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Intermediate processes and critical phenomena: Theory, method and progress of fractional operators and their applications to modern mechanics

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Science china(Physics,Mechanics & Astronomy) 2006年第3期49卷 257-272页

作者： XU Mingyu1 & TAN Wenchang2 1. Institute of applied mathematics, School of Math & System Science, Shandong University, Jinan 250100, china 2. State {3. laboratory of Turbulence and Complex Systems & Department of Mechanics and Engineering Science, Peking University, Beijing 100871, china 1. Institute of applied mathematics School of Math & System Science Shandong University Jinan 250100 China 2. State key laboratory of Turbulence and Complex Systems & Department of Mechanics and Engineering Science Peking University Beijing 100871 China

From point of view of physics, especially of mechanics, we briefly introduce fractional operators (with emphasis on fractional calculus and fractional differential equa- tions) used for describing intermediate processes and critical phenomena in physics and mechanics, their progress in theory and methods and their applications to modern me- chanics. Some authors’ researches in this area in recent years are included. Finally, prospects and evaluation for this subject are made.

关键词： fractional operators,intermediate processes,critical phenomena,modern mechanics

Stability of multiquadric quasi-interpolation to approximate high order derivatives

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Science china mathematics 2010年第4期53卷 985-992页

作者： MA LiMin 1,2 & WU ZongMin 1,1 Shanghai key laboratory for Contemporary applied {3.,School of Mathematical Sciences,Fudan University,Shanghai 20043.,china 2 Department of Information and Computer Science,Zhejiang Gongshang University,Hangzhou 3.0018,china 1. Shanghai key laboratory for Contemporary applied {3. School of Mathematical Sciences Fudan University Shanghai 200433 China2. Department of Information and Computer Science Zhejiang Gongshang University Hangzhou 310018 China

Numerical simulation of the high order derivatives based on the sampling data is an important and basic problem in numerical approximation,especially for solving the differential equations *** classical method is the divided difference ***,it has been shown strongly unstable in ***,it can only be used to simulate the lower order derivatives in *** simulate the high order derivatives,this paper suggests a new method using multiquadric *** stability of the multiquadric quasi-interpolation method is compared with the classical divided difference ***,some numerical examples are presented to confirm the theoretical *** theoretical results and numerical examples show that the multiquadric quasi-interpolation method is much stabler than the divided difference *** property shows that multiquadric quasi-interpolation method is an efficient tool to construct an approximation of high order derivatives based on scattered sampling data even with noise.

关键词： numerical differential radial basis functions (RBFs) Hardy’s multiquadric (MQ) quasiinterpolation divided difference method white noise expectation variance

Determination of Young's modulus by nanoindentation

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Science china(Technological Sciences) 2004年第4期47卷 398-408页

作者： MA Dejun1, Chung Wo Ong2, LIU Jianmin1 & HE Jiawen3.1. Surface Engineering Research Institute, CMES, Beijing 100072, china 2. Department of applied Physics and Materials Research Center, The Hong Kong Polytechnic University, Hong Kong, china 3. State {3. laboratory for Mechanical Behavior of Materials, Xian Jiaotong University, Xian 710049, china 1. Surface Engineering Research Institute CMES 100072 Beijing China 2. Department of applied Physics and Materials Research Center The Hong Kong Polytechnic University Hong Kong China 3. State key laboratory for Mechanical Behavior of Materials Xi’an Jiaotong University 710049 Xi’an China

A methodology for determining Youngs modulus of materials by non-ideally sharp indentation has been developed. According to the principle of the same area-to-depth ratio, a non-ideally pyramidal indenter like a Berkovich one can be approximated by a non-ideally conical indenter with a spherical cap at the tip. By applying dimensional and finite element analysis to the non-ideally conical indentation, a set of approximate one-to-one relationships between the ratio of nominal hardness/reduced Youngs modulus and the ratio of elastic work/total work, which correspond to different tip bluntness, have been revealed. The nominal hardness is defined as the maximum indentation load divided by the cross-section area of the conical indenter specified at the maximum indentation depth. As a consequence, Youngs modulus can be determined from a nanoindentation test only using the maximum indentation load and depth, and the work done during loading and unloading processes. The new method for determining Youngs modulus is referred to as pure energy method. The validity of the method was examined by performing indentation tests on five materials. The experimental results and the standard reference values are in good agreement, indicating that the proposed pure energy method is a promising substitution for the most widely used analysis models at present.

