Determination of Critical Slip Surface of Soil Slope by New Complex Method

A new complex method is presented considering not only the improvement upon the ＂bad ＂design point, but also the diversity of the newly generated complex, which is obtained by replacing the ＂bad ＂design point with the better design point located at the line between the ＂bad ＂design point and the ceotroid of the remaining design points of the old complex. The new complex method is applied to searching for the critical slip surface of two non-homogeneous soil slopes. The comparison of the results obtained by the new complex method with that by the basic complex method shows that the new complex method is much more likely to find the true critical surface for the randomly generated initial complex.

Synthesis of the superfine high-entropy zirconate nanopowders by polymerized complex method

The high-purity and superfine high-entropy zirconate nanopowders,namely(Y_(0.25)La_(0.25)Sm_(0.25)Eu_(0.25))_(2)Zr_(2)O_(7)nanopowders,without agglomeration,were successfully synthesized via polymerized complex method at low temperatures for the first time.The results showed that the crystallinity degree,lattice strain,and particle size of the as-synthesized powders were gradually enhanced with the increase of the synthesis temperature from 800 to 1300℃.The as-synthesized powders involved fluorite phase in the range of 800-1200℃while they underwent the phase evolution from fluorite to pyrochlore at 1300℃.It is worth mentioning that the as-synthesized powders at 900℃are of the highest quality among all the as-synthesized powders,which is due to the fact that they not only possess the particle size of 11 nm without agglomeration,but also show high purity and good compositional uniformity.

Computational Complex Method for Finite Elastic Plane Problem with Multiple Elliptical Holes

把多复变量应力函数和边界配点最小二乘法相结合，计算含有任意多个椭圆孔有限大小弹性板的应力场．每个孔的大小、位置为任意．板的边界由下列四种边界条件以及它们的组合所组成：１）已知Ｐｘ和Ｐｙ的应力边界，２）已知Ｖｘ和Ｖｙ的位移边界，３）已知法向位移ＶＮ和切向力ＰＴ的混合边界，４）已知法向力ＰＮ和切向位移ＶＴ的混合边界．编制了相应的ＦＯＲＴＲＡＮ程序，进行考题和算例分析，结果表明本方法行之有效．

Species distribution of polymeric aluminium ferrum——timed complexation colorimetric analysis method of Al-Fe-Ferron

The effects of the calorimetric buffer solutions were investigated while the two colorimetric reactions of AI-ferron complex and Fe-ferron complex occurred individually, and the effects of the testing wavelength and the pH of the solutions were also investigated. A timed complexatian colorimetric analysis method of Al-Fe-ferron in view of the total concentration of {AI + Fe} was then established to determine the species distribution of polymeric Al-Fe. The testing wavelength was recommended at 362 net and the testing pH value was 5. With a comparison of the ratios of n(Al)/n(Fe), the standard adsorption curves of the polymeric Al-Fe solutions were derived from the experimental results. Furthermore, the solutions' composition were carious in both the molar n(Al)/n(Fe) ratios, i.e. 0/0, 5/5, 9/1 and 0/10, and the concentrations associated with the total ( Al + Fe which ranged from 10(-5) to 10(-4) mol/L..

Complex variable element-free Galerkin method for viscoelasticity problems

Based on the complex variable moving least-square （CVMLS） approximation, the complex variable element-free Galerkin （CVEFG） method for two-dimensional viscoelasticity problems under the creep condition is presented in this paper. The Galerkin weak form is employed to obtain the equation system, and the penalty method is used to apply the essential boundary conditions, then the corresponding formulae of the CVEFG method for two-dimensional viscoelasticity problems under the creep condition are obtained. Compared with the element-free Galerkin （EFG） method, with the same node distribution, the CVEFG method has higher precision, and to obtain the similar precision, the CVEFG method has greater computational efficiency. Some numerical examples are given to demonstrate the validity and the efficiency of the method.

A new complex variable element-free Galerkin method for two-dimensional potential problems

In this paper, based on the element-free Galerkin （EFG） method and the improved complex variable moving least- square （ICVMLS） approximation, a new meshless method, which is the improved complex variable element-free Galerkin （ICVEFG） method for two-dimensional potential problems, is presented. In the method, the integral weak form of control equations is employed, and the Lagrange multiplier is used to apply the essential boundary conditions. Then the corresponding formulas of the ICVEFG method for two-dimensional potential problems are obtained. Compared with the complex variable moving least-square （CVMLS） approximation proposed by Cheng, the functional in the ICVMLS approximation has an explicit physical meaning. Furthermore, the ICVEFG method has greater computational precision and efficiency. Three numerical examples are given to show the validity of the proposed method.

Analysis of elastoplasticity problems using an improved complex variable element-free Galerkin method

In this paper, based on the conjugate of the complex basis function, a new complex variable moving least-squares approximation is discussed. Then using the new approximation to obtain the shape function, an improved complex variable element-free Galerkin（ICVEFG） method is presented for two-dimensional（2D） elastoplasticity problems. Compared with the previous complex variable moving least-squares approximation, the new approximation has greater computational precision and efficiency. Using the penalty method to apply the essential boundary conditions, and using the constrained Galerkin weak form of 2D elastoplasticity to obtain the system equations, we obtain the corresponding formulae of the ICVEFG method for 2D elastoplasticity. Three selected numerical examples are presented using the ICVEFG method to show that the ICVEFG method has the advantages such as greater precision and computational efficiency over the conventional meshless methods.

