Inertia Effects in High-Rate Flow Through Heterogeneous Porous Media

The paper deals with the effects of large scale permeability–heterogeneity on flows at high velocities through porous media. The media is made of a large number of homogeneous blocks where the flow is assumed to be governed by the Forchheimer equation with a constant inertial coefficient. By assuming the validity of the Forchheimer equation at the large scale, an effective inertial coefficient is deduced from numerical simulations. Different media are investigated: serial-layers, parallel-layers and correlated media. The numerical results show that: (i) for the serial-layers, the effective inertial coefficient is independent of the Reynolds number and decreases when the variance and the mean permeability ratio increases; (ii) for the parallel-layers and the correlated media, the effective inertial coefficient is function of the Reynolds number and increases when the variance and the mean permeability ratio increases. Theoretical relationships are proposed for the inertial coefficient as function of the Reynolds number and the characteristics of the media.     

Effective Diffusion Coefficient: From Homogenization to Experiment

In this paper, an example of the application of the homogenization approach (asymptotic expansion technique) to predict the effective diffusion coefficient for an equivalent continuum, together with the experimental verification of the theoretical results is presented. The experimental setup was constructed for the measurements of diffusion in a model periodic porous medium made of Plexiglas. The computer program using the FEM was elaborated to solve the local boundary value problem for a period and to calculate the effective diffusion coefficient. The comparison between the theory and the experiment indicates good agreement between the numerical and experimental values of the effective diffusion coefficient. Interpretation of the test data from the point of view of the homogenization theory is also incorporated.     

CONSOLIDATION HEORY OF UNSATURATED SOIL BASED ON THE THEORY OF MIXTURE(Ⅰ)

Unsaturated soil is a three-phase media and is composed of soil grain, water and gas. In this paper, the consolidation problem of unsaturated soil is investigated based on the theory of mixture. A theoretical formula of effective stress on anisotropic porous media and unsaturated soil is derived. The principle of effective stress and the principle of Curie symmetry are taken as two fundamental constitutive principles of unsaturated soil. A mathematical model of consolidation of unsaturated soil is proposed, which consists of 25 partial differenfial equations with 25 unknowns. With the help of increament linearizing method, the model is reduced to 5 governing equations with 5 unknowns, i.e., the three displacement components of solid phase, the pore water pressure and the pore gas pressure. 7 material parameters are involved in the model and all of them can he measured using soil tests. It is convenient to use the model to engineering practice. The well known Biot’s theory is a special case of the model.     

多孔介质的流变模型研究

多孔介质在应力作用下具有弹性变形和黏性变形两种完全不同的变形机制，多孔介质的弹性变形是由介质的本体有效力所致，而黏性变表则是由介质的结构有效应力所致。多孔介质的总变形为弹性变形和黏性变形的叠加，计算多孔介质总应变量的流变模型必须同时采用本体有效应力和结构有效应力（双重有效应力），而传统的流变模型仅采用Terzaghi有效应力是不妥当的，它无法正确描述多孔的应变行为，采用了双重有效应力之后的流变模型，通过调节介质特性参数，可以拟合介质的实际应变行为，并且把多孔介质与普通固体联系了起来。     

Notes on Convection in a Porous Medium: (i) an Effctive Rayleigh Number for an Anisotropic Layer, (ii) the Malkus Hypothesis and Wavenumber Selection

Studies of convection in a layer of a saturated anisotropic porous medium uniformly heated from below are reviewed. Emphasis is placed on the usefulness of an effective Rayleigh number, defined (for certain boundary conditions) as the square harmonic-mean square root of horizontally-based and vertically-based Rayleigh numbers. The status of the Malkus hypothesis, together with its relationship with observed cell size, is also discussed. A possible explanation is provided for the observed phenomenon that in a porous medium the cell size decreases as the amplitude of convection increases, whereas in a clear fluid the cell size increases.     

