双相介质波动方程孔隙率反演的同伦方法

从材料响应的理论合成应与实际测量数据相拟合这一出发点，将双相介质波劝方程参数的反演问题转化为非线性算子方程的零点求解问题，从而应用一种大范围收敛的同伦方尘土注来解非线性算子方程，并把这种方法用于Simon(1984)给出的具有解析的一维双相介质模型的数值模拟，最后的数值结果表明，给出的算法是十分有效的。     

具有系统参数的非线性动力系统周期解方法

给出两种形式的微分方程周期求解方法,这两种方法对称处理奇异的非线性特征值问题有独特的能力,为具有系统参数的非线性动力系统在整个系统参数范围内的动态特性分析提供了有效的方法。     

基于微分算子变换的广义卡尔曼估计方法

本文发展了一类新的动力系统参数识别方法。通过引入微分算子变换，使系统状态变量与系统参数成功地分离开来。然后，以算子变换方程作为观测方程，并引入关于系统参数的状态方程；利用广义卡尔曼滤波方法进行参数递推估计。系统仿真算例表明：本文建议的新方法，不仅可以适用于较高噪声环境情形，而且可以同时适用于线性参数系统与非线性参数系统。     

有界不确定参数结构位移范围的区间摄动法

当结构参数具有误差或有界不确定性时,区间数学可以在不同知识不确定变量的概率分布的情况下定量地考察不确定参数对结构响应的影响。为计算出不确定结构参数对结构位移影响范围的上下界,文中提出了的两种区骚动国方法。     

Non-uniform heat generation effect on heat transfer of a non-Newtonian power-law fluid over a non-linearly stretching sheet

The effects of non-uniform heat generation/absorption and viscous dissipation on heat transfer of a non-Newtonian power-law fluid on a non-linearly stretching surface have been examined. The governing nonlinear partial differential equations describing the problem are transformed to a system of non-linear ordinary differential equations by using suitable similarity transformation. The transformed system of ordinary differential equations is solved numerically using fourth order Runge-Kutta method with the shooting technique. Graphical solutions for the dimensionless temperature are presented and discussed for various values of the power-law index parameter, the Prandtl number, the heat generation/absorption parameter and the Eckert number. The results show that the local Nusselt number is reduced with increasing the Eckert number or the heat generation parameter, whereas the heat absorption parameter has the effect of enhancing the local Nusselt number.     

Effect of Hall current on MHD natural convection flow from vertical permeable fiat plate with uniform surface heat flux

The effect of the Hall current on the magnetohydrodynamic (MHD) natural convection flow from a vertical permeable flat plate with a uniform heat flux is analyzed in the presence of a transverse magnetic field.It is assumed that the induced magnetic field is negligible compared with the imposed magnetic field.The boundary layer equations are reduced to a suitable form by employing the free variable formulation (FVF) and the stream function formulation (SFF).The parabolic equations obtained from FVF are numerically integrated with the help of a straightforward finite difference method.Moreover,the nonsimilar system of equations obtained from SFF is solved by using a local nonsimilarity method,for the whole range of the local transpiration parameter ζ.Consideration is also given to the regions where the local transpiration parameter ζis small or large enough.However,in these particular regions,solutions are acquired with the aid of a regular perturbation method.The effects of the magnetic field M and the Hall parameter m on the local skin friction coefficient and the local Nusselt number coefficient are graphically shown for smaller values of the Prandtl number Pr (=0.005,0.01,0.05).Furthermore,the velocity and temperature profiles are also drawn from various values of the local transpiration parameterζ.     

Rayleigh–Benard convection subject to time dependent wall temperature/gravity in a fluid-saturated anisotropic porous medium

 The effect of time-periodic temperature/gravity modulation at the onset of convection in a Boussinesq fluid-saturated anisotropic porous medium is investigated by making a linear stability analysis. Brinkman flow model with effective viscosity larger than the viscosity of the fluid is considered to give a more general theoretical result. The perturbation method is applied for computing the critical Rayleigh and wave numbers for small amplitude temperature/gravity modulation. The shift in the critical Rayleigh number is calculated as a function of frequency of the modulation, viscosity ratio, anisotropy parameter and porous parameter. We have shown that it is possible to advance or delay the onset of convection by time-periodic modulation of the wall temperature and to advance convection by gravity modulation. It is also shown that the small anisotropy parameter has a strong influence on the stability of the system. The effect of viscosity ratio, anisotropy parameter, the porous parameter and the Prandtl number is discussed. Received on 28 July 2000 / Published online: 29 November 2001     

Solving the problem of linear viscoelasticity for multiply connected anisotropic plates

This paper describes the method for solving the problems of linear viscoelasticity for thin plates under the influence of bending moments and transverse forces. The small parameter method was used to reduce the original problem to a sequence of boundary-value problems solved via complex potentials of the bending theory of multiply connected anisotropic plates. The general representations of complex potentials and boundary conditions for their determination are obtained. The method for determining the stress state of the plate at any time with respect to complex approximation potentials is developed by replacing the powers of the small parameter by the Rabotnov operators. The problem of a plate with elliptical holes is solved. The numerical calculation results in the case of a plate with one or two holes are given. The variation of bending moments in time until stationary condition is reached is studied, and the influence of geometric characteristics of the plate on these variable is described.     

