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Parabolic equation of the m-Laplacian with nonlinear boundary condition

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Chinese science Bulletin 1998年第11期43卷 905-908页

作者： WANG Shu+ 1, 2, WANG Mingxin 3. XIE Chunhong 1 1. Department of Mathematics, Nanjing university, Nanjing 210093, china 2. Department of Mathematics, Henan university, Kaifeng 475001, china 3. Department of Applied Mathematics, Southeast university, Department of Mathernntics Nanjing University Nanjing China Department of Mathematics Henan University Kaifeng China Department of Applied Mathematics Southeast University Nanjing China

The existence and nonexistence of global positive weak solutions of parabolic equation of the m-Laplician with nonlinear boundary condition are dealt with. The necessary and sufficient conditions on the existence of a... 详细信息

关键词： nonlinear boundary condition parabolic equation of m-Laplacian global solution blow-up.

Statistical theory for hydrogen bonding fluid system of A_aD_d type (I): The geometrical phase transition

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science china Chemistry 2006年第6期49卷 499-506页

作者： WANG Haijun1,2, HONG Xiaozhong3. GU Fang1 & BA Xinwu1 1. College of Chemistry and Environment science, Hebei university, Baoding 071002, china 2. International C{3. for Materials Physics, Chinese Academy of sciences, Shenyang 110016, china 3. College of Physics science and Technology, Hebei university, Baoding 071002, china 1. College of Chemistry and Environment science Hebei University Baoding 071002 China 2. International Center for Materials Physics Chinese Academy of Sciences Shenyang 110016 China 3. College of Physics science and Technology Hebei University Baoding 071002 China

The influence of hydrogen bonds on the physical and chemical properties of hydrogen bonding fluid system of AaDd type is investigated from two viewpoints by the principle of statistical mechanics. In detail, we proposed two new ways that can be used to obtain the equilibrium size distribution of the hydrogen bonding clusters, and derived the analytical expression of a relationship between the hydrogen bonding free energy and hydrogen bonding degree. For the nonlinear hydrogen bonding systems, it is shown that the sol-gel phase transition can take place under proper conditions, which is further proven to be a kind of geometrical phase transition rather than a thermodynamic one. Moreover, several problems associated with the geometrical phase transition and liquid-solid phase transition in nonlinear hydrogen bonding systems are discussed.

关键词： hydrogen bonding fluid, equilibrium free energy, geometrical phase transition.

Characterization of plastic flow in two Zr-based bulk metallic glasses

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science china(Technological sciences) 2006年第4期49卷 414-424页

作者： XING Dongmei1,2, ZHANG Taihua1, LI Weihuo3.& WEI Bingchen3.1. State Key Laboratory of nonlinear Mechanics (LNM), Institute of Mechanics, Chinese Academy of Sci- ences, Beijing 100080, china 2. College of Physics and Electronic Information science, Tianjin Normal {3., Tianjin 3.0074, china 3. National Microgravity Laboratory, Institute of Mechanics, Chinese Academy of sciences, Beijing 100080, china 1. State Key Laboratory of nonlinear Mechanics (LNM) Institute of Mechanics Chinese Academy of Sciences Beijing 100080 China 2. College of Physics and Electronic Information science Tianjin Normal University Tianjin 300074 China 3. National Microgravity Laboratory Institute of Mechanics Chinese Academy of Sciences Beijing 100080 China

Plastic deformation behaviors of Zr65Al10Ni10Cu15 and Zr52.5Al10Ni10Cu15Be12.5 bulk metallic glasses (BMGs) are studied by using the depth-sensing nanoindentation, microindentation and uniaxial compression. The Be-containing BMG exhibits a signifi- cantly improved overall plastic strain compared with the Be-free alloy during compressive tests. Both BMGs show a loading-rate-dependent serrated flow during nanoindentation measurements, but the Be-containing alloy exhibits a much lower critical loading rate for the disappearance of the serration than the Be-free BMG. The shear band patterns de- veloped during plastic deformation are investigated by microindentation technique, wherein much higher shear band density is found in the Be-containing alloy than in the Be-free alloy, indicating an easier nucleation of shear bands in the former BMG. The dif- ference in the plastic deformation behavior of the two BMGs can be explained by a free volume model.

关键词： Bulk metallic glass, plastic deformation, shear band, nanoindentation.

