Dimensions of attractors for discretizations for Navier-Stokes equations

In this paper, we discretize the 2-D incompressible Navier-Stokes equations with the periodic boundary condition by the finite difference method. We prove that with a shift for discretization, the global solutions exist. After proving some discrete Sobolev inequalities in the sense of finite differences, we prove the existence of the global attractors of the discretized system, and we estimate the upper bounds for the Hausdorff and the fractal dimensions of the attractors. These bounds are indepent of the mesh sizes and are considerably close to those of the continuous version.     

Classical limits for the coefficient of variation for the normal distribution

The exact classical limits for the coefficient of variation c for the normal distribution are derived. The hand-calculating approximated classical limits for c having high accuracy are given to meet practical engineering needs. Using Odeh and Owen's computational method and Brent's algorithm, the tables for the r-upper exact classical limits of coefficient of variation for normal distribution are calculated for the different confidence coefficient , the sample size n=1 (1)30,40,60,120, the sample coefficient of variation =0.01(0.01)0.20. It is shown that if n8, 0.20, then the -upper exact classical limits c_u for c are slightly higher than the exact fiducial limits c_u,F for c. if n>8, 0.20, then c_u–c_u,F<5×10^–6.     

Existence of weak solution for quantum Zakharov equations for plasmas model

Zakharov equations have a fairly abundant physical background. In this paper, the existence of the weak global solution for quantum Zakharov equations for the plasmas model is obtained by means of the Arzela-Ascoli theorem, Faedo-Galerkin methods, and compactness property.     

Sufficient conditions for strong ellipticity for a class of anisotropic materials

We provide sufficient conditions for strong ellipticity for a general class of anisotropic hyperelastic materials. This general class includes as a subclass transversely isotropic materials. Our sufficient conditions require that the first partial derivatives of the reduced-stored energy function satisfy some simple inequalities and that the second partial derivatives satisfy a convexity condition. We also characterize a restricted type of strong ellipticity for a subclass of transversely isotropic materials undergoing pure homogeneous deformations. We apply our results to a model of soft tissue from the biomechanics literature.     

系统参数标定以及惯性元件安装误差测量与补偿技术研究

研究了旋转式光纤陀螺捷联惯性导航系统的标定问题。首先分析了系统的安装误差，并建立了陀螺仪、加速度计的输入输出模型，最后给出了相应的标定方法，并给出了具体的实验和数据处理方法。理论分析及实验表明，该方法能够有效地标定出系统的相关参数。     

Existence of solutions for periodic boundary value problems for second-order integro-differential equations

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Methods for obtaining sufficient conditions for the stability of autonomous conservative systems

A computational method for obtaining sufficient conditions for the stability of the stationary solution of autonomous conservative systems is proposed in the paper. This method is adapted to linear autonomous gyroscopic systems with three degrees of freedom. It is based on the positive definiteness of a parametric quadratic form composed of the gyroscopic force matrices and the potential function. The control parameters for the stability of the zero solution of the gyroscopic system are the entries of the gyroscopic force matrix. The algorithm of the computational method includes estimating one gyroscopic force parameter in the equation constructed from a necessary stability condition.A special example is used to demonstrate the application of this algorithm. Comparison is performed with some well-known methods for obtaining sufficient conditions on the basis of an incomplete set of first integrals of motion. It is shown that the positive definiteness of the modified potential energy may result in stable as well as unstable motions.     

Study of Iterative Algorithms for Solution of Dynamic Contact Problems for Elastic Cracked Bodies

A plane problem is solved for the contact interaction between the faces of a rectilinear crack under the action of a normally incident harmonic tension–compression wave. Iterative algorithms are presented to solve the problem for both given initial distribution of contact forces and given initial discontinuity in the displacements of the crack faces. The convergence rates of the algorithms, the maximum contact forces, and displacement discontinuities are compared.     

Error Bounds for Approximate Solutions for Bending of Unsymmetrically Laminated Plates

Abstract

Certain types of heterogeneous plates exhibit coupling between membrane and flexural effects in their constitutive relations. Such a situation commonly occurs in unsymmetrically laminated plates and in reinforced concrete slabs after cracking. Approximate solutions, principally the “reduced bending stiffness” approximation, have been proposed in the past. The accuracy of this approximation has been examined for several specific cases, but no general investigations have been reported. This paper presents a method for determining bounds on the relative mean square error of approximate solutions to general coupled plate bending problems.     

Method for verification of the self-consistency of experimental data for free turbulent flows of an incompressible liquid

A direct method is proposed for verification of the quality of the method of measurements of the characteristics of free self-similar turbulent flows (the longitudinal mean velocity and the components of the tensor of the turbulent stresses), consisting in the direct substitution of experimentally obtained distributions of the longitudinal mean velocity and the turbulent stresses into the Reynolds equations. Using the proposed method, a lack of consistency is observed in the experimental data for the self-similar sections of plane [1] and axisymmetric [2] jets in a flooded space.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 161–164, November–December, 1978.The authors thank V. L. Zimont for his useful evaluation of the results of the work and for his advice, which were used in preparing this article for publication.     

Conditions for the existence of a complete set of real modes for a damping vibration system

In this paper, a general damping system is transformed into an equivalent undamped system according to the transformation of general coordinates for a matrix function. The necessary and sufficient conditions for the transformability are presented, which become, after supplementing another condition as suggested, the conditions for decoupling the damping matrix of a general damping vibration system. So the Caughey's condition is insufficient for determining if a damping matrix of a general system can be decoupled.     