The complex variable reproducing kernel particle method for two-dimensional elastodynamics

On the basis of the reproducing kernel particle method （RKPM）, a new meshless method, which is called the complex variable reproducing kernel particle method （CVRKPM）, for two-dimensional elastodynamics is presented in this paper. The advantages of the CVRKPM are that the correction function of a two-dimensional problem is formed with one-dimensional basis function when the shape function is obtained. The Galerkin weak form is employed to obtain the discretised system equations, and implicit time integration method, which is the Newmark method, is used for time history analysis. And the penalty method is employed to apply the essential boundary conditions. Then the corresponding formulae of the CVRKPM for two-dimensional elastodynamics are obtained. Three numerical examples of two-dimensional elastodynamics are presented, and the CVRKPM results are compared with the ones of the RKPM and analytical solutions. It is evident that the numerical results of the CVRKPM are in excellent agreement with the analytical solution, and that the CVRKPM has greater precision than the RKPM.

The complex variable meshless local Petrov-Galerkin method of solving two-dimensional potential problems

Based on the complex variable moving least-square（CVMLS） approximation and a local symmetric weak form,the complex variable meshless local Petrov-Galerkin（CVMLPG） method of solving two-dimensional potential problems is presented in this paper.In the present formulation,the trial function of a two-dimensional problem is formed with a one-dimensional basis function.The number of unknown coefficients in the trial function of the CVMLS approximation is less than that in the trial function of the moving least-square（MLS） approximation.The essential boundary conditions are imposed by the penalty method.The main advantage of this approach over the conventional meshless local Petrov-Galerkin（MLPG） method is its computational efficiency.Several numerical examples are presented to illustrate the implementation and performance of the present CVMLPG method.

An improved complex variable element-free Galerkin method for two-dimensional elasticity problems

In this paper, the improved complex variable moving least-squares （ICVMLS） approximation is presented. The ICVMLS approximation has an explicit physics meaning. Compared with the complex variable moving least-squares （CVMLS） approximations presented by Cheng and Ren, the ICVMLS approximation has a great computational precision and efficiency. Based on the element-free Galerkin （EFG） method and the ICVMLS approximation, the improved complex variable element-free Galerkin （ICVEFG） method is presented for two-dimensional elasticity problems, and the corresponding formulae are obtained. Compared with the conventional EFC method, the ICVEFG method has a great computational accuracy and efficiency. For the purpose of demonstration, three selected numerical examples are solved using the ICVEFG method.

WAVE SUPERPOSITION METHOD BASED ON VIRTUAL SOURCE BOUNDARY WITH COMPLEX RADIUS VECTOR FOR SOLVING ACOUSTIC RADIATION PROBLEMS

By virtue of the comparability between the wave superposition method and the dynamic analysis of structures, a general format for overcoming the non-uniqueness of solution induced by the wave superposition method at the eigenfrequencies of the corresponding interior problems is proposed. By adding appropriate damp to the virtual source system of the wave superposition method, the unique solutions for all wave numbers can be ensured. Based on this thought, a novel method-wave superposition method with complex radius vector is constructed. Not only is the computational time of this method approximately equal to that of the standard wave superposition method, but also the accuracy is much higher compared with other correlative methods. Finally, by taking the pulsating sphere and oscillating sphere as examples, the results of calculation show that the present method can effectively overcome the non-uniqueness problem.

Combining the complex variable reproducing kernel particle method and the finite element method for solving transient heat conduction problems

In this paper, the complex variable reproducing kernel particle （CVRKP） method and the finite element （FE） method are combined as the CVRKP-FE method to solve transient heat conduction problems. The CVRKP-FE method not only conveniently imposes the essential boundary conditions, but also exploits the advantages of the individual methods while avoiding their disadvantages, then the computational efficiency is higher. A hybrid approximation function is applied to combine the CVRKP method with the FE method, and the traditional difference method for two-point boundary value problems is selected as the time discretization scheme. The corresponding formulations of the CVRKP-FE method are presented in detail. Several selected numerical examples of the transient heat conduction problems are presented to illustrate the performance of the CVRKP-FE method.

New complex variable meshless method for advection-diffusion problems

In this paper,an improved complex variable meshless method（ICVMM） for two-dimensional advection-diffusion problems is developed based on improved complex variable moving least-square（ICVMLS） approximation.The equivalent functional of two-dimensional advection-diffusion problems is formed,the variation method is used to obtain the equation system,and the penalty method is employed to impose the essential boundary conditions.The difference method for twopoint boundary value problems is used to obtain the discrete equations.Then the corresponding formulas of the ICVMM for advection-diffusion problems are presented.Two numerical examples with different node distributions are used to validate and investigate the accuracy and efficiency of the new method in this paper.It is shown that ICVMM is very effective for advection-diffusion problems,and has a good convergent character,accuracy,and computational efficiency.