关键词： Young's modulus, nanoindentation, nominal hardness, indentation work.

Study on the Corrosion Resistance of Multiphase TRIP Steels

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Journal of Iron and Steel Research International 2011年第S1期18卷 883-887页

作者： WANG Ji-jie 1,WU Di 2,LI Zhuang 1,GUO Xiang-min 1,HE Chun-lin 3.CAI Qing-kui 3.(1.School of Materials Science and Engineering,Shenyang University of Aeronautics and Astronautics,Shenyang 11013.,Liaoning,china 2.State key laboratory of Rolling and Automation,Northeastern University,Shenyang 110004,china 3.Liaoning province key laboratory for Advanced Materials,Shenyang University,Shenyang 110044,Liaoning,china) Shenyang Univ Aeronaut & Astronaut Sch Mat Sci & Engn Shenyang 110136 Liaoning Peoples R China Northeastern Univ State Key Lab Rolling & Automat Shenyang 110004 Peoples R China Shenyang Univ Liaoning Prov Key Lab Adv Mat Shenyang 110044 Liaoning Peoples R China

Multiphase TRIP (Transformation Induced Plasticity) steels are known to combine higher strength with higher *** this paper,the corrosion resistance of this steel has been has been investigated by accelerated corrosion tests,such as wet/dry cyclic corrosion and the weight loss in *** morphologies of their rust layers were observed by using scanning electron microscopy,and the corrosion performance of these steels was discussed by analyzing the protective *** results show that the corrosion rate of steel A is significantly greater than that of steels B and C in wet/dry cyclic corrosion and weight loss *** corrosion performance of conventional C-Mn-Si TRIP steel is deteriorated in both NaHSO 3.and 3.5 wt.% NaCl aqueous *** superior corrosion performance is exhibited for TRIP steel with low alloying contents due to its high thermodynamic *** enhancement of corrosion performance of TRIP steel is attributed to the additions of alloying elements,such as Al,Cu,Cr,Mo,Ni,*** alloying elements increase the compactness of rust layers,so electrochemical characteristic of TRIP steel is improved.

关键词： TRIP steel alloying element rust layer corrosion performance

Joint exploration of crustal structure in Fuzhou basin and its vicinities by deep seismic reflection and high-resolution refraction as well as wide-angle reflection/refraction

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Science china Earth Sciences 2005年第7期48卷 925-938页

作者： ZHU Jinfang1, XU Xiwei2, ZHANG Xiankang3. HUANG Zonglin1, CHEN Xiangxiong1, FANG Shengming3. LIU Baojin3. ZHENG Rongzhang2,4 1. Seismological Bureau of Fujian province,Fuzhou 3.0003.china 2. Institute of Geology,china Earthquake Administration,Beijing 100029,china 3. Research Center for Exploration Geophysics,china Earthquake Administration,Zhengzhou 450002,china 4. State key laboratory of Earthquake Dynamics,Institute of Geology,china Earthquake Administration,Beijing 100029,china Seismological Bureau of Fujian province Fuzhou 350003 China Institute of Geology China Earthquake Administration Beijing 100029 China Research Center for Exploration Geophysics China Earthquake Administration Zhengzhou 450002 China State key laboratory of Earthquake Dynamics Institute of Geology China Earthquake Administration Beijing 100029 China