Laminar boundary layer flow of a nanofluid along a wedge in the presence of suction/injection

The behavior of an incompressible laminar boundary layer flow over a wedge in a nanofluid with suction or injection has been investigated. The model used for the nanofluid integrates the effects of the Brownian motion and thermophoresis parameters. The governing partial differential equations of this problem, subjected to their boundary conditions, are solved by the Runge-Kutta-Gill technique with the shooting method for finding the skin friction and the rate of heat and mass transfer. The result are presented in the form of velocity, temperature, and volume fraction profiles for different values of the suction/injection parameter, Brownian motion parameter, thermophoresis parameter, pressure gradient parameter, Prandtl number, and Lewis number. The conclusion is drawn that these parameters significantly affect the temperature and volume fraction profiles, but their influence on the velocity profile is comparatively smaller.     

DTM-BF method and dual solutions for unsteady MHD flow over permeable shrinking sheet with velocity slip

An unsteady magnetohydrodynamic (MHD) boundary layer flow over a shrinking permeable sheet embedded in a moving viscous electrically conducting fluid is investigated both analytically and numerically. The velocity slip at the solid surface is taken into account in the boundary conditions. A novel analytical method named DTMBF is proposed and used to get the approximate analytical solutions to the nonlinear governing equation along with the boundary conditions at infinity. All analytical results are compared with those obtained by a numerical method. The comparison shows good agreement, which validates the accuracy of the DTM-BF method. Moreover, the existence ranges of the dual solutions and the unique solution for various parameters are obtained. The effects of the velocity slip parameter, the unsteadiness parameter, the magnetic parameter, the suction/injection parameter, and the velocity ratio parameter on the skin friction, the unique velocity, and the dual velocity profiles are explored, respectively.     

Effect of thermal conductivity on heat transfer for a power-law non-Newtonian fluid over a continuous stretched surface with various injection parameters

The two-dimensional non-Newtonian steady flow on a power-law stretched surface with suction or injection is studied. Thermal conductivity is assumed to vary as a linear function of temperature. The transformed governing equations in the present study are solved numerically using the Runge-Kutta method. Through a comparison, results for a special case of the problem show excellent agreement with those in a previous work. Two cases are considered, one corresponding to a cooled surface temperature and the other to a uniform surface temperature. Numerical results show that the thermal conductivity variation parameter, the injection parameter, and the power-law index have significant influences on the temperature profiles and the Nusselt number.     

应用并行PEST算法优化地下水模型参数

基于列文伯格-马夸尔特（Levenberg-Marquardt）算法的PEST参数优化程序具有寻优速度快、健壮性好的优点,在地下水模型参数优化研究中有许多成功的应用实例。但是,对于大尺度、高精度和高复杂性的大规模地下水模拟,使用PEST进行参数优化需要大量的计算时间,优化效率较低。本文应用OpenMP并行编程方法对PEST算法进行了并行化,使之可以在共享存储并行计算机上进行参数优化的并行计算。并将此方法应用于甘肃北山区域地下水模型的参数优化中,并行实验表明,使用并行化的PEST可以将地下水模型参数优化效率提高3.7倍。
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Tikhonovs regularization method for ill-posed problems

Frequently the determination of material characteristic functions, such as the molecular mass distribution of a polymeric sample or the relaxation spectrum of a viscoelastic fluid, leads to an ill-posed problem. When Tikhonov regularization is applied to such a problem the problem of an appropriate choice of the regularization parameter arises. Well-known methods to determine this parameter, such as the discrepancy principle, and a method based on the minimization of the predictive mean-square signal error are compared with a self-consistence method. Monte Carlo simulations have been carried out for the determination of the relaxation spectrum from small amplitude oscillatory shear flow data. The self-consistence method has proven to be much more robust and reliable.     

Proposition d'un paramètre énergétique de rupture pour les matériaux dissipatifs

We suggest an energetic fracture parameter for non elastic materials. This one is presented in a domain integral, and founded on the release rate of the total mechanical energy received by a notched solid, using a domain derivation method. This parameter is proposed for a large class of loading and materials described by internal variables. It is shown that this parameter is reduced to the Rice–Cherepanov integral when the material is either elastic or elastoplastic and submitted to proportional loading.     

