CONSISTENCY BETWEEN INDEPENDENCE THEOREMS AND GENERALIZED SELF-CONSISTENT METHOD

Recently Zheng & Hwang established a series of independence theorems concerning with planar effective elastic properties. It is manifested that the estimation of the effective elastic properties of microcracked solids through the generalized self-consistent method (GSCM) contradicts with these independence theorems. In this paper it is shown that such contradiction is actually caused by the approximate algorithm adopted, while the exact solution of GSCM is consistent with these rigorously established independence theorems. Since only an approximate algorithm in GCSM is available in dealing with problems involving non-circular inclusions or holes, an intrinsic GSCM is proposed, which can be performed based on an approximate algorithm and the corresponding estimations are consistent with the independence theorems.

A numerical Hartree self-consistent field calculation of an autoionization resonance parameters for a doubly excited 2s^2, 3s^2, and 4s^2 states of He atom with a complex absorbing potential

The self-consistent Hartree-Fock equation for the He atom is solved using the pseudospectral method. The Feshbach- type autoionization resonance parameters for doubly excited 2s2, 3s2, and 4s2 IS states of He have been determined by adding a complex absorbing potential to the Hamiltonian. The Riss-Meyer iterative and Pad6 extrapolation methods are applied to obtain reliable values for the autoionization resonance parameters, which are compared to previous results in the literature.

Exact Solutions of Non-isospectral sine-Gordon Equation with Self-consistent Sources

The non-isospectral sine-Gordon equation with self-consistent sources is derived.Its solutions are obtainedby means of Hirota method and Wronskian technique,respectively.Non-isospectral dynamics including one-solitoncharacteristics,two-soliton scattering,and ghost solitons,are investigated.

KdV Equation with Self-consistent Sources in Non-uniform Media

Two non-isospectral KdV equations with self-consistent sources are derived. Gauge transformation between the first non-isospectral KdV equation with self-consistent sources （corresponding to λt = -2aA） and its isospectral counterpart is given, from which exact solutions for the first non-isospectral KdV equation with self-consistent sources is easily listed. Besides, the soliton solutions for the two equations are obtained by means of Hirota＇s method and Wronskian technique, respectively. Meanwhile, the dynamical properties for these solutions are investigated.

Study of the Simultaneous Physical Retrieval Method for Meteorological Parameters over the Continental Plateau of China

It is common knowledge that continental retrieval especially for Qinghai-Xizang Plateau has not been solved todate. In order to explore applicable inverse model and method for continent including the plateau, in this study authors use an improved simultaneous physical retrieval method hereafter referred to as the ISPRM, for computing meteorological parameters from NOAA-10 satellite TOVS data. The retrieval results verified by nearby radiosondesshow that the ISPRM is more applicable for the continental plateau.

THE DETERMINATION OF AN EQUIVALENT ELASTIC MODULUS FOR BODIES WITH CRACKS BY BOUNDARY ELEMENT METHOD

The equivalent elastic modulus of cracked bodies with orderly distributed cracks was computed with the boundary element method. A practical self-consistent scheme has been proposed in consideration of the mutual interaction effects of the cracks. The Influence of friction coefficients and orientation of cracks has been investigated. Some computational examples have been given, and the results show that the proposed method is adequate and the scheme is efficient.

Theoretical study on dynamic effective electroelastic properties of random piezoelectric composites with aligned inhomogeneities

The closed-form solutions of the dynamic problem of heterogeneous piezoelectric materials are formulated by introducing polarizations into a reference medium and using the generalized reciprocity theorem.These solutions can be reduced to the ones of an elastodynamic problem.Based on the effective medium method,these closedform solutions can be used to establish the self-consistent equations about the frequencydependent effective parameters,which can be numerically solved by iteration.Theoretical predictions are compared with the experimental results,and good agreement can be found.Furthermore,the analyses on the effects of microstructure and wavelength on the effective properties,resonance frequencies,and attenuation are also presented,which may provide some guidance for the microstructure design and analysis of piezoelectric composites.

4-苯基嘧啶-2-硫酮互变异构的理论研究

采用B3LYP/6-311 G**方法,计算并考察了4-苯基嘧啶-2-硫酮分子的硫醇式和硫酮式构型进行结构互变质子迁移的两种可能途径:(a)分子内质子迁移,(b)水助质子迁移.计算结果表明,途经(b)所需要的活化能较小,氢键在降低反应活化能方面起着重要作用.Onsager自洽反应场溶剂模型用于水相的计算,并探讨了水溶剂化效应对异构化过程的几何结构和能量的影响.

2-硫代巴比妥酸互变异构的理论计算

采用B3LYP/6-311G**方法对处于优势构象时的2-硫代巴比妥酸各互变异构体进行了几何全优化和频率计算,CPCM反应场溶剂模型用于水相的计算,得到它们的总能量、零点振动能和溶剂化能.计算结果表明,2-硫代巴比妥酸在气相中和水相中主要以(硫)酮式结构存在.采用相同方法计算并考察了(硫)醇式与(硫)酮式结构进行结构互变质子迁移有分子内质子迁移和水助质子迁移2种可能途径.计算结果表明,水助质子迁移所需要的活化能较小,氢键在降低反应活化能方面起着重要作用.

