Galerkin-based quasi-smooth manifold element(QSME)method for anisotropic heat conduction problems in composites with complex geometry

The accurate and efficient analysis of anisotropic heat conduction problems in complex composites is crucial for structural design and performance evaluation. Traditional numerical methods, such as the finite element method(FEM), often face a trade-off between calculation accuracy and efficiency. In this paper, we propose a quasi-smooth manifold element(QSME) method to address this challenge, and provide the accurate and efficient analysis of two-dimensional(2D) anisotropic heat conduction problems in composites with complex geometry. The QSME approach achieves high calculation precision by a high-order local approximation that ensures the first-order derivative continuity.The results demonstrate that the QSME method is robust and stable, offering both high accuracy and efficiency in the heat conduction analysis. With the same degrees of freedom(DOFs), the QSME method can achieve at least an order of magnitude higher calculation accuracy than the traditional FEM. Additionally, under the same level of calculation error, the QSME method requires 10 times fewer DOFs than the traditional FEM. The versatility of the proposed QSME method extends beyond anisotropic heat conduction problems in complex composites. The proposed QSME method can also be applied to other problems, including fluid flows, mechanical analyses, and other multi-field coupled problems, providing accurate and efficient numerical simulations.

Complex behaviour of trivalent rare earth elements by humic acids

The complexation behaviours of trivalent rare earth elements (La, Ce, Ho and Yb) by two types of humic acids were investigated under a specified set of conditions. Humic acids show quite different complexation capacities an conditional formation constants with the REEs. Apparently there are two types of binding sites in the functional groups of humic acid, in which the first binding sites have stronger ability than the second. Cerium shows the largest complexation capacities and highest formation constants among the four REEs with two humic acids, this anomaly may be relative to the distribution pattern of the REEs in seawater. The experimental results were comparable to the values of other metals reported and provided the basic data for environmental geochemistry of rare earth elements.

Electrochemical behaviors of gold and its associated elements in various complex agent solutions

Thermodynamic properties and electrochemical behaviors of gold and its associated elements, such as silver, copper, nickel and iron, in various complex agent solutions were studied. Within CS（NH2）2, S2O2-3 and SCN- systems, alkaline thiourea is the optimal nontoxic lixiviating agent substituting cyanide from the viewpoint of thermodynamics. The electrochemical study indicates that the anodic dissolution current densities of gold are 2.616, （1.805,） 1.267, 1.088, 0.556, and 0.145 mA·cm-2 respectively in the solutions of cyanide, alkaline thiourea containing Na2SiO3, SCN-, acidic thiourea, alkaline thiourea and thiosulfate at the potential of 0.500 V. Comparing various lixiviating agents, the alkaline thiourea solution containing Na2SiO3 is of prominent selectivity in leaching gold, in the potential range from 0.500 to 0.600 V, which is most efficient for leaching gold selectively instead of cyanide. The effect on leaching gold is similar to that in the cyanide system.

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.

Synthesis and Characterization of Heteropolytungstosilicate Complexes with the Lanthanide Elements

Lanthanide heteropoly compounds K15[Ln(HSiW9O34)2]·28H2O(Ln = La, Ce, Nd), denoted as Ln(SiW9)2, were synthesized and characterized by element analysis, TG-DTA, IR, UV, XPS and XRD. The results show that partial oxygen in Ln(SiW9)2 was coordinated with Ln3- , where Ln-3 was in the inner side of the heteropoly anions, while the fundamental structure of SiW9 had little change. The result was supported by ion exchange experiment.

ON ALGEBRAIC SOLUTIONS OF THE SECOND-ORDER COMPLEX DIFFERENTIAL EQUATIONS WITH ENTIRE ALGEBRAIC ELEMENT COEFFICIENTS

The main purpose of this paper is to study the problems on the existence of algebraic solutions for some second-order complex differential equations with entire algebraic function element coeifficients. Several theorems on the existence of solutions are obtained, which perfect the solution theory of linear complex differential equations.

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.

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.

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.

Attempt to generalize fractional-order electric elements to complex-order ones

The complex derivative D^α±jβ, with α, β ∈ R＋ is a generalization of the concept of integer derivative, where α = 1,β = 0. Fractional-order electric elements and circuits are becoming more and more attractive. In this paper, the complexorder electric elements concept is proposed for the first time, and the complex-order elements are modeled and analyzed.Some interesting phenomena are found that the real part of the order affects the phase of output signal, and the imaginary part affects the amplitude for both the complex-order capacitor and complex-order memristor. More interesting is that the complex-order capacitor can do well at the time of fitting electrochemistry impedance spectra. The complex-order memristor is also analyzed. The area inside the hysteresis loops increases with the increasing of the imaginary part of the order and decreases with the increasing of the real part. Some complex case of complex-order memristors hysteresis loops are analyzed at last, whose loop has touching points beyond the origin of the coordinate system.