Effect of Hall current on MHD natural convection flow from vertical permeable flat plate with uniform surface heat flux

The effect of the Hall current on the magnetohydrodynamic (MHD) natural convection flow from a vertical permeable flat plate with a uniform heat flux is analyzed in the presence of a transverse magnetic field. It is assumed that the induced magnetic field is negligible compared with the imposed magnetic field. The boundary layer equations are reduced to a suitable form by employing the free variable formulation (FVF) and the stream function formulation (SFF). The parabolic equations obtained from FVF are numerically integrated with the help of a straightforward finite difference method. Moreover, the nonsimilar system of equations obtained from SFF is solved by using a local nonsimilarity method, for the whole range of the local transpiration parameter ζ. Consideration is also given to the regions where the local transpiration parameter ζ is small or large enough. However, in these particular regions, solutions are acquired with the aid of a regular perturbation method. The effects of the magnetic field M and the Hall parameter m on the local skin friction coefficient and the local Nusselt number coefficient are graphically shown for smaller values of the Prandtl number Pr (= 0.005, 0.01, 0.05). Furthermore, the velocity and temperature profiles are also drawn from various values of the local transpiration parameter ζ.     

3D Casson nanofluid flow over slendering surface in a suspension of gyrotactic microorganisms with Cattaneo-Christov heat flux

A mathematical model is proposed to execute the features of the non-uniform heat source or sink in the chemically reacting magnetohydrodynamic (MHD) Casson fluid across a slendering sheet in the presence of microorganisms and Cattaneo-Christov heat flux. Multiple slips (diffusion, thermal, and momentum slips) are applied in the modeling of the heat and mass transport processes. The Runge-Kutta based shooting method is used to find the solutions. Numerical simulation is carried out for various values of the physical constraints when the Casson index parameter is positive, negative, or infinite with the aid of plots. The coefficients of the skin factors, the local Nusselt number, and the Sherwood number are estimated for different parameters, and discussed for engineering interest. It is found that the gyrotactic microorganisms are greatly encouraged when the dimensionless parameters increase, especially when the Casson fluid parameter is negative. It is worth mentioning that the velocity profiles when the Casson fluid parameter is positive are higher than those when the Casson fluid parameter is negative or infinite, whereas the temperature and concentration fields show exactly opposite phenomena.     

Thermoelastic stresses in a cylinder or disk with cubic anisotropy

The thermoelastic stresses in a crystal in the shape of a circular cylinder or disk are considered. The crystal is a cubically-orthotropic linear elastic solid, with three independent elastic properties. The cubic anisotropy renders the problem asymmetric, despite the axisymmetry of the geometry and thermal loading. This problem is motivated by a thermoelastic model used for certain crystal growth processes. Two simplifying assumptions are made here: (a) the problem is two-dimensional with plane strain or plain stress conditions, and (b) the elastic properties do not depend on the temperature. A new Fourier-type perturbation method is devised and an analytic asymptotic solution of a closed form is obtained, based on the weak cubic anisotropy of the crystal as a perturbation parameter. A general solution technique is described which yields the asymptotic solution up to a desired order. Numerical results are presented for typical parameter values.     

Computational modeling of heat transfer over an unsteady stretching surface embedded in a porous medium

The present paper deals with the study of heat transfer characteristics in the laminar boundary layer flow of an incompressible viscous fluid over an unsteady stretching sheet which is placed in a porous medium in the presence of viscous dissipation and internal absorption or generation. Similarity transformations are used to convert the governing time dependent nonlinear boundary layer equations into a system of non-linear ordinary differential equations containing Prandtl number, Eckert number, heat source/sink parameter, porous parameter and unsteadiness parameter with appropriate boundary conditions. These equations are solved numerically by applying shooting method using Runge-Kutta-Fehlberg method. Comparison of numerical results is made with the earlier published results under limiting cases. The effects of the parameters which determine the velocity and temperature fields are discussed in detail.     

Solution of boundary layer flow and heat transfer of an electrically conducting micropolar fluid in a non-Darcian porous medium

In this paper, we have studied the effects of radiation on the boundary layer flow and heat transfer of an electrically conducting micropolar fluid over a continuously moving stretching surface embedded in a non-Darcian porous medium with a uniform magnetic field has been analyzed analytically. The governing fundamental equations are approximated by a system of nonlinear locally similar ordinary differential equations which are solved analytically by applying homotopy analysis method (HAM). The effects of Darcy number, heat generation parameter and inertia coefficient parameter are determined on the flow. Convergence of the obtained series solution is discussed. The homotopy analysis method provides us with a new way to obtain series solutions of such problems. This method contains the auxiliary parameter which provides us with a simple way to adjust and control the convergence region of series solution. By suitable choice of the auxiliary parameter, we can obtain reasonable solutions for large modulus.     

含模糊参数的随机振动

本文在抗震结构模糊随机振动的研究基础上,进一步研究含模糊参数的随机振动分析方法,为了较好地描述具有模糊性的随机干扰,首先在Zadeh定义的模糊变量的基础上,定义了含模糊参数的随机变量和含模糊参数的随机过程,并讨论了它们的概率分布和数字特征;然后将模糊随机干扰模拟为含模糊参数的随机过程,提出了在这种模糊随机干扰下振动体系的模糊随机反应分析的基本方法和数值方法;最后对于抗震结构的模糊随机振动给出了具体的分析和算例