幂律型浆液扩散压力环向分布模型

为研究幂律型浆液注浆时注浆压力的变化情况,考虑盾尾断面新注入浆液与已注入浆液间阻碍作用,假设壁后注浆时盾尾形成三维环形空隙,提出了幂律型浆液扩散压力环向分布模型,并利用流体力学理论推导了幂律型浆液扩散压力环向分布式,分析了公式适用范围以及各参数的实际意义。与实际工程数据对比,验证了模型和计算式的正确性。结果表明,计算式可以反映注浆时环向分布各个位置压力值的大小;当公式中稠度系数n=1时,该式即为牛顿流体计算式,环向压力扩散模型同样适用,且幂律型流体环向扩散压力小于牛顿流体;受浆液自重影响,注浆孔注浆时向上表现为减压,向下表现为加压;压力环向分布断面呈现出上窄下宽的不规则环形;同一注浆孔幂律型浆液水灰比越大,浆液扩散压力越小。     

非规则区域中拉普拉斯方程的有限分析5点格式

建立了非规则区域的有限分析5点格式,增加了有限分析法对不规则边界的适应性。应用所提出的方法对水利工程中常见的有压和无压流动进行了计算,与实验和前人的计算结果相比较,本文的方法都能得到较为满意的结果。本文的计算格式也可以应用到其他非规则区域的计算中。     

不同形状混合器中二元颗粒的分聚与混合研究

采用实验、模拟及理论的分析方法, 研究了在圆形混合器、椭圆形混合器、正方形混合器中, 不同转速和填充率条件下, 容器形状对二元颗粒体系分聚与混合的影响. 实验中通过改变转速与填充率, 可获得不同的颗粒分聚与混合图样, 对示踪颗粒运动轨迹的分析发现, 在圆形混合器中, 随着混合器转速的增大, 颗粒在径向的随机性减少;在正方形混合器中, 随着混合器转速的增大, 颗粒在径向的随机性增大.模拟结果发现颗粒流动分为两个区域, 在表面的快速流动和在整体的旋转运动. 通过理论分析发现颗粒分聚在圆形混合器中最明显, 在正方形混合器中最弱, 椭圆形混合器介于二者之间.      

Helical coil buckling mechanism for a stiff nanowire on an elastomeric substrate

When a stiff nanowire is deposited on a compliant soft substrate, it may buckle into a helical coil form when the system is compressed. Using theoretical and finite element method (FEM) analyses, the detailed three-dimensional coil buckling mechanism for a silicon nanowire (SiNW) on a polydimethylsiloxane (PDMS) substrate is studied. A continuum mechanics approach based on the minimization of the strain energy in the SiNW and elastomeric substrate is developed. Due to the helical buckling, the bending strain in SiNW is significantly reduced and the maximum local strain is almost uniformly distributed along SiNW. Based on the theoretical model, the energy landscape for different buckling modes of SiNW on PDMS substrate is given, which shows that both the in-plane and out-of-plane buckling modes have the local minimum potential energy, whereas the helical buckling model has the global minimum potential energy. Furthermore, the helical buckling spacing and amplitudes are deduced, taking into account the influences of the elastic properties and dimensions of SiNWs. These features are verified by systematic FEM simulations and parallel experiments. As the effective compressive strain in elastomeric substrate increases, the buckling profile evolves from a vertical ellipse to a lateral ellipse, and then approaches to a circle when the effective compressive strain is larger than 30%. The study may shed useful insights on the design and optimization of high-performance stretchable electronics and 3D complex nano-structures.     

纵向剪切三相共焦点椭圆模型的精确解及其应用

推广夹杂问题的三相同心圆模型,提出了三相共焦点椭圆模型,从而计及了夹杂形状变化的重要因素。利用保角变换结合罗朗级数展开技术获得了纵向剪切载荷下的封闭形式解。本模型和解答对夹杂、界面层附近的细观应力场分析、对复合材料和含缺陷材料的有效弹性模量预测有重要实用价值,获得了比经典公式更精确的结果。对特殊模型,可以得到许多有意义的问题（如二相模型）的解答。     

Diffusion of biostimulators into plant tissues

Biostimulators are substances able to enhance the immune system of cultivated crops and support plant metabolism. Their utilization helps to reduce the amount of chemicals used in agriculture. To perform the desired effect, a biostimulator must be able to penetrate into the plant tissue. The time of penetration however, is limited, since the biostimulator must remain in a liquid state. This is of great importance—especially in field conditions, where the treated plants are exposed to different weather condition and other extrinsic factors. A mathematical model based on diffusion mechanisms has been elaborated to describe the biostimulator transport process from penetration of the leaves into the plant’s inner tissues. By means of the effective diffusion coefficient of the prepared specific protein hydrolyzate, this model can be used to estimate the time necessary for the uptake of the minimal active amount of the biostimulator.     

