弱界面端初始失效位置的试验初探

通过双材料受压试验研究了弱奇异性界面端的界面初始脱粘点的位置问题。实验材料采用钢和有机玻璃,根据弱奇异性要求和界面端应力分布特征,设计、制作了试件,并进行了初始脱粘实验。由实验发现楔形角为30°、45°和55°试件的界面初始脱粘点位置均在界面内部,脱粘是由有限应力引起的。63°是个临界角楔形角,大于63°试件,脱粘多会从界面端开始,即脱粘由奇异的界面应力引起的。此外界面正应力若为拉应力时,它对界面脱粘有很大的贡献。     

Wavelet-numerical method in crack analysis

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Hadamard's Fundamental Solution and Conical Refraction

Conical refraction in anisotropic media shows two different light speeds, hence the charaderistic conoid is composed of two sheets. In a special case that two of the dielectric constants are equal, conic refraction is depicted by a partial differential operator which is factorizable. Thus the singular support of the fundamental solution should also be composed of two sheets. In this paper, the author gives the Hadamard construction of the fundamental solution which is just singular on these two sheets. In case of conic refraction considered, these two sheets are tangent to each other along two bi-characteristic curves, and a special singularity of the boundary-layer type appears there.     

运用小波分析处理结构优化问题

结构优化设计中,常遇到具有奇异的结构优化问题,利用小波分析在奇异性检测中的优越性,将其引入到结构优化计算中。文中分别讨论了小波分析处理低维和高维结构优化问题,并给出相应的算法及计算步骤。最后,给出较为典型的算例。通过算例表明,小波分析方法可解决具有奇异性的结构优化问题,尤其是某些较为特殊的结构优化问题。     

Singularity in Potential,Perturbation and Variational Methods

We carefully study the energy eigen-values and splitting of heavy quarkonia as there exist 1/r³ and δ³(r) singular terms in the potential which make a direct numerical solution of the Schrodinger equation impossible. We compare the results obtained in terms of perturbation and variational methods with various treatments.     

ON FINITE NORMAL SERIES SOLUTIONS OF THE SCHRÖDINGER EQUATION WITH IRREGULAR SINGULARITY

We compute all potentials with the following property: The one-dimensional nonrelativistic Schrödinger equation for these potentials has irregular singular points at infinity and/or zero and is solved by a finite normal series. We restrict to expansion order zero, discuss some properties of the potentials obtained and, as an application, calculate for some given potentials exact solutions and energies. The aim of this paper is to provide a tool for finding exact solutions of the Schrödinger equation for a large class of singular potentials.     

Dynamics of a self-propelled particle under different driving modes in a channel flow

In this paper, a model that combines the lattice Boltzmann method with the singularity distribution method is proposed to simulate a self-propelled particle swimming(exhibiting translation and rotation) in a channel flow. The results show that the velocity distribution for a self-propelled particle swimming deviates from a Maxwellian distribution and exhibits highvelocity tails. The influence of an eccentric potential doublet on the translation velocity of the particle is significant. The velocity decay process can be described using a double exponential model form. No large differences in the velocity distribution were observed for different translation Reynolds numbers, rotation Reynolds numbers, or regular intervals.     

Boundedness of semilinear Duffing equations with singularity

We prove the boundedness of all solutions for the equation x＂ ＋ V＇（x） = DxG（x,t）, where V（x） is of singular potential, i.e., limx→-1 Y（x） = ∞, and G（x, t） is bounded and periodic in t. We give sufficient conditions on V（x） and G（x, t） to ensure that all solutions are bounded.     

Bifurcation of multi-freedom gear system with spalling defect

This study focuses on the bifurcation characteristics of the four degree-of-freedom gear system with local spalling defect to explore the spalling nonlinear dynamic mechanism. The dynamic model of the gear system with spalling defect, time-variant mesh stiffness, and nonlinear clearance is established to investigate the effect of spalling defect on mesh stiffness and dynamic bifurcation. The primary resonance and internal resonance responses of the spalling model are analyzed by the averaging method, and the bifurcation characteristics with the evolvement of spall and internal excitation are studied by employing the singularity theory for the two-state variable system, which reveal the different bifurcation characteristics caused by the spalling defect. The results obtained herein can provide a theoretical basis to spalling fault diagnosis of gearbox.     

On the singularities of composition of entire functions

Let f be an entire function. A point zo is called a critical point of f if f'(zo) = 0, and f(zo) is called a critical value (or an algebraic singularity) of f. Next a ∈ (C^) is said to be an asymptotic value (or a transcendental singularity) of f if there exists a curve Γ:[0,1]→(C^) such that limt→1Γ(t)=∞ and limt→1(foΓ)(t)=a. In this paper we find relations between the asymptotic values of f, g and f o g, relations between critical points of f, g and f o g and also in the case when the two functions f and g are semi-conjugated with another entire function.