缺陷连续统理论及其在本构方程研究中的应用 Ⅱ.缺陷的规范场理论

详细评述了缺陷连续统的规范场理论,该理论是近代材料科学和固体力学中新发展起来颇有意义的一个分支。首先强调了Noether定理及其逆定理在构造缺陷规范场理论中的重要性。同时基于Yang-Mills普适规范场构造,包括对SO(3)T(3)群的最小替换和最小耦合原理,系统地介绍了Golebiewska-Lasota,Edelen,Kadic和Edelen等人的原始性工作及他们的贡献。本文表明,Kadic和Edelen的理论是基于一组缺陷动力学的线性连续性方程发展起来的,不能和关于缺陷场的现有几何理论完全协调起来。考虑到这一点,本文提供了另一种方法来建立非线性弹性规范场的相应理论,这里考虑了Poincaré规范群SO(3)T(3).采用类似于研究引力场理论的Kibble方法,导出了缺陷连续统的拉氏密度。非完整坐标变换和非欧联络系数在数学上完全等价于子Poincaré群SO(3)T(3)的规范场。因此,本文的规范场理论和4维物质流形的缺陷场的非线性几何理论是完全一致的,并证明在弱缺陷条件下,可以简化到Kadic和Edelen的结果。

Decomposition of Noncommutative U(1) Gauge Potential

We investigate the decomposition of noncommutative gauge potential (A) over cap (i), and find that it has inner structure, namely, (A) over cap (i) can he decomposed in two parts, (b) over cap (i) and (a) over cap (i), where (b) over cap (i) satisfies gauge transformations while (a) over cap (i) satisfies adjoint transformations, so close the Seiberg-Witten mapping of noncommutative, U(1) gauge potential. By, means of Seiberg-Witten mapping, we construct a mapping of unit vector field between noncommutative space and ordinary space, and find the noncommutative U(1) gauge potential and its gauge field tensor can be expressed in terms of the unit vector field. When the unit vector field has no singularity point, noncommutative gauge potential and gauge field tensor will equal ordinary gauge potential and gauge field tensor

Topological solitons in the CPN model

We investigate the solitons in the CPN supercript stop model in terms of the decomposition of gauge potential. Based on the phi-mapping topological current theory, the charge and position of solitons is determined by the properties of the typical component. Furthermore, the motion and the bifurcation of multi-soliton is discussed. And the knotted solitons in high dimension is explored also.

Guiding and confining fast electrons by transient electric and magnetic fields with a plasma inverse cone

The fast electron propagation in an inverse cone target is investigated computationally and experimentally. Two-dimensional particle-in-cell simulation shows that fast electrons with substantial numbers are generated at the outer tip of an inverse cone target irradiated by a short intense laser pulse. These electrons are guided and confined to propagate along the inverse cone wall, forming a large surface current. The propagation induces strong transient electric and magnetic fields which guide and confine the surface electron current. The experiment qualitatively verifies the guiding and confinement of the strong electron current in the wall surface. The large surface current and induced strong fields are of importance for fast ignition related researches.

Coherent tunnelling in coupled quantum wells under a uniform magnetic fields

Coherent tunnelling is studied in framework of the effective mass approximation for an asymmetric coupled quantum well. The Hartree potential due to the electron-electron interaction is considered in our calculation. The effects of the longitudinal and transverse magnetic field on coherent tunnelling characteristics are discussed. It has been found that the external field plays an important role in modulating the electron states.

Stress-strain fields and the effectiveness shear properties for three-phase composites with imperfect interface

Based on the 'average stress in the matrix' concept of Mori and Tanaka (:Mori, T., Tanaka, K., 1973. Average stress in matrix and average elastic energy of materials with misfitting inclusion. Acta Metall. 21, 571-580) a micromechanical model is presented for the prediction of the elastic fields in coated inclusion composites with imperfect interfaces. The solutions of the effective elastic moduli for this kind of composite are also obtained. In two kinds of composites with coated particulates and fibers, respectively, the interface imperfections are takes to the assumption that the interface displacement discontinues are linearly related to interface tractions like a spring layer of vanishing thickness. The resulting effective shear modulus for each material and the stress fields in the composite are presented under a transverse shear loading situation.

Influence of Local Magnetic Fields on P-Doped Si Floating Zone Melting Crystal Growth in Microgravity

A two-dimensional axisymmetric numerical model is presented to study the influence of local magnetic fields on P-doped Si floating zone melting crystal growth in microgravity. The model is developed based on the finite difference method in a boundary-fitted curvilinear coordinate system. Extensive numerical simulations are carried out, and parameters studied include the curved growth interface shape and the magnetic field configurations. Computed results show that the local magnetic field is more effective in reducing the impurity concentration nonuniformity at the growth interface in comparison with the longitudinal magnetic field. Moreover, the curved growth interface causes more serious impurity concentration nonuniformity at the growth interface than the case with a planar growth interface.

DPIV and Interferometry Technique for Velocity Field and Concentration Fields Measurement in Crystal Growth

The property of crystal depends seriously on the solution concentration distribution near the growth surface of a crystal. However, the concentration distributions are affected by the diffusion and convection of the solution. In the present experiment, the two methods of optical measurement are used to obtained velocity field and concentration field of NaClO₃ solution. The convection patterns in sodium chlorate (NaClO₃) crystal growth are measured by Digital Particle image Velocimetry (DPIV) technology. The 2-dimentional velocity distributions in the solution of NaClO3 are obtained from experiments. And concentration field are obtained by a Mach-Zehnder interferometer with a phase shift servo system. Interference patterns were recorded directly by a computer via a CCD camera. The evolution of velocity field and concentration field from dissolution to crystallization are visualized clearly. The structures of velocity fields were compared with that of concentration field.

Real-Time Measurement on Deformation Fields of Hole-Excavated Samples under Impact Tension

In this paper, the real-time deformation fields are observed in two different kinds of hole-excavated dog-bone samples loaded by an SHTB, including single hole sample and dual holes sample with the aperture size of 0.8mm. The testing system consists of a high-speed camera, a He-Ne laser, a frame grabber and a synchronization device with the controlling accuracy of I microsecond. Both the single hole expanding process and the interaction of the two holes are recorded with the time interval of 10 mu s. The observed images on the sample surface are analyzed by newly developed software based on digital correlation theory and a modified image processing method. The 2-D displacement fields in plane are obtained with a resolution of 50 mu m and an accuracy of 0.5 mu m. Experimental results obtained in this paper are proofed, by compared with FEM numerical simulations.

Elastic fields of interacting elliptic inhomogeneities

This paper presents a method for the calculation of two-dimensional elastic fields in a solid containing any number of inhomogeneities under arbitrary far field loadings. The method called 'pseudo-dislocations method', is illustrated for the solution of interacting elliptic inhomogeneities. It reduces the interacting inhomogeneities problem to a set of linear algebraic equations. Numerical results are presented for a variety of elliptic inhomogeneity arrangements, including the special cases of elliptic holes, cracks and circular inhomogeneities. All these complicated problems can be solved with high accuracy and efficiency.