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Direct numerical simulation of a supersonic turbulent boundary layer on a flat plate and its analysis

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Science china(Physics,Mechanics & Astronomy) 2005年第5期48卷 626-640页

作者： HUANG Zhangfeng1, ZHOU Heng1,2.& LUO Jisheng1,2.1. Department of Mechanics, tianjin university, tianjin 300072. china 2. Liu-Hui Center of Applied Mathematics, nankai university and tianjin university, tianjin 300072. china Department of Mechanics Tianjin University Tianjin China Liu-Hui Center of Applied Mathematics Nankai University and Tianjin University Tianjin China

Temporal mode direct numerical simulation (DNS) has been done for a supersonic turbulent boundary layer on a flat plate with Mach number 4.5. It was found that the mean flow profile, the normal-wise distribution of turbulent Mach number and the root mean square (RMS) of the fluctuations of various variables, as well as the Reynolds stresses, bore similarity in nature, when the turbulence reached a fully developed state. But the compressibility effect was strong and must be considered. The strong Reynolds analogy (SRA) and the Morkovin hypothesis were no longer valid. From the end of transition to the fully developed state of turbulence, it was in the transient period, for which the similarity did not hold.

关键词： turbulence, similarity, compressibility effect, supersonic boundary layer, direct numerical simulation.

FKBP2. in ER binds to BiP specifically

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Science china Chemistry 2004年第1期47卷 17-23页

作者： ZHANG Wanqi, LI Hui, ZHANG Xiaobin, SHEN Ye, WANG Yinong, Ml Huaifeng & HE BinglinState Key Laboratory of Functional Polymer Materials for Adsorption and Separation, Chemical school of nankai university,{2., china Hygienic school of tianjin Medical university,{2., china Medical school of nankai university,{2., china State Key Laboratory of Functional Polymer Materials for Adsorption and Separation Chemical School of Nankai University Tianjin China Hygienic school of tianjin Medical {2. Tianjin China Medical school of nankai university Tianjin China

FKBP2. was found in mouse endoplasmic reticulum (ER) in 1998. It consists of an N-terminal peptidyl-prolyl cis-trans isomerase (PPlase) domain and a C-terminal domain with Ca2. binding sites. The fusion protein of mouse FKBP2. and glutathione S-transferase (GST), GST-FKBP2., and the fusion protein of BiP, a member of heat shock protein 70 (Hsp 70) in ER, and GST, GST-BiP, were subcloned in E. coli, expressed and purified. The fusion proteins were restrictively digested by Factor Xa (FaXa) to obtain the free cloned proteins FKBP2. and BiP. With the assay of adsorption of free FKBP2. or BiP with GST-BiP or GST-FKBP2. attached to the Glutathione-Sepharose 4B, the adsorbed FKBP2. or BiP could be detected by Immunoblot. It means that FKBP2. binds to BiP. Furthermore, BiP in leukocyte ER-extract can be adsorbed with GST-FKBP2. attached to the glutathione-Sepharose 4B. It shows that FKBP2. binds to natural BiP in ER, too. These experiments show that a PPIase binds to a molecular chaperone of the Hsp70 family.

关键词： peptidyl-prolyl cis/trans isomerase, FKBP2., BiP, endoplasmic reticulum, specific binding.

Discontinuous Galerkin method for elliptic stochastic partial differential equations on two and three dimensional spaces

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Science china Mathematics 2007年第11期50卷 1661-1672页

作者： Rui-ming YAO~(1+) Li-jun BO~(1,2. 1 Department of Mathematics,Xidian university,Xi’an 710071,china 2.{2. of mathematical Sciences,nankai university,tianjin 3.0071,china Department of Mathematics Xidian University Xi’an China school of mathematical Sciences Nankai University Tianjin China

In this paper,we study a discontinuous Galerkin numerical scheme for a class of elliptic stochastic partial differential equations (*** SPDEs) driven by space white noises with homogeneous Dirichlet boundary conditions for two and three space *** also establish L2.error estimates for the *** particular,a numerical test for d = 2.is presented at the end of the article.

关键词： discontinuous Galerkin numerical scheme elliptic SPDEs white noises

Stochastic Fractional Anderson Models with Fractional Noises

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Chinese Annals of Mathematics,Series B 2010年第1期31卷 101-118页

作者： Yiming JIANG Kehua SHI Yongjin WANG school of mathematical Sciences and LPMC Nankai University Tianjin 300071 China school of mathematical Sciences and LPMC Nankai University Tianjin 300071 China

The authors are concerned with a class of one-dimensional stochastic Anderson models with double-parameter fractional noises, whose differential operators are fractional. A unique solution for the model in some appropriate Hilbert space is constructed. Moreover, the Lyapunov exponent of the solution is estimated, and its HSlder continuity is studied. On the other hand, the absolute continuity of the solution is also discussed.

