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Superconductivity of small metal grains

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Science China(physics,Mechanics & Astronomy) 2005年第4期48卷 431-441页

作者： ZHENG Renrong1 CHEN Zhiqian2.& ZHU Shunquan1,3.1. department of physics, {2. Normal {3., {2. 2.02.4, China 2. department of physics, Southwest Normal {3., Chongqing 400715, China 3. department of Computer and Electric Technology, {2. Business School, {2. 2.1400, China department of physics Shanghai Normal University Shanghai China department of physics Southwest Normal University Chongqing China department of Computer and Electric Technology Shanghai Business School Shanghai China

The formulas of the energy gap and superconducting critical temperature appropriate for systems with both odd and even number of electrons are derived; the bases of the derivations are BCS theory and energy level statistics. Numerical results qualitatively agree with the experimental phenomena. i.e., the superconductivity of small metallic grains will first enhance then decrease to zero when the grain are getting smaller and smaller. The calculations indicate that the above phenomena happen in the metallic grains belonging to Gaussian Orthogonal Ensemble (GOE) and Gaussian Unitary ensemble (GUE) with zero spin; The superconductivity of small metallic grains in Gaussian Symplectic Ensemble (GSE) will monotonically decrease to zero with the decreasing of the grain size. The analyses suggest that the superconductivity enhancements come from pairing and the balance of the strengths between spin-orbital coupling and external magnetic field. In order to take the latter into account, it is necessary to include the level statistics given by Random Matrix Theory (RMT) in describing small metallic grains.

关键词： size effect, superconductivity enhancements, small metallic grains.

A MODIFIED LEVENBERG-MARQUARDT ALGORITHM FOR SINGULAR SYSTEM OF NONLINEAR EQUATIONS

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Journal of Computational Mathematics 2003年第5期21卷 625-636页

作者： Jin-yan Fan (department of Mathematics, shanghai jiaotong university, {2. 2.02.0, China) department of Mathematics Shanghai Jiaotong University 上海 200240

Based on the work of paper [1], we propose a modified Levenberg-Marquardt algoithm for solving singular system of nonlinear equations F(x) = 0, where F(x) : Rn - Rn is continuously differentiable and F'(x) is Lipschitz continuous. The algorithm is equivalent to a trust region algorithm in some sense, and the global convergence result is given. The sequence generated by the algorithm converges to the solution quadratically, if ||F(x)||2.provides a local error bound for the system of nonlinear equations. Numerical results show that the algorithm performs well.

关键词： Singular nonlinear equations Levenberg-Marquardt method Trust region al- gorithm Quadratic convergence.

Ultrafast excitation relaxation in light-harvesting complex LH2.from *** 601

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Science China Chemistry 2004年第3期47卷 192-199页

作者： GUO Lijun1,2. LIU Yuan3. LIU Weimin2. GUO Junhua1, XU Chunhe3.& QIAN Shixiong2.1. School of {3. and Information Optoelectronics, Henan university, Kaifeng 475001, China 2. {3. {3., Fudan university, shanghai 2.043., China 3. shanghai Institute of Plant Physiology, Chinese Academy of Sciences, shanghai 2.003., China School of physics and Information Optoelectronics Henan University Kaifeng China physics department Fudan University Shanghai China shanghai Institute of Plant Physiology Chinese Academy of Sciences Shanghai China

The energy relaxation and kinetic evolution of transient spectra of bacteriochloro- phylls (BChls) in light-harvesting complex LH2.from Rb. sphaeroides 601 were investigated using femtosecond pump-probe technique. Upon 783.nm excitation, the energy at B800 BChls ex-periences an intramolecular redistribution with 0.3. ps time constant before transferring to B850 BChls. With tuning the excitation wavelength, the dynamical evolution of excited BChls was clearly observed, which indicates an obvious competition between the ground state bleaching and excited state absorption (ESA) of BChls involved and an isosbestic point near 818 nm, and also demonstrates that from the lower electronic excited state of B800 BChls to the higher exci-tonic state of B850 BChls is an efficient routine for energy transfer. The excitation energy in higher excitonic states of B850 BChls relaxes rapidly to the next lowest excitonic state by inter-conversion, delocalization to adjacent molecular, populating the lowest excitonic state and the change of molecular conformation.

关键词： photosynthesis, light-harvesting complex, energy transfer, ultrafast, dynamics, purple bacteria.

Some variational principles in electroelastic media under finite deformation

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Science China(physics,Mechanics & Astronomy) 2008年第9期51卷 1390-1402页

作者： KUANG ZhenBang department of Engineering Mechanics,shanghai {2. {3.,shanghai 2.02.0,China department of Engineering Mechanics Shanghai Jiaotong University Shanghai China

It is proposed that the universal thermodynamic energy variational principle is in-cluded in the first law of thermodynamics. Some variational principles in the elec-troelastic media under finite deformation are derived from this universal thermo-dynamic variational principle. It is suggested that in the general electroelastic analysis the environment should be considered together with the discussed elec-troelastic medium. For the variational principle of nonlinear electroelastic media the variation of the electric potential is coupled with the virtual displacement,and the variation of the initial volume should be considered. The Maxwell stress in the initial configuration is naturally derived from this variational principle and it is unique in the second order precision.