Pressure Drop for Low Reynolds-Number Flows Through Regular and Random Screens

Creeping flow through both regular and irregular screens was simulated by the lattice-Boltzmann method, and the dependence on screen porosity and Reynolds number of the pressure drop across the screen was analyzed. Regular structures were planar arrays of straight fibers or woven one-layer structures. The irregular planar structures were composed of randomly located and oriented fibers of finite length. A simple function of screen porosity based on partly numerical scaling arguments was found to describe accurately the simulated pressure drop across all regular screens. Due to their bigger surface area, the flow resistance of woven screens was found to be about 15% larger than that of regular planar screens with the same porosity. The pressure drop across irregular planar screens was found to be described by the same screen-porosity function with a slightly different ‘scaling’ exponent which thus appears to be dependent on the structure of the screen. The flow resistance of irregular structures was found to be clearly smaller than that of regular structures because of channelling of the flow through very few largest pores.     

具有大量椭圆随机分布区域的数值模拟及应用

利用椭圆的参数方程,首先给出平面上的点位于椭圆内部与外部的判别条件,再把计算点到椭圆距离问题,化为一个求最值问题,使得可以用搜索法较快地得到有效的近似解,从而得到一个新的产生具有大量椭圆随机分布区域的方法,基本思想是：（1） 对于模拟区域内随机生成的点,先判断该点是否在所有已生成椭圆的外部,若是,计算它与所有已生成椭圆边界的距离;（2） 如果所求的距离大于或等于欲生成的椭圆的长半轴,则以该点为中心,生成一个新的椭圆。这样,不必用一个多边形覆盖来判别椭圆之间是否相交或重叠,可以使生成的椭圆与椭圆之间的距离更小一些（甚至可以是零）,从而提高了模拟区域中椭圆的密度。试验表明,针对混凝土,可以在比较短的时间内,按3级配生成骨料含量可高达70%以上的模拟试件,按2级配生成骨料含量可高达60%以上的模拟试件。对所生成的混凝土试件,做了简单的加载力学实验。计算结果表明,该方法生成的模型能够满足力学分析的需要;进一步,基于椭圆随机分布区域,使用椭圆作为覆盖,建立了高含量的参数化不规则骨料模型试件。     

Numerical solutions for the transient flow in the homogenous closed circle reservoirs

There are many fault block fields in China. A fault block field consists of fault pools. The small fault pools can be viewed as the closed circle reservoirs in some case. In order to know the pressure change of the developed formation and provide the formation data for developing the fault block fields reasonably, the transient flow should be researched. In this paper, we use the automatic mesh generation technology and the finite element method to solve the transient flow problem for the well located in the closed circle reservoir, especially for the well located in an arbitrary position in the closed circle reservoir. The pressure diffusion process is visualized and the well-location factor concept is first proposed in this paper. The typical curves of pressure vs time for the well with different well-location factors are presented. By comparing numerical results with the analytical solutions of the well located in the center of the closed circle reservoir, the numerical method is verified.     

NEW THEORY FOR EQUATIONS OF NON-FUCHSIAN TYPE——REPRESENTATION THEOREM OF TREE SERIES SOLUTION (Ⅱ)

Our main result consists in proving the representation theorem. Irregular integral is a new type of analytic function, represented by a compound Taylor-Fourier tree series, in which each coefficient of the Fourier series is a Taylor series, while the Taylor coefficients are tree series in terms of equations parameters, higher order correction terms to each coefficient having tree structure with inexhaustible proliferation.The solution obtained is proved to be convergent absolutely and uniformly in the region defined by coefficient functions of the original equation, provided the structure parameter is less than unity. Direct substitution shows that our tree series solution satisfies the equation explicity generation by generation.As compared with classical theory our method not only furnishes explicit expression of irregular integral, leading to the solution of Poincare problem, but also provides possibility of extending the scope of investigation for analytic theory to equations with various kinds of singularities in a unifying way.Exact explicit analytic expression for irregular integrals can be obtained by means of correspondence principle.It is not difficult to prove the convergence of the tree series solution obtained. Direct substitution shows it satisfies the equation.The tree series is automorphic, which agrees completely with Poincaré’s conjecture.     