关键词： Anderson models Fractional noises Lyapunov exponent Holder continuity Absolute continuity

The regular representation and regular covariant representation of crossed products of Woronowicz C^(*)-algebras

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Science china Mathematics 2005年第9期48卷 1245-1259页

作者： ZHANG Xiaoxia~(1,2. & GUO Maozheng~(1,3) 1. school of mathematical Sciences,Peking {2.,Beijing 100871,china 2. Department of Mathematics,Yantai {2.,Yantai 2.4005,china 3. LMAM,Peking {2.,Beijing 100871,china school of mathematical Sciences Peking University Beijing China Department of Mathematics Yantai University Yantai China LMAM Peking University Beijing China

In this paper,it is shown that the regular representation and regular covariant representation of the crossed products A×α G correspond to the twisted multiplicative unitary operators,where A is a Woronowicz C~*-algebra acted upon by a discrete group ***,it is also shown that the regular covariant C~*-algebra is the Woronowicz C~*-algebra which corresponds to a multiplicative ***,an explicit description of the multiplicative unitary operator for C(SU_q(2. )×α (?) is given in terms of those of the Woronowicz C~*-algebra C(SU_q(2. ) and the discrete group G.

关键词： multiplicative unitary operator, Woronowicz C*-algebra, crossed product.

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

The evolution and morphological stability of a spherical crystal

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Science china(Technological Sciences) 2008年第3期51卷 225-243页

作者： CHEN MingWen1,2. WANG ZiDong2.& XU JianJun3,4 1 school of Applied Sciences, university of Science and Technology Beijing, Beijing 100083,{2. 2.school of Materials Science and Engineering, university of Science and Technology Beijing, Beijing 100083,{2. 3.school of mathematical Sciences, nankai university, tianjin 3.0071,{2. 4 Department of Mathematics and Statistics, McGill university, Montreal H3A 2.6, Canada school of Applied Sciences University of Science and Technology Beijing Beijing China school of Materials Science and Engineering University of Science and Technology Beijing Beijing China school of mathematical Sciences Nankai University Tianjin China Department of Mathematics and Statistics McGill University Montreal Canada

The growth model of a spherical crystal in the undercooled melt including the surface energy, interfacial kinetics and convective flow is established. The effect of the convective flow induced by a small far field flow on the evolution and morphological stability of the interface of the spherical crystal is studied. The interface shape of the spherical crystal, which is affected by the far field flow, and the dispersion relation of the growth rate of amplitude of the perturbed interface are derived. It is shown that the convection induced by the far field flow makes the interface of the growing spherical crystal further grow in the upstream direction of the far field flow and inhibit growth in the downstream direction; the interface of the decaying spherical crystal further decays in the upstream direction and inhibits decay in the downstream direction. The theoretical result suggests that both the growth of the sphere in the upstream direction and the decay of the sphere in the downstream direction make the spherical crystal tend to evolve into an oval; the morphological stability of the interface depends on a certain radius R c such that the spherical crystal is unstable when its radius is greater than R c and stable when its radius is less than R c . The surface energy and interfacial kinetics have strong stabilizing effects on the growth of the spherical crystal. In the meantime interfacial kinetics is a table factor of the interface when the interface of the sphere is growing; it is an unstable factor of the interface when the interface is decaying.

关键词： solid-liquid interface spherical crystal convective flow crystal growth morphological stability

Totally geodesic submanifolds of maximal rank in symmetric spaces

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Science china Mathematics 2004年第2期47卷 264-271页

作者： ZHU Fuhai & LIANG Keschool of mathematical Sciences and LMAM, Peking {2., Beijing 100871, china College of mathematical Sciences and LPMC, nankai university, tianjin 3.0071, china school of mathematical Sciences and LMAM Peking University Beijing China College of mathematical Sciences and LPMC Nankai University Tianjin China

We gave a complete list of totally geodesic submanifolds of maximal rank in symmetric spaces of noncompact type. The compact cases can be obtained by the duality.

关键词： totally geodesic submanifold, Lie triple system, maximal rank.

A NEW FAMILY OF FILTRATION s+6 IN THE STABLE HOMOTOPY GROUPS OF SPHERES

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Acta Mathematica Scientia 2006年第2期26卷 193-201页

作者：刘秀贵 school of mathematical Sciences and LMPC{2. Tianjin 300071China

In the year 2.02. Lin detected a nontrivial family in the stable homotopy groups of spheres ;π-6S which is represented by hngoγ^-3 ∈ Ext^6tA（Zp, Zp） in the Adams spectral sequence, where t = 2.^n（p- 1）＋ 6（p^2.＋p ＋ 1）（p- 1） and p ≥ 7 is a prime number. This article generalizes the result and proves the existence of a new nontrivial family of filtration s ＋ 6 in the stable homotopy groups of spheres πt1-8-6S which is represented by bygoγ^s＋3 ∈ Ext^s＋6＋t1Atl （Zp, Zp） in the Adams spectral sequence, where n≥ 4, 0 ≤ s 〈 p - 4, t1 = 2.^n（p- 1）＋ 2.p- 1）（（s ＋ 3）p^2.＋（s ＋ 3）p ＋（s ＋ 3））＋ s.

关键词： Stable homotopy groups of spheres Adams spectral sequence Toda-Smith spectrum May spectral sequence