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A complex variable meshless method for fracture problems

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Science china(physics,Mechanics & Astronomy) 2006年第1期49卷 46-59页

作者： CHENG Yumin1 & LI Jiuhong2.1. shanghai institute of {2. Mathematics and Mechanics, shanghai University, shanghai 2.0072. china 2. Department of Building Engineering, Xi’an University of Technology, Xi’an 710048, china shanghai institute of {2. Mathematics Mechanics Shanghai University Shanghai 200072 China Department of Building Engineering Xi’an University of Technology Xi’an 710048 China

Based on the moving least-square (MLS) approximation, the complex variable moving least-square approximation (CVMLS) is discussed in this paper. The complex variable moving least-square approximation cannot form ill-conditioned equations, and has greater precision and computational efficiency. Using the analytical solution near the tip of a crack, the trial functions in the complex variable moving least-square approxi- mation are extended, and the corresponding approximation function is obtained. And from the minimum potential energy principle, a complex variable meshless method for fracture problems is presented, and the formulae of the complex variable meshless method are obtained. The complex variable meshless method in this paper has greater precision and computational efficiency than the conventional meshless method. Some examples are given.

关键词： moving least-square approximation, complex variable moving least-square approximation, meshless method, complex variable meshless method, fracture.

Direct CP violation in hadronic B decays

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Science china(physics,Mechanics & Astronomy) 2006年第3期49卷 357-366页

作者： HONG Bihai1,2.& Lü Caidian3 1. Department of physics, Lishui University, Lishui 32.000,china 2. Department of physics, shanghai Jiaotong University, shanghai 2.0030, china 3. institute of High Energy physics, Beijing 100049,china Department of physics Lishui University Lishui 323000 China Department of physics Shanghai Jiaotong University Shanghai 200030 China institute of High Energy physics Beijing 100049 China

There are different approaches for the hadronic B decay calculations, recently. In this paper, we upgrade three of them, namely factorization, QCD factorization and the perturbative QCD approach based on kT factorization, using new parameters and full wave functions. Although they get similar results for many of the branching ratios, the direct CP asymmetries predicted by them are different, which can be tested by recent experimental measurements of B factories.

关键词： CP violation hadronic B decay factorization.

A pulse radiolysis study on electron affinity of piperonal

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Science china Chemistry 2005年第5期48卷 476-480页

作者： MA Jianhua1, LIN Weizhen2. WANG Wenfeng2.& YAO Side2.1. College of Biology Engineering, Jimei University, Xiamen 36102., china 2. shanghai institute of applied physics, Chinese Academy of Sciences,{2., china 1. College of Biology Engineering Jimei University 361021 Xiamen China 2. shanghai institute of applied physics Chinese Academy of Sciences 201800 Shanghai China

The piperonal electron affinity was studied using pulse radiolysis technique. The electron transfer reaction process between piperonal and anthraquinone-2.sulfate was observed in the pH 7 phosphoric acid salt buffer. The transient absorption spectra of electron transfer re-action between piperonal and anthraquinone-2.sulfate were obtained, and the initial proof of the electron transfer between electron donor and acceptor was provided directly. The one-electron reduction potential of piperonal was determined to be ?0.457 V.

关键词： piperonal, pulse radiolysis, one-electron reduction potential.

Steady-state responses of axially accelerating viscoelastic beams: Approximate analysis and numerical confirmation

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Science china(physics,Mechanics & Astronomy) 2008年第11期51卷 1707-1721页

作者： CHEN LiQun1,2.& DING Hu2.1 Department of Mechanics, shanghai University, shanghai 2.0444,{2. 2.shanghai institute of applied Mathematics and Mechanics, shanghai 2.0070,{2. Department of Mechanics Shanghai University Shanghai 200444 China shanghai institute of {2. Mathematics and Mechanics Shanghai 200070 China

Nonlinear parametric vibration of axially accelerating viscoelastic beams is inves-tigated via an approximate analytical method with numerical confirmations. Based on nonlinear models of a finite-small-stretching slender beam moving at a speed with a periodic fluctuation, a solvability condition is established via the method of multiple scales for subharmonic resonance. Therefore, the amplitudes of steady-state periodic responses and their existence conditions are derived. The amplitudes of stable steady-state responses increase with the amplitude of the axial speed fluctuation, and decrease with the viscosity coefficient and the nonlinear coefficient. The minimum of the detuning parameter which causes the existence of a stable steady-state periodic response decreases with the amplitude of the axial speed fluctuation, and increases with the viscosity coefficient. Nu-merical solutions are sought via the finite difference scheme for a nonlinear par-tial-differential equation and a nonlinear integro-partial-differential equation. The calculation results qualitatively confirm the effects of the related parameters pre-dicted by the approximate analysis on the amplitude and the existence condition of the stable steady-state periodic responses. Quantitative comparisons demonstrate that the approximate analysis results have rather high precision.