关键词： first law of thermodynamics variational principle the electroelastic media the governing equation

Boundary element-free method for elastodynamics

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Science China(physics,Mechanics & Astronomy) 2005年第6期48卷 641-657页

作者： CHENG Yumin1 & PENG Miaojuan2.1. shanghai Institute of Applied Mathematics and Mechanics, shanghai {2., shanghai 2.0072. China 2. department of Civil Engineering, shanghai {2., shanghai 2.0072. China shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai China department of Civil Engineering Shanghai University Shanghai China

The moving least-square approximation is discussed first. Sometimes the method can form an ill-conditioned equation system, and thus the solution cannot be obtained correctly. A Hilbert space is presented on which an orthogonal function system mixed a weight function is defined. Next the improved moving least-square approximation is discussed in detail. The improved method has higher computational efficiency and precision than the old method, and cannot form an ill-conditioned equation system. A boundary element-free method (BEFM) for elastodynamics problems is presented by combining the boundary integral equation method for elastodynamics and the improved moving least-square approximation. The boundary element-free method is a meshless method of boundary integral equation and is a direct numerical method compared with others, in which the basic unknowns are the real solutions of the nodal variables and the boundary conditions can be applied easily. The boundary element-free method has a higher computational efficiency and precision. In addition, the numerical procedure of the boundary element-free method for elastodynamics problems is presented in this paper. Finally, some numerical examples are given.

关键词： moving least-square approximation, improved moving least-square approximation, elastodynamics, boundary integral equation, meshless method, boundary element-free method, Fourier eigen transform.

One of the origins for curved edges of polyethylene singlecrystals

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Chinese Science Bulletin 1998年第7期43卷 564-568页

作者： YAN Deyue department of Applied Chemistry, shanghai jiaotong university,{2., China department of Applied Chemistry Shanghai Jiaotong University Shanghai China

A new concept of lattice strain was developed to explain the origin of the curved edges of polyethylene (PE) single crystals. In the crystallization of PE from poor solvents, the length of critical nucleus generated is rather short. The thin lamellae are thermodynamically unstable especially at high temperature. Thereby, during the growth of PE single crystals an annealing process is going on simultaneously, which results in a reduction of thickness from the center to growing faces of lamellae. It is known that the thinner the single crystals, the bigger the unit-cell dimensions. Consequently, unit-cells in the central part of single crystals formed are somewhat smaller than those in the outer part of the same crystals. In order to fit in with the gradual enlargement of unit-cell dimensions from the center to the edges of single crystals, the lattice planes of a faster growing dominant {110} deform to be a set of parallel arcs of concentric circles. Accordingly, the edge of a slower growing subordinate {200} becomes a part of an ellipse with obvious curvature while the edge of a {110} sector remains almost straight for it is a small part of a large circumference.

关键词： PE single crystals curved lateral habit lattice strain.

An improvement in stability of delay difference systems

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Chinese Science Bulletin 1998年第7期43卷 544-547页

作者： ZHANG Shunian department of Applied Mathematics, shanghai jiaotong university, {2. 2.02.0, China department of Applied Mathematics Shanghai Jiaotong University Shanghai China

A new result on the stability of delay difference equations is established, in which a kind of weighted norm for x is adopted in order to estimate the upper bound of Liapunov functional.

关键词： delay difference systems uniform asymptotic stability in terms of two measures Liapunov functionals.

Different-Periodic Travelling Wave Solutions for Nonlinear Equations

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Communications in Theoretical physics 2004年第4期41卷 481-486页

作者： YE Li-Jun~1 LIN Ji~(1,2.1 department of physics,Zhejiang Normal {2.,Jinhua 3.0}004,China2.physics department,shanghai Jiao Tong {2.,shanghai 2.003.,China department of physics Zhejiang Normal University Jinhua 321004 China physics department Shanghai Jiao Tong University Shanghai 200030 China

Using Jacobi elliptic function linear superposition approach for the(1+1)-dimensional Caudrey-Dodd-Gibbon-Sawada-Kotera(CDGSK)equation and the(2.1)-dimensional Nizhnik-Novikov-Veselov(NNV)equation,many new periodic travelling wave solutions with different periods and velocities are obtained based on the knownperiodic *** procedure is crucially dependent on a sequence of cyclic identities involving Jacobi ellipticfunctions sn(ξ,m),cn(ξ,m),and dn(ξ,m).

关键词： linear superposition nonlinear equation travelling wave solution

Characteristics of fMRI BOLD signal and its neurophysiological mechanism

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Progress in Natural Science:Materials International 2007年第6期17卷 630-638页

作者： Zhao Xiaohu1,2. Wu Yigen3.and Guo Shengli3.1. College of Life Sciences, Zhejiang university, Hangzhou 3.0058, China 2. Imaging {3. of Tongji Hospital of Tongji university, {3. 2.0065, China 3. College of Mathematics and physics, Nanjing university of Information Science and Technology, Nanjing 2.0044, China) College of Life Sciences Zhejiang University Hangzhou 310058 China Imaging department Tongji Hospital Tongji University Shanghai 200065 China College of Mathematics and physics Nanjing University of Information Science and Technology Nanjing 210044 China

The functional magnetic resonance imaging (fMRI) based on blood oxygen level dependent (BOLD) contrast has emerged as one of the most potent noninvasive tools for mapping brain function and has been widely used to explore physiological, pathological changes and mental activity in the brain. Exploring the nature and property of BOLD signal has recently attracted more attentions. Despite that great progress has been made in investigation of the characteristics and neurophysiological basis, the exact nature of BOLD signal remains unclear. In this paper we discuss the characteristics of BOLD signals, the nonlinear BOLD response to external stimuli and the relation between BOLD signals and neural electrophysiological recordings. Furthermore, we develop our new opinions regarding nonlinear BOLD response and make some perspectives on future study.

关键词： functional magnetic resonance imaging blood oxygen level dependent nonlinear response neural electrophysiological activity.