Quasi-optimal complexity of adaptive finite element method for linear elasticity problems in two dimensions

This paper introduces an adaptive finite element method （AFEM） using the newest vertex bisection and marking exclusively according to the error estimator without special treatment of oscillation. By the combination of the global lower bound and the localized upper bound of the posteriori error estimator, perturbation of oscillation, and cardinality of the marked element set, it is proved that the AFEM is quasi-optimal for linear elasticity problems in two dimensions, and this conclusion is verified by the numerical examples.

Complex Fuzzy Structured Element and Its Properties

The first part of this paper gives the definition about complex fuzzy structured element on the basis of one-dimensional fuzzy structured element and some of its property. The following part introduces its limit and continuity. All of this has opened up a vision for the research of fuzzy structured element, and also played an important role in promoting its progress.

An Unsteady Two-Dimensional Complex Variable Boundary Element Method

The Complex Variable Boundary Element Method (CVBEM) procedure is extended to modeling applications of the two-dimensional linear diffusion partial differential equation (PDE) on a rectangular domain. The methodology in this work is suitable for modeling diffusion problems with Dirichlet boundary conditions and an initial condition that is equal on the boundary to the boundary conditions. The underpinning of the modeling approach is to decompose the global initial-boundary value problem into a steady-state component and a transient component. The steady-state component is governed by the Laplace PDE and is modeled using the Complex Variable Boundary Element Method. The transient component is governed by the linear diffusion PDE and is modeled by a linear combination of basis functions that are the products of a two-dimensional Fourier sine series and an exponential function. The global approximation function is the sum of the approximate solutions from the two components. The boundary conditions of the steady-state problem are specified to match the boundary conditions from the global problem so that the CVBEM approximation function satisfies the global boundary conditions. Consequently, the boundary conditions of the transient problem are specified to be continuously zero. The initial condition of the transient component is specified as the difference between the initial condition of the global initial-boundary value problem and the CVBEM approximation of the steady-state solution. Therefore, when the approximate solutions from the two components are summed, the resulting global approximation function approximately satisfies the global initial condition. In this work, it will be demonstrated that the coupled global approximation function satisfies the governing diffusion PDE. Lastly, a procedure for developing streamlines at arbitrary model time is discussed.

Element mapping the Merensky Reef of the Bushveld Complex

The Merensky Reef hosts one of the largest PGE resources globally.It has been exploited for nearly 100 years,yet its origin remains unresolved.In the present study,we characterised eight samples of the reef at four localities in the western Bushveld Complex using micro-X-ray fluorescence and field emission scanning electron microscopy.Our results indicate that the Merensky Reef formed through a range of diverse processes.Textures exhibited by chromite grains at the base of the reef are consistent with supercooling and in situ growth.The local thickening of the Merensky chromitite layers within troughs in the floor rocks is most readily explained by granular flow.Annealing and deformation textures in pyroxenes of the Merensky pegmatoid bear testament to recrystallisation and deformation.The footwall rocks to the reef contain disseminations of PGE rich sulphides as well as olivine grains with peritectic reaction rims along their upper margins suggesting reactive downward flow of silicate and sulphide melts.Olivine-hosted melt inclusions containing Cl-rich apatite,sodic plagioclase,and phlogopite suggest the presence of highly evolved,volatile-rich melts.Pervasive reverse zonation of cumulus plagioclase in the footwall of the reef indicates dissolution or partial melting of plagioclase,possibly triggered by flux of heat,acidic fluids,or hydrous melt.Together,these data suggest that the reef formed through a combination of magmatic,hydrodynamic and hydromagmatic processes.

A Conceptual Numerical Model of the Wave Equation Using the Complex Variable Boundary Element Method

In this work, a conceptual numerical solution of the two-dimensional wave partial differential equation (PDE) is developed by coupling the Complex Variable Boundary Element Method (CVBEM) and a generalized Fourier series. The technique described in this work is suitable for modeling initial-boundary value problems governed by the wave equation on a rectangular domain with Dirichlet boundary conditions and an initial condition that is equal on the boundary to the boundary conditions. The new numerical scheme is based on the standard approach of decomposing the global initial-boundary value problem into a steady-state component and a time-dependent component. The steady-state component is governed by the Laplace PDE and is modeled with the CVBEM. The time-dependent component is governed by the wave PDE and is modeled using a generalized Fourier series. The approximate global solution is the sum of the CVBEM and generalized Fourier series approximations. The boundary conditions of the steady-state component are specified as the boundary conditions from the global BVP. The boundary conditions of the time-dependent component are specified to be identically zero. The initial condition of the time-dependent component is calculated as the difference between the global initial condition and the CVBEM approximation of the steady-state solution. Additionally, the generalized Fourier series approximation of the time-dependent component is fitted so as to approximately satisfy the derivative of the initial condition. It is shown that the strong formulation of the wave PDE is satisfied by the superposed approximate solutions of the time-dependent and steady-state components.