关键词： nonlinearity parametric vibration axially accelerating beam method of multiple scales numerical confir-mation

A New Approach to Nonlinear Partial Differential Equations

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Communications in Nonlinear Science and Numerical Simulation 1997年第4期2卷 230-235页

作者： Jihuan HE (shanghai University,shanghai {2. of applied Mathematics and Mechanics,shanghai 2.0 0 0 72.,china) shanghai University Shanghai Institute of Applied Mathematics and Mechanics Shanghai 200072 China

In this paper,a novel method called variational iteration method is proposed to solve nonlinear partial differential equations without linearization or small *** this method,a correction functional is constructed by a general Lagrange multiplier,which can be identified via variational *** analytical solution can be obtained from its trial- function with possible unknown constants,which can be identified by imposing the boundary conditions,by successively iteration.

关键词： Nonlinear Problems Partial Differential Equations Variational Iteration Method Variational Theory

Variational Iteration Method for Delay Differential Equations

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Communications in Nonlinear Science and Numerical Simulation 1997年第4期2卷 235-236页

The variational iteration method is shown to be applicable to delay differential equations for analytical approximate solutions

关键词： Variational Iteration Method for Delay Differential Equations

On two transverse nonlinear models of axially moving beams

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Science china(Technological Sciences) 2009年第3期52卷 743-751页

作者： DING Hu1 & CHEN LiQun1,2.1 shanghai institute of {2. Mathematics and Mechanics, shanghai University, shanghai 2.0072. china 2.Department of Mechanics, shanghai University, shanghai 2.0444, china 1. shanghai institute of {2. Mathematics and Mechanics Shanghai University Shanghai 200072 China 2. Department of Mechanics Shanghai University Shanghai 200444 China

Nonlinear models of transverse vibration of axially moving beams are computationally investigated. A partial-differential equation is derived from the governing equation of coupled planar motion by omit- ting its longitudinal terms. The model can be reduced to an integro-partial-differential equation by av- eraging the beam disturbed tension. Numerical schemes are respectively presented for the governing equations of coupled planar and the two governing equations of transverse motion via the finite dif- ference method and differential quadrature method under the fixed boundary and the simple support boundary. A steel beam and a copper beam are treated as examples to demonstrate the deviations of the solutions to the two transverse equations from the solution to the coupled equation. The numerical results indicate that the differences increase with the amplitude of vibration and the axial speed. Both models yield almost the same precision results for small amplitude vibration and the inte- gro-partial-differential equation gives better results for large amplitude vibration.

关键词： axially moving beam nonlinearity transverse vibration finite difference method differential quadrature method

New Exact Solutions to (2.1)-Dimensional Variable Coefficients Broer-Kaup Equations

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Communications in Theoretical physics 2006年第9期46卷 393-396页

作者： ZHU Jia-Min~(1,2.+) MA Zheng-Yi~(1,2. ~1 Department of physics, Zhejiang Lishui University, Lishui 32.000, china ~2.{2. institute of applied Mathematics and Mechanics, {2. 2.0072. china Department of physics Zhejiang Lishui University shanghai institute of {2. Mathematics and Mechanics

In this paper, using the variable coefficient generalized projected Ricatti equation expansion method, we present explicit solutions of the (2.1)-dimensional variable coefficients Broer-Kaup (VCBK) equations. These solutions include Weierstrass function solution, solitary wave solutions, soliton-like solutions and trigonometric function solutions. Among these solutions, some are found for the first time. Because of the three or four arbitrary functions, rich localized excitations can be found.

关键词： variable coefficient generalized projected Ricatti equation method (2.1)-dimensional variable coefficients Broer Kaup equations Weierstrass function solution solitary wave solution trigonometric function solution

Transient species and its properties of melatonin

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Science china Chemistry 2006年第4期49卷 308-314页

作者： ZHU Hongping1,2. ZHANG Zhaoxia1,2. ZHAO Hongwei1, WANG Wenfeng1 & YAO Side1 1. shanghai institute of {2. physics, Chinese Academy of Sciences, shanghai 2.1.00, china 2. Graduate University of the Chinese Academy of Sciences, Beijing 100049, china 1. shanghai institute of {2. physics Chinese Academy of Sciences Shanghai 201800 China 2. Graduate University of the Chinese Academy of Sciences Beijing 100049 China

The photo-physical and photo-chemical properties of melatonin (ML) werestudied by 2.6 nm laser flash photolysis (LFP). ML undergoes photo-ionization to produce radicalcation of ML (ML^(·+))and hydrated electrons (e_(aq)^-), while excited triplet state ~3ML~* is alsoformed during photolysis. The oxidation via one electron transfer from ML to SO_4^(·+) and thetriplet state of riboflavin (~3RF~*) has been also investigated and the rate constants for theprocess have been determined to be 8.0x10^9 and 1.4x10^9 L·mol^(-1)·s^(-1) respectively. Theradical cation of 2.2.'-azinobis(3-ethylbenzothiazoline-6-sulfonic acid)(ABTS^(·+)) scavengingcapacities of melatonin and other antioxidants are compared in this paper.

关键词： melatonin, laser flash photolysis, photoionization, triplet state.