The effective properties of piezocomposites, part II: The effective electroelastic moduli

Since piezoelectric ceramic/polymer composites have been widely used as smart materials and smart structures, it is more and more important to obtain the closed-from solutions of the effective properties of piezocomposites with piezoelectric ellipsoidal inclusions. Based on the closed-from solutions of the electroelastic Eshelby's tensors obtained in the part I of this paper and the generalized Budiansky's energy-equivalence framework, the closed-form general relations of effective electroelastic moduli of the piezocomposites with piezoelectric ellipsoidal inclusions are given. The relations can be applicable for several micromechanics models, such as the dilute solution and the Mori-Tanaka's method. The difference among the various models is shown to be the way in which the average strain and the average electric field of the inclusion phase are evaluated. Comparison between predicted and experimental results shows that the theoretical values in this paper agree quite well with the experimental results. These expression can be readily utilized in analysis and design of piezocomposites. The project supported by the National Natural Science Foundation of China     

基于多因素的焊接结构疲劳裂纹扩展速率分析

以Donahue等提出的疲劳裂纹扩展速率计算模型为基础,通过引入形状系数、张开比和残余应力等参数,建立了适用于焊接结构的疲劳裂纹扩展速率计算模型,分析了多种因素对焊接结构疲劳裂纹扩展速率的影响规律。结果表明,焊板厚度和焊缝余高的变化均会对焊接结构疲劳裂纹的扩展速率产生影响,在对焊接结构表面形状进行设计时应保有一定的焊缝余高;有效应力比的增大会降低焊接结构疲劳裂纹的扩展速率,且裂纹深度的变化不会改变有效应力比对焊接结构疲劳裂纹扩展速率的影响;残余应力的增大会提高焊接结构疲劳裂纹的扩展速率,且残余应力对疲劳裂纹扩展速率的促进作用随着裂纹深度的增加而增大,在对焊接结构的疲劳性能进行设计时须考虑残余应力对结构性能的影响。     

A Simple Framework of Conservative Algorithms for the Coupled Nonlinear Schrodinger Equations with Multiply Components

Considering the coupled nonlinear Schrodinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite difference method, Fourier pseudospectral method and wavelet collocation method for spatial discretizations, a series of high accurate conservative algorithms are presented. The proposed algorithms can preserve the corresponding discrete charge and energy conservation laws exactly, which would guarantee their numerical stabilities during long time computations. Furthermore, several analogous multi-symplectic algorithms are constructed as comparison. Numerical experiments for the unstable plane waves will show the advantages of the proposed algorithms over long time and verify the theoretical analysis.     

低串扰大模场面积多芯光纤的设计与优化

当前光通信网络正朝着大规模、大容量的方向迅速发展,传输带宽所面临的巨大增长压力对通信光纤提出了更高的要求。在此背景下,基于空分复用的多芯光纤充分利用了空间维度,可以有效解决传统单模光纤的理论传输容量极限导致的容量紧缩问题,而大容量传输系统要求多芯光纤具有低串扰大模场面积的光学特性。通过采用光束传输法和有限元法模拟仿真了多芯光纤中各结构参量对芯间串扰和有效模场面积的影响,并利用两种不同参数的多芯光纤进行了实验验证,对芯间距、纤芯/沟道的尺寸和折射率进行了优化,在理论上完成了串扰小于-45dB、模场面积大于130μm2多芯光纤的设计。     

Mechanical properties of the thermal equilibrium Friedmann–Robertson–Walker universe model

The mechanical property of the thermal-equilibrium Friedmann-Robertson-Walker （TEFRW） universe is first studied. The equation of state and the scale factor of the TEFRW universe take the forms ofw = w（a;zT） and a = a（a;zT,Ho）. For the universe consisting of the nonrelativistic matter and the dark energy, the behavior of the dark energy depends on the value of the present-day matter fraction. For the TEFRW universe consisting of N ingredients, the effective temperature is introduced. Lastly, a simple TEFRW universe model is analyzed.