A new approach for flow simulation in complex hydraulic fracture morphology and its application:Fracture connection element method

Efficient flow simulation and optimization methods of hydraulic fracture morphology in unconventional reservoirs are effective ways to enhance oil/gas recovery.Based on the connection element method(CEM)and distribution of stimulated reservoir volume,the complex hydraulic fracture morphology was accurately described using heterogeneous node connection system.Then a new fracture connection element method(FCEM)for fluid flow in stimulated unconventional reservoirs with complex hydraulic fracture morphology was proposed.In the proposed FCEM,the arrangement of dense nodes in the stimulated area and sparse nodes in the unstimulated area ensures the calculation accuracy and efficiency.The key parameter,transmissibility,was also modified according to the strong heterogeneity of stimulated reservoirs.The finite difference and semi-analytical tracking were used to accurately solve the pressure and saturation distribution between nodes.The FCEM is validated by comparing with traditional numerical simulation method,and the results show that the bottom hole pressure simulated by the FCEM is consistent with the results from traditional numerical simulation method,and the matching rate is larger than 95%.The proposed FCEM was also used in the optimization of fracturing parameters by coupling the hydraulic fracture propagation method and intelligent optimization algorithm.The integrated intelligent optimization approach for multi-parameters,such as perforation number,perforation location,and displacement in hydraulic fracturing is proposed.The proposed approach was applied in a shale gas reservoir,and the result shows that the optimized perforation location and morphology distribution are related to the distribution of porosity/permeability.When the perforation location and displacement are optimized with the same fracture number,NPV increases by 70.58%,which greatly improves the economic benefits of unconventional reservoirs.This work provides a new way for flow simulation and optimization of hydraulic fracture morphology of multi-fractured horizontal wells in unconventional reservoirs.

Rare-earth and trace element imprints on the origin and tectonic setting of gabbro-diorite complex in the Pan-African belt of Southeast Obudu Plateau,Nigeria

A gabbro-diorite plutonic complex from the Southeast Obudu Plateau, representing limited volumes of magma, was studied for its trace and rare-earth element characteristics, in an attempt to document its genetic and geodynamic history. Geochemical studies indicate that the gabbro samples are characterized by variable concentrations and low averages of such index elements as Cr (40×10-6–200×10-6; av. 80×10-6), Ni (40×10-6–170×10-6; 53.33×10-6) and Zr (110×10-6–240×10-6; 116.67×10-6); variable and high averages of Rb (3×10-6–270×10-6; 80.67×10-6), Sr (181×10-6–1610×10-6; 628.17×10-6) and U (0.14×10-6–3.46×10-6; 1.51×10-6), and fairly uniform Co (34×10-6–49×10-6; 36.33×10-6) and Sc (23×10-6–39×10-6; 34.5×10-6), while the diorite samples exhibit higher trace element compositions. The range of REE contents and distinctive chondrite-normalized patterns indicate moderate fractionation with slight positive Eu anomaly in the diorites to very low fractionation with flat patterns and slight positive Eu anomaly in the gabbros. However, the general element systematics of the samples, especially LILE (Ba, Rb, Sr, Cs and Pb), HFSE (Zr, Th, U, Hf, Mo, W, Nb and Sn), relatively immobile elements (Zr, Ni, Cr) and REE, suggests a differentiation model, involving fractional crystallization of olivine and clinopyroxene from a partial melt generated beneath an island arc complex. A possible model for the complex is therefore an island arc setting, the development of which was dominated by calc-alkaline magmatism across the Obudu Plateau.

A Finite Element Analysis on Static Strength of a Complex Section

A static finite element analysis (FEA) of an impulsive controller section is presented. The boundary condition and a part of the loads are applied. Considering the grades of the stress around the holes being large, the dense grids are adjusted accordingly. Four cases with different loads are compared, thus the influences of different loads on the section are analyzed. Numerical results show that the maximum stress of the section is lower than the strength limit of the material, and the section will not be broken with the static loads.

Modularized and Parametric Modeling Technology for Finite Element Simulations of Underground Engineering under Complicated Geological Conditions

The surrounding geological conditions and supporting structures of underground engineering are often updated during construction,and these updates require repeated numerical modeling.To improve the numerical modeling efficiency of underground engineering,a modularized and parametric modeling cloud server is developed by using Python codes.The basic framework of the cloud server is as follows:input the modeling parameters into the web platform,implement Rhino software and FLAC3D software to model and run simulations in the cloud server,and return the simulation results to the web platform.The modeling program can automatically generate instructions that can run the modeling process in Rhino based on the input modeling parameters.The main modules of the modeling program include modeling the 3D geological structures,the underground engineering structures,and the supporting structures as well as meshing the geometric models.In particular,various cross-sections of underground caverns are crafted as parametricmodules in themodeling program.Themodularized and parametric modeling program is used for a finite element simulation of the underground powerhouse of the Shuangjiangkou Hydropower Station.This complicatedmodel is rapidly generated for the simulation,and the simulation results are reasonable.Thus,this modularized and parametric modeling program is applicable for three-dimensional finite element simulations and analyses.