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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 Applied mathematics and Mechanics, Shanghai University, Shanghai 2.0072. china 2. {2. of Building Engineering, Xi’an University of Technology, Xi’an 710048, china Shanghai Institute of Applied 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.

The mechanism of breakdown in laminar-turbulent transition of a supersonic boundary layer on a flat plate-temporal mode

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Science china(Physics,Mechanics & Astronomy) 2005年第5期48卷 614-625页

作者： HUANG Zhangfeng 1, CAO Wei 1,2.& ZHOU Heng 1,2.1. department of Mechanics, Tianjin University, Tianjin 300072. china 2. Liu-Hui Center of Applied {2., Nankai University and Tianjin University, Tianjin 300072. china 1. department of Mechanics Tianjin University 300072 Tianjin China 2. Liu-Hui Center of Applied mathematics Nankai University and Tianjin University 300072 Tianjin China

Temporal mode direction numerical simulation has been done for the transition of a supersonic boundary layer on a flat plate with Mach number 4.5. Analysis of the result showed that during the breakdown process in laminar-turbulent transition, the mechanism causing the mean flow profile to evolve swiftly from laminar to turbulent was that the modification of mean flow profile by the disturbances,when they became larger,led to a remarkable change of its stability characteristics. Though the most unstable T-S wave was of second mode for laminar flow, the first mode waves played the key role in the breakdown process in laminar-turbulent transition.

关键词： supersonic boundary layer, transition, breakdown.

Thermal-rheological structure of the lithosphere beneath Jiyang Depression:Its implications for geodynamics

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Science china Earth Sciences 2005年第10期48卷 1569-1584页

作者： LIU Shaowen1,2. WANG Liangshu2. GONG Yuling2. LI Cheng2. LI Hua2.& HAN Yongbing2.1. department of Urban and Resources, nanjing University,{2., china 2. department of Earth Sciences, nanjing University,{2., china department of Urban and Resources nanjing University nanjing china department of Earth Sciences nanjing University nanjing china

Jiyang Depression, located in the southeast Bohai Bay Basin, has the geomorpho-logic framework of multiple uplifts intervening with sags. Combined the abundant geo-temperature data and thermo-physical parameters of rock samples derived from oil and gas exploration during the past years, with geothermal approaches, here we investigate the litho-spheric thermal regime of this depression. Consequently, based on the obtained thermal struc-ture of the lithosphere, along with rheological modeling, the lithospheric rheological profiles of Jiyang Depression are then determined. Our results show that the temperature at the bottom of sedimentary cover within depression varies from 12.℃ to 2.8 ℃ , accompanied with the base-ment heat flow ranging between 54.3 and 60.5 mW/m2. and 406℃-436℃ for temperature at the bottom of the upper crust, along with heat flow varying from 47.7 to 52.6 mW/m2. while the tem-perature at the bottom of the middle crust is between 537 ℃ and 572.℃, as well as heat flow ranging from 41.3 to 56.3 mW/m2. The temperature at Moho ranges from 669 ℃ to 72. ℃, the heat flow derived from mantle is between 38.1 and 43.1 mW/m2. and calculated thickness of the thermal lithosphere beneath depression varies from 71 to 90 km. Lithospheric thermal regime is a close correlation with such factors as crustal thickness and surface heat flow, etc. Usually, the larger the surface heat flow, the larger the deep temperature and heat flow within lithosphere, and the thinner the thermal lithospheric thickness. This high thermal regime of the lithosphere in Jiyang Depression is thought to be related to Cenozoic back-arc spreading during the western Pacific plate subduction into Eurasian continent. Lithospheric rheological modeling shows that the lithosphere in Jiyang Depression is characterized by its distinct rheological stratification as follows: The upper and most part of the middle crust are of brittle, while the lower crust and the lower part of middle crust are all ductile

关键词： Jiyang Depression, geothermics, rheology, effective elastic thickness, geodynamics.

A note on n-edge chromatic number

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Chinese Science Bulletin 1997年第23期42卷 1952-1954页

作者： SUN Liang and ZHANG Zhongfu1. department of Applied mathematics, Beijing Institute of Technology, Beijing 100081,{2. 2. Institute of Applied mathematics, Lanzhou Institute of Railway, Lanzhou 730070,{2. department of Applied mathematics Beijing Institute of Technology Beijing 100081 China

ALL graphs appearing in this note are simple. A graph with p vertices and q edges will becalled a (p, q )-graph. The maximum degree of G is denoted by Δ(G).Let n≥2.be an integer. The n-edge chromatic number X_n (G) of a simple graph G is theminimum cardinality of a set of colors with which one can assign the colors to the edges of Gsuch that the edges on a path of length less than or equal to n receive different *** aim of this note is to explore the bounds for X’_n (G) and X’_n (G) + X’_n (G). It is

关键词： graph complement n-edge chromatic number.