A UNIFIED ENERGY APPROACH TO A CLASS OF MICROMECHANICS MODELS FOR COMPOSITE MATERIALS

Several micromechanics models for the determination of composite moduli are investigated in this paper,including the dilute solution,self-consistent method,generalized self-consistent method,and Mori-Tanaka's method.These mi- cromechanical models have been developed by following quite different approaches and physical interpretations.It is shown that all the micromechanics models share a common ground,the generalized Budiansky's energy-equivalence framework.The dif- ference among the various models is shown to be the way in which the average strain of the inclusion phase is evaluated.As a bonus of this theoretical development,the asymmetry suffered in Mori-Tanaka's method can be circumvented and the applica- bility of the generalized self-consistent method can be extended to materials contain- ing microcracks,multiphase inclusions,non-spherical inclusions,or non-cylindrical inclusions.The relevance to the differential method,double-inclusion model,and Hashin-Shtrikman bounds is also discussed.The application of these micromechanics models to particulate-reinforced composites and microcracked solids is reviewed and some new results are presented.

Effective electroelastic constants for three-phase confocal elliptical cylinder model in piezoelectric quasicrystal composites

A three-phase confocal elliptical cylinder model is proposed to analyze micromechanics of one-dimensional hexagonal piezoelectric quasicrystal （PQC） compos- ites. Exact solutions of the phonon, phason, and electric fields are obtained by using the conformal mapping combined with the Laurent expansion technique when the model is subject to far-field anti-plane mechanical and in-plane electric loadings. The effective elec- troelastic constants of several different composites made up of PQC, quasicrystal （QC）, and piezoelectric （PE） materials are predicted by the generalized self-consistent method. Numerical examples are conducted to show the effects of the volume fraction and the cross-sectional shape of inclusion （or fiber） on the effective electroelastic constants of these composites. Compared with other micromechanical methods, the generalized self- consistent and Mori-Tanaka methods can predict the effective electroelastic constants of the composites consistently.

Mechanical properties of irradiated multi-phase polycrystalline BCC materials

Structure materials under severe irradiations in nuclear environments are known to degrade because of irradiation hardening and loss of ductility,resulting from irradiation-induced defects such as vacancies,interstitials and dislocation loops,etc.In this paper,we develop an elastic-viscoplastic model for irradiated multi-phase polycrystalline BCC materials in which the mechanical behaviors of individual grains and polycrystalline aggregates are both explored.At the microscopic grain scale,we use the internal variable model and propose a new tensorial damage descriptor to represent the geometry character of the defect loop,which facilitates the analysis of the defect loop evolutions and dislocation-defect interactions.At the macroscopic polycrystal scale,the self-consistent scheme is extended to consider the multiphase problem and used to bridge the individual grain behavior to polycrystal properties.Based on the proposed model,we found that the work-hardening coefficient decreases with the increase of irradiation-induced defect loops,and the orientation/loading dependence of mechanical properties is mainly attributed to the different Schmid factors.At the polycrystalline scale,numerical results for pure Fe match well with the irradiation experiment data.The model is further extended to predict the hardening effect of dispersoids in oxide-dispersed strengthened steels by the considering the Orowan bowing.The influences of grain size and irradiation are found to compete to dominate the strengthening behaviors of materials.

Collective Hamiltonian for Multi-O（4） Model

The collective Bamiltonian up to the fourth order for multi-O（4） model is derived based on the self-consistent collective-coordinate （SCC） method, which is formulated in the framework of the time-dependent Hartree-Bogoliubov （TDHB） theory. The validity of the collective Hamiltonian is checked in the two special cases of the multi-O（4） model： the case where the number of the shells is equal to one （a single j-shell case）, and the case where the Hartree-Bogoliubov equilibrium point is spherical （the spherical case）. The collective Hamiltonian constitutes a good starting point to study nuclear shape coexistence.

An efficient numerical approach to electrostatic microelectromechanical system simulation

Computational analysis of electrostatic microelectromechanical systems （MEMS） requires an electrostatic analysis to compute the electrostatic forces acting on micromechanical structures and a mechanical analysis to compute the deformation of micromechanical structures. Typically, the mechanical analysis is performed on an undeformed geometry. However, the electrostatic analysis is performed on the deformed position of microstructures. In this paper, a new efficient approach to self-consistent analysis of electrostatic MEMS in the small deformation case is presented. In this approach, when the microstructures undergo small deformations, the surface charge densities on the deformed geometry can be computed without updating the geometry of the microstructures. This algorithm is based on the linear mode shapes of a microstructure as basis functions. A boundary integral equation for the electrostatic problem is expanded into a Taylor series around the undeformed configuration, and a new coupled-field equation is presented. This approach is validated by comparing its results with the results available in the literature and ANSYS solutions, and shows attractive features comparable to ANSYS.