Effective moduli of piezoelectric material with microcavities

The effective electroelastic moduli of microcavity-weakened piezoelectric plates are investigated by the dilute, self-consistent, Mori-Tanaka and differential micromechanics theories. The results of perturbed heat intensity, strain and electric field (SEF) due to the presence of voids are obtained for two-dimensional (2-D) piezoelectric plates with microcavities of various shapes, and then the above four micromechanics models can be established with the results. These models can be applicable to a wide range of microcavities such as ellipse, circle, crack, triangle, square and pentagon. Some numerical results are presented to illustrate the applicability of these models.     

A brief note on upwind collocation

Upwind collocation on Hermite cubics is compared to orthogonal collocation with respect to effective diffusion. The one-dimensional constant coefficient advection-diffusion equation is employed to this end. The effective diffusion coefficient is determined exactly and is found to be dependent on the nodal solution values. The effective diffusion coefficients of three other upwinding schemes are also presented. Upwind collocation is found to have an effective diffusion coefficient like other upwinding schemes plus an extra term which may enhance or reduce the non-advective flux, depending on the problem solution and point location within the domain.     

Image encryption algorithm with circle index table scrambling and partition diffusion

This paper introduces an image encryption algorithm shorted as CITSPD, manipulated by circle index table scrambling and partition diffusion. Firstly, the circle index table is obtained through the generation, circle shift and transposition of the benchmark sequence. Secondly, the plain image is transformed into the wavelet coefficient and is then scrambled by the circle index table. Thirdly, the permutated image is disturbed by different noises and is further divided into four subsections. Finally, the forward and inverse partition diffusions are performed to the subsections for getting the cipher image. The main feature of this algorithm is that the robust chaos-based keystream and encryption process are highly sensitive to the plaintext, which will effectively resist against chosen-plaintext and known-plaintext attacks. In addition, the encryption scheme is free of noise attack since the inverse diffusion differs from the forward one. And the diffusion effect can be effectively enhanced by, as much as possible, increasing the small pixel value and decreasing the large pixel value. Experimental tests and security analyses are carried out to verify the advantages of the scheme.

     

Equation of convective diffusion of a multicomponent mixture in a capillary for an arbitrary velocity field

It is shown that the convective transport in a binary mixture in the presence of vortex convection can be described in terms of Fick’s law with an effective diffusion coefficient independent of the concentration. The form of the effective diffusion coefficient is found for arbitrary convection in the mixture. A generalization of the Stefan-Maxwell diffusion equation is proposed to include an arbitrary rotational mixture velocity field. The characteristics of convective transport are considered with reference to a three-component mixture. A solution of the equation of three-component mixture transport through a long capillary in the presence of convection homogeneous along the capillary axis is presented. It is established that for sharply different component diffusion coefficients a mixture density extremum may appear inside the capillary and then change or disappear depending on the convective flow intensity.     

Numerical investigation of fully developed laminar flow in irregular annuli: Square‐circular ducts

Numerical study is carried out on fully developed laminar axial flow of incompressible Newtonian fluid in irregular annuli of different cross‐sectional geometry. Accurate prediction of the friction factor of this flow was obtained using high‐order finite element method. Investigations are performed for the annular flow between rectangular and circular ducts under all possible arrangements. The governing equations are solved by an efficient finite element technique. It was found that a higher annular area‐ratio will lead to a monotonic increase in (f Re) value in the case of regular annuli, and will lead to an increase followed by a decrease in (f Re) value in the case of irregular annuli. Furthermore, this study illustrates that irregular annuli have lower (f Re) value than regular annuli, and that the square‐in‐circle case (SC‐case) has the lowest (f Re) value whereas the circle‐in‐circle case (CC‐case) has the highest (f Re) value. The finite element technique developed in this study was validated against the already reported numerical results in the literature, and the results presented in this work show excellent agreement. Copyright © 2009 John Wiley & Sons, Ltd.     

An efficient second‐order accurate cut‐cell method for solving the variable coefficient Poisson equation with jump conditions on irregular domains

A numerical method is presented for solving the variable coefficient Poisson equation on a two‐dimensional domain in the presence of irregular interfaces across which both the variable coefficients and the solution itself may be discontinuous. The approach involves using piecewise cubic splines to represent the irregular interface, and applying this representation to calculate the volume and area of each cut cell. The fluxes across the cut‐cell faces and the interface faces are evaluated using a second‐order accurate scheme. The deferred correction approach is used, resulting in a computational stencil for the discretized Poisson equation on an irregular (complex) domain that is identical to that obtained on a regular (simple) domain. In consequence, a highly efficient multigrid solver based on the additive correction multigrid (ACM) method can be applied to solve the current discretized equation system. Several test cases (for which exact solutions to the variable coefficient Poisson equation with and without jump conditions are known) have been used to evaluate the new methodology for discretization on an irregular domain. The numerical solutions show that the new algorithm is second‐order accurate as claimed, even in the presence of jump conditions across an interface. Copyright © 2006 John Wiley & Sons, Ltd.     

