Closed-form solutions for a rectangular layer with central crack under anti-plane shear stress

We consider the problem of determining the stress distributionin a finite rectangular elastic layer containing a Griffithcrack which is opened by internal shear stress acting alongthe length of the crack. The mode III crack is assumed to belocated in the middle plane of the rectangular layer. The followingtwo problems are considered: (A) the central crack is perpendicularto the two fixed lateral surfaces and parallel to the othertwo stress-free surfaces; (B) all the lateral surfaces of therectangular layer are clamped and the central crack is parallelto the two lateral surfaces. By using Fourier transformations,we reduce the solution of each problem to the solution of dualintegral equations with sine kernels and a weight function whichare solved exactly. Finally, we derive closed-form expressionsfor the stress intensity factor at the tip of the crack andthe numerical values for the stress intensity factor at theedges of the cracks are presented in the form of tables.     

Shear banding in strained semicrystalline polyamide 6 films as revealed by atomic force microscopy: Role of the amorphous phase

Atomic force microscopy (AFM) has been used to visualize the plastic deformation mechanisms that are responsible for the yielding of semicrystalline polymers of low degree of crystallinity (<50%). Indeed, AFM, if operated in suitable conditions, is able to image both the amorphous and the crystalline phases. Polyamide 6 films have been drawn at temperatures T < 160 °C. Postmortem AFM observations show that, at yield, shear bands nucleate and propagate in the amorphous phase. They cross the crystalline lamellae and run over the whole surface of the sample. By crossing the lamellae, they form nanoblocks of uniform size. Neither the size of the nanoblocks nor the angle between the tensile axis and the shear bands can be explained in terms of crystal plasticity. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 687–701, 2004     

逆（反）对策问题与“奇门遁甲”预测理论（术）

本文首先提出逆（反）对策这一新问题，给出了数学模型；探讨了“奇门遁甲”预测理论（术）中的数学问题；通过系统分析“专门遁甲”预测过程，可知它的预测过程隐含着一个特殊的逆（反）对策问题；最后指出逆（反）对策问题的广泛存在并给出案例分析．     

Separation of screw-sensed particles in a homogeneous shear field

The Stokes motions of three-dimensional screw-sensed slender particles in a homogeneous shear field are investigated, including the effects of buoyancy. Conclusions are drawn about the possibility of achieving a separation of mixtures of right- and left-handed particles. The linearity of the Stokes equations allows complex flows to be solved by adding the effects of the several terms which describe the flow in which the particle is immersed. The homogeneous shear flow considered here consists of three such terms; solutions for a series of 12 unit motions are sufficient to determine the hydrodynamic resistance tensors. The forces and torques experienced by screw-sensed particles are calculated from these 51 resistance tensors, using slender-filament theory. The results allow an estimate of the range of buoyancy parameters for which gravitational sedimentation can be neglected. The fundamental component of the particle motion is a rotation, at approximately the same angular velocity as that of the fluid. Superimposed on this are variations, of large period, in the particle orientation. A phase plane analysis is used to find the terminal orientations. Very long calculation times are required for the phase portrait. An approximate method based on azimuthally-averaged equations is developed to avoid the requirements for long time integration.     

Measurements and simulations of particle dispersion in a turbulent flow

A particle imaging technique has been used to collect droplet displacement statistics in a round turbulent jet of air. Droplets are injected on the jet axis, and a laser sheet and position-sensitive photomultiplier tube are used to track their radial displacement and time-of-flight. Dispersion statistics can be computed which are Lagrangian or Eulerian in nature. The experiments have been simulated numerically using a second-order closure scheme for the jet and a stochastic simulation for the particle trajectories. Results are presented for non-vaporizing droplets of sizes from 35 to 160 μm. The simulations have underscored the importance of initial conditions and early droplet displacement history on the droplet trajectory for droplets with large inertia relative to the turbulence. Estimates of initial conditions have been made and their effect on dispersion is quantified.     

A generalized Adadorov theory for anisotropic thin-walled beams

This paper presents a generalized Adadorov theory for anisotropic thin—walled beams. The theory takes account of the shear strain of the middle surface, which exerts a significant influence on the anisotropic thin-walled beams. A new approach is established to solve the governing equations, which have the same form for both open and closed section beams. The numerical examples show that the effects of the shear strain cannot be neglected for this class of beams.This work was part of research project supported by the National Natural Science Foundation of China     

Statistical approach to light scattering from deformed textured heterogeneous polymer materials

A statistical theory of light scattering from deformed isotropic and textured heterogeneous polymer materials is formulated. Two types of textured structures are analyzed: assemblies of optically isotropic and anisotropic rods and a spatially anisotropic distribution of isotropic spherical inclusion centers. The small-angle H_v light-scattering patterns are calculated. The appearance of scattering from isotropic rods and spheres in deformed materials has been demonstrated. The changes of the H_v scattering patterns as a function of elongation and strucuture parameters are discussed. © 1993 John Wiley & Sons, Inc.     

狭义相对论效应──运动时钟变慢的计算机模拟演示实验

利用精炼的C语言进行程序设计，定量模拟狭义相结论的运动时钟变慢，并对处于两种不同时空观的时钟运行进行对比，使得时间膨胀效应变得直观。     

STUDY ON THE DUCTILE DEFORMATION DOMAIN OF THE SIMPLE SHEAR IN ROCKS——TAKING BRITTLE FAULTS OF THE COVERING STRATA IN THE SOUTHERN JIANGSU AREA AS AN EXAMPLE

A study on the ductile deformation domain of the brittle fault in the shallow level ofthe crust is a new probe field for the modern structural geology. Taking the southern Jiang-su Province area as an example the orientation measurement of quartz crystals, the com-positional texture observation of three pressure sensitive minerals and the rheological param-eter determination of dislocation densities, etc. have been demonstrated and analysed basedon typical samples in the present paper. In addition, their generation mechanisms arealso discussed from the cataclastic rheology, the dynamic differentiation and the simpleshearing, specially, from the Ode strength theory. Finally, a generative relationship betweenthe ductile deformation domain of the brittle fault system, in the regional layer--slip andthe formation of the stratabound ore deposit is shown as well.     

THE PARAMETER KERNELS FOR THE LINEAR INVERSION OF THE FREE OSCILLATION OF THE EARTH (Ⅰ)

In the linear inversion of the radial variation of the parameters of the Earth by usingthe observed frequencies of various normal modes of free oscillation of the earth, it is neces-sary to know the values of the kernels of the parameters ρ, μ and λ. This paper describesthe methods of the derivation of the formulas of these kernels. This is the first part of thepaper in which only the toroidal oscillations are considered. They are much simpler thanthose of the spheroidal ones, that we will consider in the second part of the paper. The data of the two types of oscillations are equally important in the solution of theinversion problem, and should be employed simultaneously, and we know that the toroidaloscillations are much simpler than the spheroidal ones, it seems wise to divide the whole programof the inversion problem into steps: first, by employing the toroidal data to correct the twoparameters ρ and μ in the mantle, then by using the spheroidal data to correct the remain-ing parameters, i.e. th