平行电磁场中里德堡氢原子的自相似结构研究

利用半经典方法研究了平行电磁场中里德堡氢原子的分形自相似现象. 通过研究平行电磁场中里德堡氢原子的逃逸时间和初始出射角间的关系, 发现了逃逸时间图的自相似结构, 并通过研究与图中冰柱对应的逃逸轨道, 得到了自相似结构和逃逸轨道之间的关系, 发现了该类自相似逃逸轨道满足的规律. 进一步研究了标度能量和标度磁场对体系动力学的影响, 表明标度能量和标度磁场均控制体系的分形自相似结构. 当标度能量或标度磁场比较小时, 没有自相似现象, 随着标度能量或标度磁场的增大, 自相似出现, 体系变复杂.     

Revisiting Aromaticity and Chemical Bonding of Fluorinated Benzene Derivatives

The electron delocalization of benzene (C₆H₆) and hexafluorobenzene (C₆F₆) was analyzed in terms of the induced magnetic field, nucleus-independent chemical shift (NICS), and ring current strength (RCS). The computed out-of-plane component of the induced magnetic field at a distance (r) greater than or equal to 1.0 Å above the ring center correlates well (R²>0.99) with the RCS value. According to these criteria, fluorination has two effects on the C₆ skeleton; concomitantly, the resonant effects diminish the π electron delocalization and the inductive effects decrease the charge density at the ring center and therefore reduce the magnitude of the paratropic current generated in this region. The equilibrium between both effects decreases aromaticity in the fluorinated benzene derivatives. These results can be extrapolated to determine the aromaticity of any derivative within the series of fluorinated benzene derivatives (C₆H_(6−n)F_n, where n=1–5).     

Shock induced Richtmyer-Meshkov instability in the presence of a wall boundary layer

An experimental investigation on gaseous mixing zones originated from the Richtmyer-Meshkov instability has been undertaken in a square cross section shock tube. Mass concentration fields, of one of the two mixing constituents, have been determined within the mixing zone when the shock wave passes from the heavy gas to the light one, from one gas to an other of close density, and from the light gas to the heavy one. Results have been obtained before and after the coming back of the reflected shock wave. The diagnostic method is based on the infrared absorption of one of the two constituents of the mixing zone. It is shown that the mixing zone is strongly deformed by the wall boundary layer. The consequence is the presence of strong gradients of concentration in the direction perpendicular to the shock wave propagation. Finally, it is pointed out that the mixing goes more homogeneous when the Atwood number tends to zero.     

Three-dimensional analysis of defects in a piezoelectric material

In this paper, the Green's function technique is used to develop a solution of an infinite, piezoelectric medium containing either an ellipsoidal cavity or a flat elliptical crack. The coupled elastic and electric fields both inside the cavity and on the boundary of the cavity are obtained, and the stress intensity factor and the electric field intensity factor are also obtained for an elliptical crack. It is found that; (1) the coupled elastic and electric fields inside the cavity keep uniform when the external elastic field and electric field are constant; (2) the behavior of the stress and electric field components in the neighborhood of the crack tip shows the classical type of singularity. The project supported by National Natural Science Foundation of China     

On the relationship between the solutions of static contact problems of elasticity and electroelasticity for a half-space

The paper establishes the relationship between the static contact problems of elasticity and electroelasticity (in the absence of friction) for a transversely isotropic half-space whose surface is the isotropy plane. This makes it possible to avoid solving the electroelastic problem by finding all the characteristics of electroelastic contact from known cases of purely elastic interaction. Moreover, the electroelastic state of the half-space can be fully described using a known harmonic function, which is a solution of the purely elastic problem. The approach is exemplified by solving contact problems of electroelasticity for flat, elliptic, two circular, conical, and paraboloidal (circular and elliptic in plan) punches __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 11, pp. 69–84, November 2006.     

Thermomechanical Behavior of Electrically Conducting Solids Exposed to an External Electromagnetic Field

This paper describes a procedure for the mathematical and numerical modeling of the thermomechanical behavior of electrically conducting solid bodies exposed to an external electromagnetic field. The constitutive equations for the electromagnetic field are the Maxwell equations written for the region of the solid body and the ambient medium. The stress-strain state of the solid is described using the relations for nonisothermal elastoplastic flow. The effects of the electromagnetic field on the heat-transfer and deformation processes are taken into account via heat release and ponderomotive forces, respectively. The relations between the electric and magnetic inductions and the corresponding field strengths are considered nonlinear. All physicomechanical parameters of the body material are temperature dependent.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 14–26, September–October, 2005.     

Efficient approximation of random fields for numerical applications

This article is dedicated to the rapid computation of separable expansions for the approximation of random fields. We consider approaches based on techniques from the approximation of non‐local operators on the one hand and based on the pivoted Cholesky decomposition on the other hand. Especially, we provide an a posteriori error estimate for the pivoted Cholesky decomposition in terms of the trace. Numerical examples are provided to validate and quantify the presented methods. Copyright © 2015 John Wiley & Sons, Ltd.     

Subcritical Hamilton–Jacobi fractional equation in

Solvability of Cauchy's problem in for fractional Hamilton–Jacobi equation (1.1) with subcritical nonlinearity is studied here both in the classical Sobolev spaces and in the locally uniform spaces. The first part of the paper is devoted to the global in time solvability of subcritical equation (1.1) in locally uniform phase space, a generalization of the standard Sobolev spaces. Subcritical growth of the nonlinear term with respect to the gradient is considered. We prove next the global in time solvability in classical Sobolev spaces, in Hilbert case. Regularization effect is used there to guarantee global in time extendibility of the local solution. Copyright © 2014 John Wiley & Sons, Ltd.