The Fuzhou basin and its vicinities are located at the northern end of the southeastern coastal seismic zone of the mainland of china. By the joint explorations of high-resolution seismic refraction and wide-angle reflection/refraction as well as deep seismic reflection in the region, which is the first synthetic profile in china, its fine velocity structure and geometric structure from the ground to Moho discontinuity is obtained. The result shows that the crust is obviously layered with a thickness of about 3. km. Basically, it consists of two parts: upper crust and lower crust. The velocity of the upper crust is 5.9-6.2 km/s in which there is a 3.4-km-thick weak low-velocity layer between the depths of 10-15 km, while the velocity of the lower crust in the range of 6.3.7.2 km/s. There exists a strong velocity gradient layer about 3.km thick above the Moho discontinuity whose velocity increases from 6.5 to 7.27 km/s. There exist high-angle normal faults that are small in size and extend only in the shallow crust. These faults are the secondary developed on the hanging wall of westward dipping low-angle normal faults. Thus, their seismogenic ability is limited, however, there exists a high-angle deep fault in the crust from Changle-Zaoan fault zone to seashore fault zone. This deep fault has cut the interface between the upper and lower crusts and Moho discontinuity, and may be the deep structure to trigger destructive earthquake source in future to affect Fuzhou City. These results have advanced the detecting precision of the deep structure in the southeastern coastal seismic zone of the mainland of china. In the aspect of the combined feature of the deep and shallow extensional structures that consist of the westward dipping low-angle normal faults and secondary normal faults on their hanging walls in the upper crust, it is firstly obtained that a united structural interpretation has deepened the knowledge about the deep dynamic process in the southeastern coasta

关键词： deep seismic reflection high-resolution seismic refraction wide-angle.

Spatiotemporal model of open-pit based on 3.D deposit model

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中国有色金属学会会刊：英文版 2011年第S3期21卷 616-620页

作者： XIA Chun-lin1, ZHOU Hui1, LI Qing-yuan2, MA Zhen-li3.1. School of Geomatics, Liaoning Technical University, Fuxin 123.00, china 2. State key laboratory for GIS Engineering, Chinese Academy of Surveying and Mapping, Beijing 10083., china 3. Yinchuan College, china University of Mining and Technology, Yinchuan 750011, china [a] School of Geomatics Liaoning Technical University Fuxin 123000 China [b] State key laboratory for GIS Engineering Chinese Academy of Surveying and Mapping Beijing 100830 China [c] Yinchuan College China University of Mining and Technology Yinchuan 750011 China

A new method was put forward to make up the three-dimensional deposit model, and the spatiotemporal models of open-pit with temporal dynamics were also studied combined with the corrected models of multilevel ground states so as to bring the three-dimensional open-pit model at different time and its model serial formed from the evolvement into the management of temporal dimension in order to realize the spatial three-dimension and temporal dynamic for the mining management in open-pits,which makes this model easy to query and analyze 3.D information, also help surface mining replaying and stope evolution forecasting. Finally, the time-spatial model was established to show the dynamic mining on some open-pit under the windows XP and VC++ environment.

关键词： 3. model of deposit three-dimensional model mixed model temporal model open-pit

Economical cascadic multigrid method (ECMG)

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Science china mathematics 2007年第12期50卷 1765-1780页

作者： Zhong-ci SHI~1 Xue-jun XU~(1+) Yun-qing HUANG~2 ~1 LSEC,Institute of Computational mathematics,Academy of mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100080,china ~2 Hunan {3. laboratory for Computation and Simulation in Science and Engineering,Institute for Computational and applied mathematics,Xiangtan University,Xiangtan 411105,china LSEC Institute of Computational Mathematics Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing 100080 China Hunan key laboratory for Computation Simulation in Science Engineering Institute for Computational applied mathematics Xiangtan University Xiangtan 411105 China

In this paper, an economical cascadic multigrid method is proposed. Compared with the usual cascadic multigrid method developed by Bornemann and Deuflhard, the new one requires less iterations on each level, especially on the coarser grids. Many operations can be saved in the new cascadic multigrid algorithms. The main ingredient is the control of the iteration numbers on the each level to preserve the accuracy without over iterations. The theoretical justification is based on the observations that the error reduction rate of an iteration scheme in terms of the smoothing property is no longer accurate while the iteration number is big enough. A new formulae of the error reduction rate is employed in our new algorithm. Numerical experiments are reported to support our theory.