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 University, Shanghai 2.0072. china 2. {2. of Civil Engineering, Shanghai University, Shanghai 2.0072. china 1. Shanghai Institute of Applied mathematics and Mechanics Shanghai University 200072 Shanghai China 2. department of Civil Engineering Shanghai University 200072 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.

EPR studies of Mn^(2.) in the Loess Plateau of central china: Implication for variation of the East Asia summer monsoon

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Chinese Science Bulletin 1998年第1期43卷 72-75页

作者： CHEN Jun\+1, JI Junfeng\+1, SU Yuanxia\+2.and LU Huayu\+31. department of Earth Sciences, nanjing University,{2., china 2. Center of Material Analysis, nanjing University,{2., china 3. Xi’an Laboratory of Loess and Qu department of Earth Sciences Nanjing University Nanjing China Center of Material Analysis Nanjing University Nanjing China Xi’an Laboratory of Loess and Quaternary Geology Chinese Academy of Sciences Xi’an China

Mn 2. EPR intensity recorded in the Chinese loess_paleosol sequence shows close correlation with magnetic susceptibility and Sr content as well as the oscillation of paleoclimate. Thus Mn 2. EPR signal can serve as an... 详细信息

关键词： paleomonsoon loess paleosol EPR signal of Mn 2.

Synthesis and Lubrication of Phosphorylcholine Derivative

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Journal of Bionic Engineering 2010年第3期7卷 254-258页

作者： Zhenliang Qiao~1, Dangsheng Xiong~1, Lude Lu~2. Pengju Jiang~2.1. department of Materials Science and Engineering, nanjing University of Science and Technology, nanjing 2.0094, P.R. china 2. School of Chemical Engineering, nanjing University of Science and Technology, nanjing 2.0094, P. R. china [a] department of Materials Science Engineering Nanjing University of Science Technology Nanjing 210094 P.R. China [b] School of Chemical Engineering Nanjing University of Science Technology Nanjing 210094 P. R. China

The monomer of phosphorylcholine derivative, O-(5-（2.methacryloxy）-3, 3-dimethyl-3-azapentyl)-O’-（ω-hydroxy-octyl）-phosphatequaternary ammonium salt, was designed and synthesized successfully. It was characterized by the spectra ofHNMR and Mass spectra （ESI+）, and every signal was assigned. Then the lubricating characteristics of the phosphorylcholinederivative were investigated on the tribological setup of ball-oh-flat. The Ultra-High Molecular Weight Polyethylene（UHMWPE） flat was rotated against a stainless steel ball with 6 mm diameter. The load was 2.3 N, which corresponded to amaximal Hertz contact pressure of 2. MPa. Water, phosphorylcholine derivative, and Acrylic Acid （AA） solution were used aslubricants, respectively. Compared with AA, the phosphorylcholine derivative shows significant lubrication. It can be stronglyhydrated under water due to the charged segment in chemical structure. The thick water layers within the chains serves asboundary lubricants, and this is thought to be the molecular origins of lubricating behavior.

关键词： artificial joint articular cartilage molecular lubrication mechanism phosphorylcholine synthesis UHMWPE

On the variational principle for the topological pressure for certain non-compact sets

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Science china mathematics 2010年第4期53卷 1117-1128页

作者： PEI Yu 1 & CHEN ErCai 1,2.1 department of mathematics,{2. Normal University,{2. 2.0097,china 2.Center for Nonlinear Science,{2. University,{2. 2.0093,china 1. department of mathematics Nanjing Normal University Nanjing 210097 China2. Center for Nonlinear Science Nanjing University Nanjing 210093 China

Let (X,d,T) be a dynamical system,where (X,d) is a compact metric space and T:X → X is a continuous *** assume that the dynamical system satisfies g-almost product property and the uniform separation *** compute the topological pressure of saturated sets under these two *** the uniform separation property does not hold,we compute the topological pressure of the set of generic *** give an application of these results to multifractal analysis and finally get a conditional variational principle.

关键词： uniform separation property g-almost product property topological pressure of non-compact sets variational principle BS-dinmension

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 310058, china 2. Imaging department of Tongji Hospital of Tongji University, Shanghai 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.