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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 {2., tianjin 300072. china 2. Liu-Hui Center of Applied Mathematics, Nankai {2. and tianjin {2., 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.

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 {2., tianjin 300072. china 2. Liu-Hui Center of Applied Mathematics, Nankai {2. and tianjin {2., 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 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 The strong Reynolds analogy (SRA) and the Morkovin hypothesis were no longer valid.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.

Universal approximation of polygonal fuzzy neural networks in sense of K-integral norms

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Science china(Information Sciences) 2011年第11期54卷 2307-2323页

作者： WANG GuiJun 1 & LI XiaoPing 2.1 School of Mathematics Science,tianjin normal {2.,tianjin 300387,china 2.School of Management,tianjin normal {2.,tianjin 300387,china 1. School of Mathematics Science Tianjin Normal University Tianjin 300387 China2. School of Management Tianjin Normal University Tianjin 300387 China

In this paper,we introduce polygonal fuzzy numbers to overcome the operational complexity of ordinary fuzzy numbers,and obtain two important inequalities by taking advantage of their fine *** presenting an actual example,we demonstrate that the approximation capability of polygonal fuzzy numbers is ***,the concepts of K-quasi-additive integrals and K-integral norms are *** the polygonal fuzzy numbers space satisfies separability,the density problems for several functions spaces can be studied,by means of fuzzy-valued simple functions and fuzzy-valued Bernstein *** establish that the class of the integrally-bounded fuzzy-valued functions spans a complete and separable metric space in the K-integral ***,in the sense of K-integral norms,the universal approximation of fourlayer regular polygonal fuzzy neural networks for fuzzy-valued simple functions is ***,we show that this type of networks also possesses universal approximation for the class of integrally-bounded fuzzyvalued *** result indicates that the approximation capability which regular polygonal fuzzy neural networks for continuous fuzzy systems can be extended as for general integrable systems.

关键词： polygonal fuzzy numbers K-quasi-additive integrals K-integral norms polygonal fuzzy neural networks universal approximations

K-quasi-additive fuzzy integrals of set-valued mappings

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Progress in Natural Science:Materials International 2006年第2期16卷 125-132页

作者： WANG Guijun and LI Xiaoping ( School of Mathematics Science, tianjin normal university, tianjin 300074,{2. School of Management, tianjin normal university, tianjin 300074,{2.) [a]School of Mathematics Science Tianjin Normal University Tianjin China [b]School of Management Tianjin Normal Universit Tianjin China

We first define the quasi-addition and quasi-multiplication operations by introducing the inductive operator, and then, in the K-quasi-additive fuzzy measure space, we establish the K-quasi-additive fuzzy integral of a generally measurable set-valued mapping. Applying the integral transformation theorem, some basic properties of the K-quasi-additive fuzzy integrals with respect to this kind of set-valued mapping are studied. Finally, the generalized monotone convergence theorems of this kind of fuzzy integrals are obtained.

关键词： set-valued mapping inductive operator integrable selections K-quasi-additive fuzzy integrals.

Homotopy type of smooth weighted complete intersections

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Science china Mathematics 2010年第6期53卷 1583-1594页

作者： WANG JianBo1,& WANG YuYu2.1department of Mathematics,tianjin {2.,tianjin 300072.china 2.ollege of Mathematical Science,tianjin normal {2.,tianjin 300387,china 1. department of Mathematics Tianjin University Tianjin 300072 China2. College of Mathematical Science Tianjin Normal University Tianjin 300387 China

If the total degree d has no prime divisors less than(n+3)/2.then we prove that the homotopy type of complex odd dimensional smooth weighted complete intersection Xn(d;w) is determined by the dimension n,the total degree d,the Euler characteristic and the Kervaire invariant,provided that the weights w =(ω0,...,ωn+r) is pairwise relatively prime.

关键词： weighted projective space weighted complete intersection homotopy type connected sum

A combined numerical model of three-dimensional tidal motion and sediment transport in tidal current and its application

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Acta Oceanologica Sinica 2000年第1期19卷 145-154页

作者： Dong Wenjun Bai Yuchuan Li Shisen (1. department of Mathematics, tianjin {2., tianjin 300072. china 2. department of Hydraulics, tianjin {2., tianjin 300072. china) department of Mathematics Tianjin University Tianjin 300072 China department of Hydraulics Tianjin University Tianjin 300072 China

A calculation scheme, which combines a horizontal upwind finite element method with vertical implicit differences, is used to establish a three-dimensional mathematical model of tidal motion and sediment transport in tidal current. Compared with those of the relative theoretical formula, the results are satisfactory. The model mentioned above has been applied to the water area of the Lianzhou Bay, Guangxi Province. On the basis of the analysis and comparison with the field data, it shows clearly that the model calculation results are reasonable.