Structures and stability of isomers of[C,N,N,P]system

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science china Chemistry 2005年第5期48卷 415-423页

作者： KAN Wei1,2, ZHONG Hua1, YU Haitao1, FU Honggang1,3.& SUN Jiazhong1,3.1. School of Chemistry and Materials science, Heilongjiang university, Harbin 150080, china 2. School of Chemistry and Chemical Engineering, Qiqihar university, Qiqihar 161006, china 3. State Key Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin university, Changchun 13.023. china 1. School of Chemistry and Materials science Heilongjiang University 150080 Harbin China 2. School of Chemistry and Chemical Engineering Qiqihar University 161006 Qiqihar China 3. Jilin university State Key Laboratory of Theoretical and Computational Chemistry Institute of Theoretical Chemistry 130023 Changchun China

Nine isomers, twenty transition states, and some relative dissociation fragments of [C,N,N,P] system were located at the B3.YP/6-3.1G(d) and QCISD(t)/6-3.1+G(2df) (single-point) levels of theory, and the isomerization, structures, and stability of these obtained isomers were suggested. The results indicate that four nonlinear chainlike isomers NCNP, NCPN, CNPN, and CNNP with 2A′ electronic state are kinetically stable. Other isomers are kinetically unstable to-wards isomerization or dissociation because of the corresponding smaller reaction barriers. Furthermore, calculated vibrational frequencies, rotational constants, dipole moments, the first adiabatic ionization energies, and adiabatic electron affinities of the four isomers may provide some theoretical information that is helpful for identifying their existence in future laboratory and interstellar investigations. The results are also compared with [Si,N,N,P] system.

关键词： potential energy surface, [C,N,N,P] system, isomerization, kinetic stability.

Structural control of the Gagua “Wedge” Zone east of Taiwan Island on the southern Okinawa Trough

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science china Earth sciences 2005年第8期48卷 1165-1174页

作者： ZHENG Yanpeng1,2,3. LIU Baohua2,3. WU Jinlong2, LIANG Ruicai2,3. LIU Chenguang2,3.& ZHANG Zhengmin1 1. Marine Geology College, Ocean university of china, Qingdao 266003. china 2. First Institute of Oceanography, State Oceanic Administration, Qingdao 266061, china 3. Key Laboratory of Marine Sedimentology and Environmental Geology, State Oceanic Administration, Qingdao 266061, china 1. Marine Geology College Ocean University of China 266003 Qingdao China 2. First Institute of Oceanography State Oceanic Administration 266061 Qingdao China 3. Key Laboratory of Marine Sedimentology and Environmental Geology State Oceanic Administration 266061 Qingdao China

Based on compositive analysis and interpretation of the observed and historical data, the geophysical field characters and structural properties of the Gagua “Wedge” Zone of the sea area east of Taiwan Island and the primary tectonic stress direction and its variabilities of backarc spreading in the southern Okinawa Trough are studied. It is concluded from the study results that the Gagua “Wedge” Zone is structurally consistent with the Gagua ridge and two fault basins on both sides of the Gagua ridge, and adjusts the moving direction and distance of the western Philippine Sea plate to make the northwestward motion of the plate on its east side change to the northward subduction of the plate on its west side so that the primary tectonic stress direction of the Okinawa Trough changed from NW-SE to nearly N-S, which provided the stress source for the Okinawa Trough to enter the second spreading stage.

关键词： east of Taiwan Island, Gagua "Wedge" Zone, Okinawa Trough, structural control.

A relative local variational principle for topological pressure

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science china Mathematics 2010年第6期53卷 1491-1506页

作者： MA XianFeng1,CHEN ErCai2,3.& ZHANG AiHua2,4 1Department of Mathematics,East china university of science and Technology,Shanghai 20023.,china 2School of Mathematics and Computer science,Nanjing Normal university,Nanjing 210097,china 3.enter of nonlinear science,Nanjing university,Nanjing 210093.china 4College of Mathematics and Physics,Nanjing university of Posts and Telecommunications,Nanjing 210046,china 1. Department of Mathematics East China University of Science and Technology Shanghai 200237 China2. School of Mathematics and Computer Science Nanjing Normal University Nanjing 210097 China3. Center of Nonlinear Science Nanjing University Nanjing 210093 China4. College of Mathematics and Physics Nanjing University of Posts and Telecommunications Nanjing 210046 China

We define the relative local topological pressure for any given factor map and open cover,and prove the relative local variational principle of this *** precisely,for a given factor map π:(X,T)→(Y,S) between two topological dynamical systems,an open cover U of X,a continuous,real-valued function f on X and an S-invariant measure ν on Y,we show that the corresponding relative local pressure P(T,f,U,y) satisfies sup μ∈M(X,T){ hμ(T,U|Y)+∫X f(x)dμ(x) :πμ=ν}=∫Y P(T,f,U,y)dν(y),where M(X,T) denotes the family of all T-invariant measures on ***,the supremum can be attained by a T-invariant measure.