Some Exact Conditions for the Solvability of the Initial-Value Problem for Systems of Linear Functional-Differential Equations

We obtain exact, in a sense, conditions sufficient for the unique solvability of the Cauchy problem for systems of linear functional-differential equations of the general form. Efficient criteria for the unique solvability of the initial-value problem for systems of equations with deviating argument are given.__________Translated from Neliniini Kolyvannya, Vol. 7, No. 4, pp. 538–554, October–December, 2004.     

Nonlinear models for the adoption and diffusion of innovations for industrial energy conservation

Four different theoretical models for explaining the diffusion of innovation were compared for 13 energy-related innovations--the Theory of Planned Behavior, the S-curve for Diffusion of Innovations, the power law distribution, and the cusp catastrophe. The substantive concern was to explore the roles of facilitative and obstructive factors in diffusing industrial and commercial innovations. Participants were 102 industrial plant and facilities managers from sites that were among the top users of electrical energy and natural gas in the United States. They completed a survey that contained measurements of positive attitudes toward innovation, organizational resistance to innovation, and the extent to which they had investigated or adopted each of the target innovations. Seven of the 13 innovations exhibited strong cusp catastrophe models (via nonlinear regression, average R2 = .91) compared to linear alternative models (average R2 = .31) for those innovations; the S-curve for diffusion was regarded as a simplified version of the cusp. One innovation was characterized best by a power law distribution (R2 = .94), and the remaining five were characterized best by a linear model that was based on the Theory of Planned Behavior (R2 = .41). Different underlying dynamics for the various innovations were implied by these results.     

Examination of the computational model for the layer-removal method for residual-stress measurement

An analytical solution is presented to examine the accuracy of the ‘layer-removal’ method for measuring localized residual stresses. In this approach, strips, which may have been cut from a pipe or a plate, have strain-gage rosettes placed on one face and layers removed from the other face. The strain measurements are used to deduce the residual stress in the layers removed. The stress measured is that along the axis of the strip. It may vary rapidly with axial distance, as for example when the strip is taken from a welded part. The present analysis shows that the actual stress distribution may be quite different from that predicted by the computational model normally used in the layer-removal method. It shows that the difference increases as the ratio of the heighth of the strip from which a layer is removed to the half dimensiona of the localized residual-stress zone increases. It is recommended that the layer-removal method can be used for measuring residual stresses for cases in which the ratio ofh/a is less than or equal to unity.     

Model B-I for macro rectangular element and problems of influence surface for plate structures

Model B-I for marco rectangular element is presented for the first time in this paper. To establish the influence surface for resultant R of bending plates, a number of generalized distributive loads q are defined. It is shown by numerical examples that Model B-I and the formula for the generalized distributive loads advanced in this paper are featured by high accuracy, low memory space and flexibility in practical application, and that they are especially effective for plate structures subject to moving loads, such as the two-dimensional continuous plates of highway bridges and the flat stabs in piled jetty engineering.     

试油测试射孔管柱的间隙元分析

建立了管柱接触非线性问题的间隙元法。用此方法对试油测试射孔管柱的受力状态进行了分析，并通过现场应用实例证明了此方法的可靠性和准确性。根据此方法开发的应用软件可为井下管柱的结构设计提供理论依据。     

A procedure for the design of nozzles used for the production of turbulent liquid jets

Where turbulent liquid jets are used for cutting and mining purposes the pressure generated by impact must be maximized. Initial jet behaviour has an important influence on subsequent jet impact pressures at medium range. Nozzle wall boundary layer history has a strong influence on the initial jet, and certain boundary layer features can be linked to poor jet performance. The procedure outlined in this paper was developed to eliminate new nozzle designs or changes in operating conditions on the grounds of badly behaved nozzle boundary flow. The design procedure consists of a potential flow analysis and a boundary layer analysis coupled to empirical correlations for boundary layers in accelerated flows. The procedure is exemplified by application to the design of a nozzle to be used for the specific purpose of mining china clay.     

波动方程数值模拟的一种显式方法——-界面节点公式的构建

针对成层介质中标量波动的数值模拟, 基于波速有限原理和波动方程柯西问题的解, 导出了界面点在一个短时间窗内的精确解, 由此给出了具有高阶精度的界面节点显式递推公式的一种构建方法, 并以构造弹性杆界面节点的递推公式为例说明其要点. 给出了与已有内节点递推公式的精度阶匹配的二阶和四阶界面节点递推公式. 由此构成的计算格式具有``异质格式'编程简便的特性, 更合理地考虑了界面影响. 最后, 通过数值试验检验这一匹配方案的精度和稳定性.      

Prediction of sinkage for wetland vehicles

A kind of rheometer is developed by the authors, with which the rheological parameters for paddy soils can be measured in situ. The optimum area of the measuring disk for this apparatus, which is about 38.5 cm², is determined according to the principle of fuzzy analysis on experimental results, and the effect of impact load is found by experiments.Tests are made with this apparatus for cracked and tyre-wheeled wetland vehicles moving in paddy fields. The predicted and measured sinkages for both vehicles are compared. The results show that for the tracked vehicle, there is not much difference between the predicted and measured sinkages, while for the wheeled vehicle, the predicted sinkages are less than the measured ones, perhaps due to the fact that the slip of the wheel is greater than that of the track, and the sinkage due to slip is quite significant.