Asymptotic form of the admixture transport equation for a channel flow with an anisotropic diffusion tensor

The problem of the asymptotically correct reduction of a 3-D mass (heat) transfer equation to a 1-D equation in a flow with anisotropic diffusion properties is considered. The convective mass (heat) transfer domain is a cylindrical channel of arbitrary cross section. The diffusion coefficient matrix is assumed to be independent of the spatial coordinates. In the equivalent diffusion equation constructed, a certain effective diffusion (dispersion [1]) coefficient is introduced. Formulas for this coefficient are obtained. A relation between the effective diffusion coefficient calculations and the problem of minimization of a certain functional is established, i. e. the possibility of calculations based on variational methods is noted. An example of an exact calculation of the effective diffusion coefficient is considered. The possibility of a generalization of the problem, in which the effective diffusion (heat conduction) equation is essentially a nonlinear equation of general form for the one-dimensional case, is indicated. Sankt-Peterburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 110–123, March–April, 2000.     

SIMULATION OF THE FLOW OVER ELLIPTIC AIRFOILS OSCILLATING AT LARGE ANGLES OF ATTACK

The incompressible, viscous flow over two-dimensional elliptic airfoils oscillating in pitch at large angles of attack, such that flow separation occurs, has been simulated numerically for a Reynolds number of 3000. A vortex method is used to solve the two-dimensional Navier–Stokes equations in vorticity/stream-function form using a time-marching approach. Using an operator-splitting method the convection and diffusion equations are solved sequentially at each time step. The convection equation is solved using a vortex-in-cell method, and the diffusion equation using a second-order ADI finite-difference scheme. Elliptic profiles are obtained by mapping a circle in a computational domain into the physical domain using a Joukowski transformation. The effects of several parameters on the flow field are considered, such as: frequency of oscillation, mean angle of attack, location of pitch-axis and the thickness ratio of the ellipse. The results obtained are shown to compare favourably with available experimental results.     

Computation of Saturation Dependence of Effective Diffusion Coefficient in Unsaturated Argillite Micro-fracture by Lattice Boltzmann Method

Getting access to the effective diffusion coefficient is a key point to provide realistic predictions of migration of radionuclides from radioactive waste repository in deep argillaceous geological formations. In the present work, the effective diffusion coefficient was computed inside an argillite micro-fracture as a function of its saturation level. The micrometric fracture geometry was extracted from the X-ray \(\mu \)-tomography image (\(0.7\,\upmu \mathrm{m}\) voxel resolution) of an Opalinus clay sample. It was collected in the host rock excavated damaged zone surrounding a borehole in the Mont Terri laboratory. The computations were performed using two two-relaxation-time lattice Boltzmann models. The first one, a phase separation model, was used to extract the connected liquid phase inside the fracture for given saturations. The second, a diffusion model, was used to compute non-reactive tracer diffusion in the connected liquid phase of the fracture and to calculate the effective diffusion coefficient for the associated saturations. The dependence of the effective diffusion coefficient on saturation was found to be quasi-linear and to qualitatively match the Maxwell expression for saturations lower than 0.8.     

THEORETICAL MODEL OF EFFECTIVE STRESS COEFFICIENT FOR ROCK/SOIL-LIKE POROUS MATERIALS

Physical mechanisms and influencing factors on the effective stress coefficient for rock/soil-like porous materials are investigated, based on which equivalent connectivity index is proposed. The equivalent connectivity index, relying on the meso-scale structure of porous material and the property of liquid, denotes the connectivity of pores in Representative Element Area （REA）. If the conductivity of the porous material is anisotropic, the equivalent connectivity index is a second order tensor. Based on the basic theories of continuous mechanics and tensor analysis, relationship between area porosity and volumetric porosity of porous materials is deduced. Then a generalized expression, describing the relation between effective stress coefficient tensor and equivalent connectivity tensor of pores, is proposed, and the expression can be applied to isotropic media and also to anisotropic materials. Furthermore, evolution of porosity and equivalent connectivity index of the pore are studied in the strain space, and the method to determine the corresponding functions in expressions above is proposed using genetic algorithm and genetic programming. Two applications show that the results obtained by the method in this paper perfectly agree with the test data. This paper provides an important theoretical support to the coupled hydro-mechanical research.