关键词： pressure conditional entropy relative local variational principle

A three-dimensional variational ocean data assimilation system:Scheme and preliminary results

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science china Earth sciences 2006年第11期49卷 1212-1222页

作者： ZHU Jiang1,2, ZHOU Guangqing1, YAN Changxiang1, FU Weiwei1 & YOU Xiaobao1,3.1. International Center for Climate and Environment sciences, Institute of Atmospheric Physics, Chinese Academy of sciences, Beijing 100029, {3. 2. Jiangsu Key Laboratory of Meteorological Disaster, Nanjing university of Information science and Technology, Nanjing 210044, {3. 3. Beijing Institute of Applied Meteorology, Beijing 100029, {3. 1. International Center for Climate and Environment sciences Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029 China 2. Jiangsu Key Laboratory of Meteorological Disaster Nanjing University of Information Science and Technology Nanjing 210044 China 3. Beijing Institute of Applied Meteorology Beijing 100029 China

A new 3.VAR-based Ocean Variational Analysis System (OVALS) is developed. OVALS is capable of assimilating in situ sea water temperature and salinity observations and satellite altimetry data. As a component of OVALS, a new variational scheme is proposed to assimilate the sea surface height data. This scheme considers both the vertical correlation of background errors and the nonlinear temperature-salinity relationship which is derived from the generalization of the linear balance constraints to the nonlinear in the 3.VAR. By this scheme, the model temperature and salinity fields are directly adjusted from the altimetry data. Additionally, OVALS can assimilate the temperature and salinity profiles from the ARGO floats which have been implemented in recent years and some temperature and salinity data such as from expendable bathythermograph, moored ocean buoys, etc. A 21-year assimilation experiment is carried out by using OVALS and the Tropical Pacific circulation model. The results show that the assimilation system may effectively improve the estimations of temperature and salinity by assimilating all kinds of observations. Moreover, the root mean square errors of temperature and salinity in the upper depth less than 420 m reach 0.63. and 0.3. psu.

关键词： data assimilation, 3.VAR, sea surface height, ARGO floats.

nonlinear optical properties and superluminal propagation in the ruby

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Chinese science Bulletin 2010年第6期55卷 473-477页

作者： GAO Feng1,2,3.XU JingJun1,2,3.ZHANG GuoQuan1,2,3.& ZHANG WenDing1,2,3.1 Photonics Center,College of Physics science,Nankai university,Tianjin 3.0457,{3. 2 The Key Laboratory of Advanced Technique and Fabrication for Weak-Light nonlinear Photonics Materials of Ministry of Education,Nankai university,Tianjin 3.0457,{3. 3.Tianjin Key Laboratory of Photonics Materials and Technology for Information science,Nankai university,Tianjin 3.0457,{3. Photonics Center College of Physics Science Nankai University Tianjin 300457 China Key Laboratory of Advanced Technique and Fabrication for Weak-Light nonlinear Photonics Materials of Ministry of Education Nankai University Tianjin 300457 China Tianjin Key Laboratory of Photonics Materials and Technology for Information science Nankai University Tianjin 300457 China

In this review article,we summarized the study of the weak light nonlinear properties associated with group velocity change in the *** ruby could be reduced to a two-level system,in which population oscillations could lead to a subluminal *** the modulated TEM00 beam introduced into the ruby,self-phase modulation together with Fraunhofer diffractions and nondegenerate two-wave coupling between different spatial frequency components of the beam occurs at the same *** oscillations,self-phase modulation together with Fraunhofer diffractions and nondegenerate two-wave coupling mechanism competes with each other,which brings a new phenomenon of self-superluminal group velocity propagation in the ruby.

关键词：非线性光学性质超光速传播红宝石自相位调制 TEM00模速度变化光束耦合空间频率

Mechanism of Breakdown in Laminar-Turbulent Transition of Incompressible Boundary Layer on a Flat Plate

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Transactions of Tianjin university 2007年第2期13卷 79-87页

作者：唐洪涛罗纪生周恒 School of Mechanical Engineering Tianjin University

Temporal mode direct numerical simulation was done for the process of laminar-turbulent transition in an incompressible boundary layer on a flat plate. The analysis of the results showed that during the breakdown process of laminar-turbulent transition, the modification of the mean flow profile by the disturbances led to a remarkable change in its stability characteristics, manifested in the significant enlargement of the linear unstable zone and the maximum amplification rate, and led to that many more disturbances were excited and enhanced rapidly, correspondingly the turbulent energy also increased rapidly, and the mean flow profiles evolved swiftly from laminar to turbulent. It was also found that if the oblique waves in the initial disturbances did not form symmetrical pairs, the subsequent span-wise mean velocities would, in general, be nonzero due to nonlinear interaction, which would have a great effect on the stability characteristics and also implied that the turbulence obtained by direct numerical simulation might not be fully a random process.

关键词： boundary layer transition direct numerical simulation breakdown