关键词： Tidal current sediment transport in tidal current upwind finite element three- dimensional numerical simulation

The reliability of the improved e^N method for the transition prediction of boundary layers on a flat plate

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Science china(Physics,Mechanics & Astronomy) 2012年第5期55卷 837-843页

作者： SU CaiHong1,2.1 department of Mechanics,tianjin {2.,tianjin 300072.china 2.tianjin Key Laboratory of Modern Engineering Mechanics,tianjin 300072.china 1. department of Mechanics Tianjin University Tianjin 300072 China2. Tianjin Key Laboratory of Modern Engineering Mechanics Tianjin 300072 China

The transition criterion in the improved eN method is that transition would occur whenever the velocity amplitude of disturbance reaches 1%-2. of the free stream velocity,while in the conventional eN method,the N factor is an empirical *** this paper the reliability of this key assumption in the improved eN method is checked by results of transition prediction by using the Parabolized Stability Equations(PSE).Transition locations of an incompressible boundary layer and a hypersonic boundary layer at Mach number 6 on a flat plate are predicted by both the improved eN method and the PSE *** from both methods agree fairly well with each other,implying that the transition criterion proposed in the improved eN method is reliable.

关键词： transition prediction boundary layer eN PSE

Influence of moisture content and time on the mechanical behavior of polymer material

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Science china(Technological Sciences) 2004年第5期47卷 595-607页

作者： ZHENG Gaofei1, 2. KANG Yilan1, SHENG Jing3, QIN Qinghua1, WANG Huaiwen1 & FU Donghui1 1. department of Mechanics, tianjin {2., tianjin 300072. china 2. department of Mechanics, tianjin Polytechnic {2., tianjin 300160, china 3. department of Material Engineering, tianjin {2., tianjin 300072. china Correspondence should be addressed to Kang Yilan 1. department of Mechanics Tianjin University 300072 Tianjin China 2. department of Mechanics Tianjin Polytechnic University 300160 Tianjin China 3. department of Material Engineering Tianjin University 300072 Tianjin China

The effects of moisture content and time on mechanical behavior of polymer materials are investigated both theoretically and experimentally in this paper. An equivalence relationship between time intervals and the moisture content for polymer nylon-6 has been established by way of experimental observation and measured results. The relationship shows that there exists equivalence between moisture and service time in affecting mechanical properties. In other words, an increase in moisture can be replaced by prolonging acting time in producing the same effect on material properties. Consequently, a moisture-time superposition principle is presented based on the experimental results and the analogy of temperature-time superposition principle. Numerical results such as stress-strain curves with different moisture contents are presented to verify the applicability and correctness. The proposed method appears very promising in study on the effect of moisture content on mechanical behavior of polymer materials.

关键词： equivalence relationship of moisture-time, moisture content, mechanical properties, shift function.

Transition prediction of a hypersonic boundary layer over a cone at small angle of attack——with the improvement of e^N method

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Science china(Physics,Mechanics & Astronomy) 2009年第1期52卷 115-123页

作者： SU CaiHong1 & ZHOU Heng1,2.1 department of Mechanics, tianjin {2., tianjin 300072. china 2.Liu-Hui Center of Applied Mathematics, Nankai {2. and tianjin {2., tianjin 300072. china 1. department of Mechanics Tianjin University Tianjin 300072 China 2. Liu-Hui Center of Applied Mathematics Nankai University and Tianjin University Tianjin 300072 China

The problem of transition prediction for hypersonic boundary layers over a sharp cone has been studied in this work. The Mach number of the oncoming flow is 6, the cone half-angle is 5°, and the angle of attack is 1°. The conventional e N method is used, but the transition location so obtained is obviously incorrect. The reason is that in the conventional method, only the amplifying waves are taken into account, while in fact, for different meridians the decay processes of the disturbances before they begin to grow are different. Based on our own previous work, new interpretation and essential improvement for the e N method are proposed. Not only the amplification process but also the decay process is considered. The location, where by linear stability theory, the amplitude of disturbance wave is amplified from its initial small value to 1%, is considered to be the transition location. The new result for transition prediction thus obtained is found to be fairly satisfactory. It is also indicated that for the calculation of base flow, boundary layer equations can be used for a small angle of attack. Its computational cost is much smaller than those for DNS.

关键词： angle of attack cone transition eN method

Transition prediction for supersonic and hypersonic boundary layers on a cone with angle of attack

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Science china(Physics,Mechanics & Astronomy) 2009年第8期52卷 1223-1232页

作者： SU CaiHong1 & ZHOU Heng1,2.1 department of Mechanics,tianjin {2.,tianjin 300072.china 2.Liu-Hui Center of Applied Mathematics,Nankai {2. and tianjin {2.,tianjin 300072.china department of Mechanics Tianjin University Tianjin 300072 China Liu-Hui Center of Applied Mathematics Nankai University and Tianjin University Tianjin 300072 China

Transition prediction for boundary layers has always been one of the urgent problems waiting for a solution for the development of aero-space technology,yet there is no reliable and effective method due to the complexity of the *** eN method has been regarded as an effective method for the transition prediction of boundary ***,it heavily relies on experiment or *** in cases with three-dimensional base flow,for instance,the boundary layer on a cone with angle of attack,the result of its application is not *** authors have found its cause and proposed the method for its improvement,which did yield the fairly satisfactory result for a given test case,and also did not rely so much on experiment or ***,before people can really apply this method to practical problems,more test cases have to be *** this paper,more test cases for the application of the improved eN method to problems of transition prediction of supersonic and hypersonic boundary layers on cones with angle of attack will be *** results are compared with those obtained by experiments and/or direct numerical simulations,confirming that the improved eN method is effective and *** also find that there may be more than one ZARF for each meridian plane,and which one should be chosen for the eN method has been clarified.

关键词： angle of attack cone boundary layer transition eN method