Generalized rayleigh principle and its applications

In this paper, we mainly deal with cigenvalue problems of non-self-adjoint operator. To begin with, the generalized Rayleigh variational principle, the idea of which was due to Morse and Feshbach, is examined in detail and proved more strictly in mathematics. Then, other three equivalent formulations of it are presented. While applying them to approximate calculation we find the condition under which the above variational method can be identified as the same with Galerkin's one. After that we illustrate the generalized variational principle by considering the hydrodynamic stability of plane Poiseuille flow and Bénard convection. Finally, the Rayleigh quotient method is extended to the cases of non-self-adjoint matrix in order to determine its strong eigenvalne in linear algebra.

Failure process analysis of cement under explosive loading with a generalized driven nonlinear threshold model

The microstructural heterogeneity and stress fluctuation play important roles in the failure process of brittle materials. In this paper, a generalized driven nonlinear threshold model with stress fluctuation is presented to study the effects of microstructural heterogeneity on continuum damage evolution. As an illustration, the failure process of cement material under explosive loading is analyzed using the model. The result agrees well with the experimental one, which proves the efficiency of the model.

Numerical investigation of crack growth in concrete subjected to compression by the generalized beam lattice model

The beam lattice-type models, such as the Euler-Bernoulli (or Timoshenko) beam lattice and the generalized beam (GB) lattice, have been proved very effective in simulating failure processes in concrete and rock due to its simplicity and easy implementation. However, these existing lattice models only take into account tensile failures, so it may be not applicable to simulation of failure behaviors under compressive states. The main aim in this paper is to incorporate Mohr-Coulomb failure criterion, which is widely used in many kinds of materials, into the GB lattice procedure. The improved GB lattice procedure has the capability of modeling both element failures and contact/separation of cracked elements. The numerical examples show its effectiveness in simulating compressive failures. Furthermore, the influences of lateral confinement, friction angle, stiffness of loading platen, inclusion of aggregates on failure processes are respectively analyzed in detail.

On the contact width in generalized plain strain JKR model for isotropic solids

Adhesive contact model between an elastic cylinder and an elastic half space is studied in the present paper, in which an external pulling force is acted on the above cylinder with an arbitrary direction and the contact width is assumed to be asymmetric with respect to the structure. Solutions to the asymmetric model are obtained and the effect of the asymmetric contact width on the whole pulling process is mainly discussed. It is found that the smaller the absolute value of Dundurs' parameter beta or the larger the pulling angle theta, the more reasonable the symmetric model would be to approximate the asymmetric one.

Work and energy equations and the principle of generalized effective stress for unsaturated soils

The effective stress principle has been efficiently applied to saturated soils in the soil mechanics and geotechnical engineering practice; however, its applicability to unsaturated soils is still under debate. The appropriate selection of stress state variables is essential for the construction of constitutive models for unsaturated soils. Owing to the complexity of unsaturated soils, it is difficult to determine the deformation and strength behaviors of unsaturated soils uniquely with the previous single-effective-stress variable theory and two-effective-stress-variable theory in all the situations. In this paper, based on the porous media theory, the specific expression of work is proposed, and the effective stress of unsaturated soils conjugated with the displacement of the soil skeleton is further derived. In the derived work and energy balance equations, the energy dissipation in unsaturated soils is taken into account. According to the derived work and energy balance equations, all of the three generalized stresses and the conjugated strains have effects on the deformation of unsaturated soils. For considering these effects, a principle of generalized effective stress to describe the behaviors of unsaturated soils is proposed. The proposed principle of generalized effective stress may reduce to the previous effective stress theory of single-stress variable or the two-stress variables under certain conditions. This principle provides a helpful reference for the development of constitutive models for unsaturated soils.

Angular distributions of multiphoton detachment of H- in various infrared laser fields

Using a nonperturbative quantum scattering theory, the photoelectron angular distributions (PADs) from the multiphoton detachment of H- ions in strong, linearly polarized infrared laser fields are obtained to interpret recent experimental observations. In our theoretical treatment, the PADs in n-photon detachment are determined by the nth-order generalized phased Bessel (GPB) functions X-n(Z(f),eta). The advantage of using the GPB scenario to calculate PADs is its simplicity: a single special function (GPB) without any mixing coefficient can express PADs observed by recent experiments. Thus, the GPB scenario can be called a parameterless scenario.

The gated integration technique for the accurate measurement of the autocorrelation function of speckle intensities scattered from random phase screens

A new approach based on the gated integration technique is proposed for the accurate measurement of the autocorrelation function of speckle intensities scattered from a random phase screen. The Boxcar used for this technique in the acquisition of the speckle intensity data integrates the photoelectric signal during its sampling gate open, and it repeats the sampling by a preset number, in. The average analog of the in samplings output by the Boxcar enhances the signal-to-noise ratio by root m, because the repeated sampling and the average make the useful speckle signals stable, while the randomly varied photoelectric noise is suppressed by 1/ root m. In the experiment, we use an analog-to-digital converter module to synchronize all the actions such as the stepped movement of the phase screen, the repeated sampling, the readout of the averaged output of the Boxcar, etc. The experimental results show that speckle signals are better recovered from contaminated signals, and the autocorrelation function with the secondary maximum is obtained, indicating that the accuracy of the measurement of the autocorrelation function is greatly improved by the gated integration technique. (C) 2006 Elsevier Ltd. All rights reserved.

Optical interconnection for neural networks by use of a self-imaging function

A grating-lens combination unit is developed to form a scaling self-transform function that can self-image on scale. Then an array of many such grating-lens units is used for the optical interconnection of a two-dimensional neural network, and experiments are carried out. We find that our idea is feasible, the optical interconnection system is simple, and optical adjustment is easy. (C) 1998 Optical Society of America.

Computation of the ambiguity function for circularly symmetric pupils

A method of computing the ambiguity function (AF) for a circularly symmetric pupil function is presented. The AFs of a clear aperture and two shaded apertures are considered in detail and an explicit expression for the first of these AFs is given. We explain these results in the context of the well-known optical transfer function theory and show a primary application of these computations. A good analytic approximation is also introduced, providing an alternative method for calculating the AF, in a simpler way.

Analysis of optical systems with extended depth of field using the Wigner distribution function

We describe the use of a Wigner distribution function approach for exploring the problem of extending the depth of field in a hybrid imaging system. The Wigner distribution function, in connection with the phase-space curve that formulates a joint phase-space description of an optical field, is employed as a tool to display and characterize the evolving behavior of the amplitude point spread function as a wave propagating along the optical axis. It provides a comprehensive exhibition of the characteristics for the hybrid imaging system in extending the depth of field from both wave optics and geometrical optics. We use it to analyze several well-known optical designs in extending the depth of field from a new viewpoint. The relationships between this approach and the earlier ambiguity function approach are also briefly investigated. (c) 2006 Optical Society of America.

相干模表示的部分相干高斯谢尔光束的相位空间积

与传统的相干激光光束的评价不同, 对部分相干光束质量进行评价时, 不仅要反映其远场发散特性, 而且还要能体现光源本身的部分相干性。根据部分相干光的相干模表示法, 推导了由部分相干光源所产生光束的相位空间积Q。与前人在相干光源情形下得到的结论相比, 得出的相位空简积Q不仅包含各个全相干模基元线性组合的贡献, 而且还有来自不同的全相干模基元之间相互作用的贡献。