A new theory for symmetry orbital and tensor (Ⅱ)——Symmetric reduction of molecular integrals and self-consistent field calculations

The symmetry orbital-symmetry orbital tensor method is applied to the evaluation of molecular integrals (one-electron and two-electron integrals) and the symmetry-orbital-tensor and self-consistent-field (SOT-SCF) calculations. A calculation scheme is proposed to simplify the evaluation of integrals and a key equation is derived to reduce the computation efforts in SCF iterations. According to the key equation, compared with the traditional SCF method, the computation efficiencies including CPU timing and external disk (or internal memory) requirement increase in the magnitude of the square of the order of a point group. The new SOT method is expected to be useful in the theoretical calculations of large molecular systems of high point group symmetries.

A Limit Symmetry of Modified KdV Equation and Its Applications

In this letter we consider a limit symmetry of the modified KdV equation and its application. The similarity reduction leads to limit solutions of the modified KdV equation. Besides, a modified KdV equation with new self-consistent sources is obtained and its solutions are derived.

Equivalent inclusions in micromechanics with interface energy effect

In order to apply classical micromechanics in predicting the effective prop- erties of nanocomposites incorporating interface energy, a concept of equivalent inclusion （EI） is usually adopted. The properties of EI are obtained by embedding a single inclusion with the interface into an infinite matrix. However, whether such an EI is universal for different micromechanics-based methods is rarely discussed in the literature. In this pa- per, the interface energy theory is used to study the applicability of the above mentioned EI. It is found that some elastic properties of the EI are related only to the properties of the inclusion and the interface, whereas others are also related to the properties of the matrix. The former properties of the EI can be applied to both the classical Mori-Tanaka method （MTM） and the generalized self-consistent method （GSCM）. However, the latter can be applied only to the MTM. Two kinds of new EIs are proposed for the GSCM and used to estimate the effective mechanical properties of nanocomposites.

EFFECTS OF MICROSTRUCTURE ON THE MACROSCOPIC ELASTO-PLASTIC PROPERTIES OF METAL MATRIX COMPOSITES

The generalized self-consistent finite-element iterative averaging method was adopted to analyze the elasto-plastic tensile properties of SiC whiskers reinforced aluminum matrix composites. The effects of varying fiber's aspect ratio and volume fraction on the macroscopic elasto-plastic deformation of the composites were studied. By the analysis of microscopic stress fields, the relation between the propagation of the elasto-plastic region in the matrix and the macroscopic elasto-plastic deformation of composites was discussed. It was found that the propagation of the plastic region in the matrix between the fiber's ends would affect prominently the elasto-plastic tensile behaviour of the composites. It was shown that the characterization of the stress-strain response in terms of the 0.2% offset yield strength is incomplete.

AN EXPLICIT EXPRESSION OF THE EFFECTIVE MODULI FOR COMPOSITE MATERIALS FILLED WITH COATED INCLUSIONS

The obvious shortcoming of the generalized self-consistent method (GSCM) is that the effective shear modulus of composite materials estimated by the method can not be expressed in an explicit form. This is inconvenient in engineering applications. In order to overcome that shortcoming of GSCM, a reformation of GSCM is made and a new micromechanical scheme is suggested in this paper. By means of this new scheme, both the effective bulk and shear moduli of an inclusion-matrix composite material can be obtained and be expressed in simple explicit forms. A comparison with the existing models and the rigorous Hashin-Shtrikman bounds demonstrates that the present scheme is accurate. By a two-step homogenization technique from the present new scheme, the effective moduli of the composite materials with coated spherical inclusions are obtained and can also be expressed in an explicit form. The comparison with the existing theoretical and experimental results shows that the present solutions are satisfactory. Moreover, a quantitative comparison of GSCM and the Mori-Tanaka method (MTM) is made based on a unified scheme.

Ab Initio Calculation of Accurate Electronic and Transport Properties of Zinc Blende Gallium Antimonide (zb-GaSb)

This article reports the results of our investigations on electronic and transport properties of zinc blende gallium antimonide (zb-GaSb). Our ab-initio, self-consistent and non-relativistic calculations used a local density approximation potential (LDA) and the linear combination of atomic orbital formalism (LCAO). We have succeeded in performing a generalized minimization of the energy, using the Bagayoko, Zhao and Williams (BZW) method, to reach the ground state of the material while avoiding over-complete basis sets. Consequently, our results have the full physical content of density functional theory (DFT) and agree with available, corresponding experimental data. Using an experimental room temperature lattice constant of 6.09593?, we obtained a direct band gap of 0.751 eV, in good agreement with room temperature measurements. Our results reproduced the experimental locations of the peaks in the total density of valence states as well as the measured electron and hole effective masses. Hence, this work points to the capability of ab-initio DFT calculations to inform and to guide the design and the fabrication of semiconductor based devices—provided a generalized minimization of the energy is performed.