen cathode films （SCFs）. The copper （II） ions in the film assembled onto the surfaces of the conductive blocks and were then reduced under an appropriate voltage. It is important that the copper nanoparticles grew only on the surfaces of the conductive blocks. PVA which acted as the matrix of the composites played a role in stabilizing the resulting copper nanoparticles. Morphologies of these polymeric composite films were studied by various characterization methods. Moreover, the mechanism of migration of copper （II） ions, the formation of these polymeric composites, and the overall procedure were investigated in detail.     

Optimization of highly nonlinear dispersion-flattened photonic crystal fiber for supercontinuum generation

A simple type of photonic crystal fiber (PCF) for supercontinuum generation is proposed for the first time. The proposed PCF is composed of a solid silica core and a cladding with square lattice uniform elliptical air holes, which offers not only a large nonlinear coefficient but also a high birefringence and low leakage losses. The PCF with nonlinear coefficient as large as 46 W 1 · km-1 at the wavelength of 1.55 μm and a total dispersion as low as ±2.5 ps · nm-1 · km-1 over an ultra-broad waveband range of the S-C-L band (wavelength from 1.46 μm to 1.625 μm) is optimized by adjusting its structure parameter, such as the lattice constant Λ , the air-filling fraction f , and the air-hole ellipticity η. The novel PCF with ultra-flattened dispersion, highly nonlinear coefficient, and nearly zero negative dispersion slope will offer a possibility of efficient super-continuum generation in telecommunication windows using a few ps pulses.     

梯度变化对密度梯度蜂窝材料力学性能的影响

为确定一定质量蜂窝材料的密度梯度大小对材料能量吸收性能的影响,基于二维圆环系,通过改 变圆环的壁厚,建立了具有不同密度梯度的二维密度梯度圆环蜂窝材料模型。在此基础上讨论了不同冲击速 度下,密度梯度大小对蜂窝材料能量吸收特性的影响。研究结果表明,对于相对密度从冲击端到固定端递减 的情况,在高速冲击条件下,梯度系数越大,材料单位质量的能量吸收率越高。研究结果可为完善密度梯度 蜂窝材料动力学性能的设计提供参考。     

改进的Park-Ang再生混凝土柱地震破坏模型的试验研究

通过对不同配比的6根再生混凝土(RAC)柱进行低周反复加载试验。由于现有普通混凝土结构地震破坏损伤模型均为基于普通混凝土结构所构建的,是否适用于RAC结构的地震损伤破坏计算仍不明确;为能够有效考虑RAC中再生骨料取代率及混杂纤维掺量等因素所造成的普通混凝土结构地震破坏损伤模型中循环荷载系数β的不确定性及其对损伤指数计算结果的影响,同时提高计算模型的预见性与可靠性,本文提出了一种适用于RAC结构的改进的双参数损伤模型。通过模型的计算结果与实际结构各震害破损度D_c的对比,确定了适用于RAC结构的双参数损伤模型中循环荷载系数β的值。     

无网格法在三维复杂超音速流场模拟中的应用研究

对最小二乘无网格方法在含复杂外形三维超音速流场中的应用进行了研究.选用分解法求解采用最小二乘法得到的对称方程组,针对最小二乘无网格方法的计算特点生成近似正交均匀分布的离散点,对B1AC2R常规导弹超音速流场采用最小二乘无网格方法进行了无粘数值模拟,计算了B1AC2R常规导弹在不同攻角下的轴向力、法向力及俯仰力矩系数,并将数值结果与实验结果进行了比较.结果表明,最小二乘无网格方法在求解含复杂外形超音速流场时具有较高的准确度,将其应用于三维含复杂外形超音速流场的模拟是完全可行的.     

Describing spatiotemporal couplings in ultrashort pulses using coupling coefficients

Three coupling coefficients are defined to describe spatiotemporal coupling in ultrashort pulses. With these coupling coefficients, the first-order spatiotemporal couplings of Gaussian pulse and beam are described analytically. Also, the first-order and the second-order spatiotemporal couplings caused by angular dispersion elements are studied using these coupling coefficients. It can be shown that these coupling coefficients are dimensionless and normalized, and readily indicate the severity of spatiotemporal coupling.     

坐标图对试题难度的影响及启示

2011年高考试题中有较多的以“坐标图”呈现信息的试题,试题着重考查学生的图形转换能力。信息呈现方式的变化,在多大程度上引起试题难度的变化,这种相关性的研究就显得及时和非常必要,并且能够对教学有所帮助和启发。学生信息采集能力和转换能力的培养问题业已摆在教育者的面前,由于存在不同的教育观念,于是就有着不同的取舍和迥异的教育行动。