关键词： economical cascadic multigrid method (ECMG), cascadic multigrid method (CMG)

Adsorption and Insecticidal Activity of Toxin from Bacillus thuringiensis on Rectorite

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Pedosphere 2007年第4期17卷 513-521页

作者： ZHOU Xue-Yong HUANG Qiao-Yun CAI Peng YU Zi-Niu hubei province key {3. of Refractories and Ceramics Wuhan University of Science and Technology Wuhan 430081 （China）. College of Biotechnology and Chemical Engineering Tianjin University of Technology Tianjin 300191 （China） State key laboratory of Agricultural Microbiology College of Resources and Environment Huazhong Agricultural Uni- versity Wuhan 430070 （China）

The adsorption and desorption of the toxin from Bacillus thuringiensis strain WG-001 on rectorite were studied at different toxin and/or rectorite concentrations, pH values and temperatures. The insecticidal activity of the adsorbed toxin was evaluated by determining the lethal concentration to kill 50% of the larvae of Heliothis armigera （LC50）. The adsorption of the toxin on rectorite in sodium carbonate buffer （pH 9） reached equilibrium within 0.5-1.0 h and the adsorption isotherm of the toxin followed the Langmuir equation （R^2 〉 0.99）. In the pH range from 9 to 11 （carbonate buffer）, the adsorbed toxin decreased with increasing pH. The adsorption amounts decreased with increasing rectorite：toxin ratio. The adsorption was not significantly affected by the temperature between 10 and 50 ℃. The X- ray diffraction analysis indicated occurrence of the intercalation of the rectorite by the toxin. The infrared absorption spectrum showed that the binding of the toxin did not alter its structure. The LC50 wlues of the adsorbed toxin were smaller than those of the free toxin. The rectorite protected the toxin from ultraviolet irradiation damage. The desorption of the adsorbed toxin in water ranged from 3..5% to 56.4% and from 27.4% to 41.8% in a carbonate buffer. The desorption percentage also decreased with increasing rectorite：toxin ratio.

关键词： Bacillus thuringiensis insecticidul uctivity rectorite toxin udsorption und desorption

Temporal variations of δ^(18)O of atmospheric water vapor at Delingha

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Science china Earth Sciences 2008年第7期51卷 966-975页

作者： YIN ChangLiang1, YAO TanDong2, TIAN LiDe2, LIU DongNian3. YU WuSheng2 & QU DongMei2 1 State key laboratory of Cryoshperic Science, Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, Lanzhou 73.000, china 2 laboratory of Environment and Processes, Institute of Tibetan Plateau Research, Chinese Academy of Sciences, Beijing 100085, china 3.Meteorological Observatory of Haixi Prefecture of Qinghai province, Delingha 817000, china 1. State key laboratory of Cryoshperic Science Cold and Arid Regions Environmental and Engineering Research Institute Chinese Academy of Sciences Lanzhou 730000 China 2. laboratory of Environment and Processes Institute of Tibetan Plateau Research Chinese Academy of Sciences Beijing 100085 China 3. Meteorological Observatory of Haixi Prefecture of Qinghai province Delingha 817000 China

Oxygen stable isotope of atmospheric water vapor is widely used to study the modern process of cli- mate. Atmospheric water vapor samples were collected at Dlingha, northeast of Tibetan Plateau during the period from July 2005 to February 2006. The variation of δ18O and the relationships between δ18O and both the temperature and specific humidity are analyzed in this paper. Results show that the sea- sonal variation of δ18O of atmospheric water vapor at Delingha is remarkable with higher δ18O in summer and lower δ18O in winter. The temporal variation of vapor δ18O shows obvious fluctuations, with magnitude of over 3.‰. The daily variation of the δ18O is highly correlated with air temperature. The relationship between δ18O and atmospheric water vapor content is complex. Study shows that δ18O of atmospheric water vapor is positively correlated with specific humidity in winter in seasonal scale and inversely correlated with specific humidity in summer rainy period. The δ18O values of at- mospheric water vapor are lower than those of precipitation at Delingha, and the average difference is 10.7‰. Variations of δ18O of atmospheric water vapor is also found to be affected by precipitation events, The model results show that the precipitation effect could have caused the vapor δ18O in the raining season to lower by 7% in average in July and August.

关键词： Delingha δ18O atmospheric water vapor