Vibration of an infinite inhomogeneous transversely isotropic viscoelastic medium with cylindrical hole

This paper investigates the influences of higher order viscoelasticity and the inhomogeneities of the transversely isotropic elastic parameters on the disturbances in an infinite medium, caused by the presence of a transient radial force or twist on the surface of a cylindrical hole with circular cross section. Following Voigt＇s model for higher order viscoelasticity, the nonvanishing stress components valid for a transversely isotropic and higher order viscoelastic solid medium have been deduced in terms of radial displacement component. Considering the power law variation of elastic and viscoelastic parameters, the stress equation of motion has been developed. Solving this equation under suitable boundary conditions, due to transient forces and twists, radial displacement and relevant stress components have been determined in terms of modified Bessel functions. The problem for the presence of transient radial force has been numerically analysed. Modulations of displacement and stresses due to different order of viscoelasticity and inhomogeneity have been graphically depicted. The numerical study of the disturbance caused by the presence of twist on the surface may be similarly done but is not pursued in this paper.     

湍流基础问题研究进展:能量传递,相互作用尺度,各向同性衰减的自保持性

为了更深入地了解湍流的物理过程,本文综述了各向同性湍流的基础问题．在评述了Ｋｏｌｍｏｇｏｒｏｖ能谱及能量级串过程后,深入讨论了Ｋｏｌｍｏｇｏｒｏｖ局部各向同性假设．接着综述了涉及能量传递的以及包括三元组相互作用的各向同性湍流相互作用尺度的详细物理过程．还讨论了惯性区、自相似性以及小尺度对大尺度各向异性的响应和末期衰减过程．之后为了举例说明这些论点,详细讨论了根据各向同性湍流直接模拟及大涡模拟得到的结果（包括对亚格子模型的讨论）.最后,综述了各向同性湍流的自保持性,并展望了今后的研究方向．文末列出了１５５篇参考文献     

满旗流形SO(8)=T上不变爱因斯坦度量

本文研究了迷向表示分为12个不可约子空间的满旗流形SO(8)=T上不变爱因斯坦度量的问题.利用计算机计算满旗流形SO(8)=T爱因斯坦方程组的方法, 得到了满旗流形SO(8)=T上有160 个不变爱因斯坦度量(up to a scale)的结果, 在等距情况下考虑这160个不变爱因斯坦度量, 其中1个是凯莱爱因斯坦度量, 4 个是非凯莱爱因斯坦度量. 推广了只对迷向表示分为小于等于6个不可约子空间的满旗流形上不变爱因斯坦度量的研究.     

光频三维各向同性左手超材料结构单元模型的仿真设计

基于树枝结构单元思想,提出了光频三维各向同性左手超材料球刺结构单元模型.采用金属的Drude原理,运用等效媒质理论,仿真研究了结构的电磁响应特性.在晶格间距与工作波长的比值满足等效媒质理论要求的前提下,通过调节结构单元的几何参数,发现它能在光波段出现介电常数和磁导率同时为负值的区域,实现折射率小于零的左手超材料响应特性.该模型结构简单,具有各向同性特点.研究结果为采用"由下向上"方法制备光波段的三维左手超材料指出了新的途径. 关键词： 球刺模型 光波段 三维 各向同性     

各向异性的红外背景预测方法

为了减少红外图像中起伏背景对弱小目标检测的影响,提出一种各向异性的红外背景预测方法。根据红外图像目标区域和平稳背景区域、起伏背景区域的局部梯度特性的差异,引入各向异性微分的思想,并将其边缘停止函数改进为方向梯度值的递增函数,然后用边缘停止函数最小两个方向值的均值作为背景预测值,实现了对不同方向特性背景区域的差异化预测。仿真实验表明,该算法选择性地保留了红外图像的平稳背景和起伏背景区域,达到了良好的背景预测效果。     

Very large‐scale computation of very small‐scale motions in a fully developed pipe flow

Local isotropy theory is examined using direct numerical simulation in a fully developed pipe flow at two Reynolds numbers Re_τ=1285.6 and 684.8. The approach to local isotropy is assessed with reference to the two Kolmogorov classical equations for longitudinal and transverse velocity structure functions. The results for the second‐order longitudinal structure functions in both the dissipative and inertial ranges indicate an improved agreement with the local isotropy hypothesis as the centreline is approached. However, the transverse structure functions satisfy isotropy neither in the dissipative range or in the inertial range. The distribution of the longitudinal and transverse structure functions also shows a substantial Reynolds number dependance in the logarithmic region of the flow and beyond. The results for the third‐order longitudinal structure function demonstrate an increased Reynolds number influence, and a deteriorating tendency to local isotropy for large separations. Contour images of axial velocity differences in the dissipative and inertial ranges have exhibited interesting patterns in relation to those of the instantaneous axial velocity. Finally, the results obtained in this investigation are in very good agreement with other published experimental and numerical data on channel and duct flows. Copyright © 2010 John Wiley & Sons, Ltd.     

四边简支各向同性矩形厚板的插值矩阵法解

针对强厚度矩形板四边简支情况,论文根据状态变量法思想,基于三维弹性理论基本方程,以3个位移分量及3个应力分量按双三角级数展开,将三维弹性力学控制方程转化为常微分方程边值问题.尽管一些各向异性弹性矩形厚板早已由状态空间法获得分析解,可是各向同性厚板的分析解至今难以获得,因为状态空间解法中特征方程有重根问题而不易于收敛.论文提出采用插值矩阵法直接对常微分方程进行求解,获得各向同性矩形厚板在四边简支边界条件下三维理论的位移和应力解,并与有限元精细结果进行比较,证明了本文解的准确性.     

Isomorphisms Between Groups of Homeomorphisms

We give simple conditions which ensure that the topological structure of a manifold is completely determined by a group of homeomorphisms. The reasonings are still valid in the smooth category.     

Characterization of Convex Isotropic Functions

Necessary and sufficient conditions are given for the convexity of a scalar valued function of tensors that is proper isotropic, or invariant under rotations. These conditions are also appropriate for functions defined only for orientation preserving tensors. They are weaker than Ball's convexity conditions for fully isotropic functions (invariant under all orthogonal tensors) [B1]. The results are applied in obtaining polyconvexity conditions for the stored energy function. This revised version was published online in August 2006 with corrections to the Cover Date.     

Mass transport theory for the Toda lattices, dispersive and dissipative

To establish mass transport theory on nonlinear lattices, we formulate the Korteweg–deVries (KdV) equation and the Burgers equation using the flow variable representation so as to facilitate comparison with the Boltzmann equation and with the Cahn–Hilliard equation in classical statistical mechanics. We also study Toda lattice microdynamics using the Flaschka representation, and compare with the Liouville equation. Like the linear diffusion equation, the Boltzmann equation and the Liouville equation are to be solved for a distribution function, which is intrinsically probabilistic. Transport theory in linear systems is governed by the isotropic motions of the kinetic equations. In contrast, the KdV perturbation equation derived from the Toda lattice microdynamics expresses hydrodynamic mass transport. The KdV equation in hydrodynamics and the Burgers equation in thermodynamics do not involve a probability distribution function. The nonlinear lattices do not retain isotropy of the mass transport equations. In consequence, it is proposed that in the presence of hydrodynamic flows to the left, KdV wave propagation proceeds to the right. This basic property of the KdV system is extended to thermodynamics in the Burgers system. These features arise because linear systems are driven towards an equilibrium by molecular collisions, whereas the inhomogeneities of the nonlinear lattices are generated by the potential energy of interaction. Diffusion as expressed by the Burgers equation is governed not only by a chemical potential, but also by the Toda lattice potential energy.