Synthesis and Characterization of LaNixCo1-xO3 Perovskites via Complex Precursor Methods

This work presents a study on the synthesis of LaNixCo1-xO3 perovskites via complex precursor methods. Perovskite oxides with the composition LaNixCo1-xO3 were synthesized by chelating precursor and polymeric precursor methods using nickel and/or cobalt nitrates, lanthanum nitrate, ethylene glycol, citric acid, and EDTA as starting source. The obtained perovskite were characterized by thermogravimetric analysis, infrared spectroscopy, X-ray diffraction and the morphology of the samples were investigated by N2 adsorption experiments and average medium particle size. TG curves and FTIR spectra were particularly useful in establishing of the optimal calcination temperature of the precursor powders. X-ray diffraction patterns revealed the formation of the perovskite structure in all samples prepared by both synthesis method and after calcinations at 700℃. The results showed that the preparation method resulted in oxides with the intended structure. The specific surface area values were influenced by preparation method.

Risk calculation method for complex engineering system

This paper presents a rapid and simple risk calculation method for large and complex engineering systems, the simulated maximum entropy method （SMEM）, which is based on integration of the advantages of the Monte Carlo and maximum entropy methods, thus avoiding the shortcoming of the slow convergence rate of the Monte Carlo method in risk calculation. Application of SMEM in the calculation of reservoir flood discharge risk shows that this method can make full use of the known information under the same conditions and obtain the corresponding probability distribution and the risk value. It not only greatly improves the speed, compared with the Monte Carlo method, but also provides a new approach for the risk calculation in large and complex engineering systems.

A complex variable meshless local Petrov-Galerkin method for transient heat conduction problems

On the basis of the complex variable moving least-square （CVMLS） approximation, a complex variable meshless local Petrov-Galerkin （CVMLPG） method is presented for transient heat conduction problems. The method is developed based on the CVMLS approximation for constructing shape functions at scattered points, and the Heaviside step function is used as a test function in each sub-domain to avoid the need for a domain integral in symmetric weak form. In the construction of the well-performed shape function, the trial function of a two-dimensional （2D） problem is formed with a one-dimensional （1D） basis function, thus improving computational efficiency. The numerical results are compared with the exact solutions of the problems and the finite element method （FEM）. This comparison illustrates the accuracy as well as the capability of the CVMLPG method.

Simulation of incompressible multiphase flows with complex geometry using etching multiblock method

The incompressible two-phase flows are simulated using combination of an etching multiblock method and a diffuse interface （DI） model, particularly in the com- plex domain that can be decomposed into multiple rectangular subdomains. The etching multiblock method allows natural communications between the connected subdomains and the efficient parallel computation. The DI model can consider two-phase flows with a large density ratio, and simulate the flows with the moving contact line （MCL） when a geometric formulation of the MCL model is included. Therefore, combination of the etch- ing method and the DI model has potential to deal with a variety of two-phase flows in industrial applications. The performance is examined through a series of numerical exper- iments. The convergence of the etching method is firstly tested by simulating single-phase flows past a square cylinder, and the method for the multiphase flow simulation is vali- dated by investing drops dripping from a pore. The numerical results are compared with either those from other researchers or experimental data. Good agreement is achieved. The method is also used to investigate the impact of a droplet on a grooved substrate and droplet generation in flow focusing devices.

Extended Complex tanh-Function Method and Exact Solutions to （2＋1）-Dimensional Hirota Equation

在这篇论文，一个新扩大复杂 tanh 功能方法为构造旅行波浪，非旅行的波浪，和系数函数被介绍“非线性的方程的象 soliton 一样解决方案。这个方法比复杂 tanh 功能方法更强大[混乱， Solitons 和分数维图形 20 (2004 ) 1037 ] 。丰富的新答案(2+1 ) 维的 Hirota 方程被使用这个方法和符号的计算系统枫树获得。

A new complex variable meshless method for transient heat conduction problems

In this paper, based on the improved complex variable moving least-square （ICVMLS） approximation, a new complex variable meshless method （CVMM） for two-dimensional （2D） transient heat conduction problems is presented. The variational method is employed to obtain the discrete equations, and the essential boundary conditions are imposed by the penalty method. As the transient heat conduction problems are related to time, the Crank-Nicolson difference scheme for two-point boundary value problems is selected for the time discretization. Then the corresponding formulae of the CVMM for 2D heat conduction problems are obtained. In order to demonstrate the applicability of the proposed method, numerical examples are given to show the high convergence rate, good accuracy, and high efficiency of the CVMM presented in this paper.

COMPLEX INNER PRODUCT AVERAGING METHOD FOR CALCULATING NORMAL FORM OF ODE

This paper puts forward a complex inner product averaging method for calculating normal form of ODE. Compared with conventional averaging method, the theoretic analytical process has such simple forms as to realize computer program easily. Results can be applied in both autonomous and non-autonomous systems. At last, an example is resolved to verify the method.