Stability of Navier-Stokes Equation(Ⅰ)

ＳＴＡＢＩＬＩＴＹＯＦＮＡＶＩＥＲ－ＳＴＯＫＥＳＥＱＵＡＴＩＯＮ（Ⅰ）ＳｈｉＷｅｉ－ｈｕｉ（施惟慧）（ＳｈａｎｇｈａｉＵｎｉｖｅｒｓｉｔｙ，Ｓｈａｎｇｈａｉ）（ＲｅｃｅｉｖｅｄＤｅｃ．１０，１９９３；ＣｏｍｍｕｎｉｃａｔｅｄｂｙＣｈｉｅｎＷｅｉ－ｚａ...     

Stability of Navier-Stokes Equation(Ⅱ)

ＳＴＡＢＩＬＩＴＹＯＦＮＡＶＩＥＲ－ＳＴＯＫＥＳＥＱＵＡＴＩＯＮ（ＩＩ）ＳｈｉＷｅｉ－ｈｕｉ（施惟慧）;ＦａｎｇＸｉａｏ－ｚｕｏ（方晓佐）（ＳｈａｎｇｈａｉＵｎｉｖｅｒｓｉｔｙ）,Ｓｈａｎｇｈａｉ（ＲｅｃｅｉｖｅｄＤｅｃ．１１,１９９３;Ｃｏｍｍｕｎ...     

The “Arch of equilibration” of Charles Hutton (1772)

This paper is a historical re-visitation of the work of C. Hutton, a mathematician of the XVIII century, who wrote an innovative essay on the shape of arches, whose intrados he identifies with the curve of pressure, that he names “arch of equilibration”. His solution was mostly ignored by his contemporaries and after the middle of the XIX century forgotten. But Hutton’s problem is important, also because it offers the first example of an inverse problem in structural mechanics.     

Investigation of calculation method for anti-penetration of reactive power steel fiber concrete (RPC)

为了解决评估超高强活性粉末钢纤维混凝土的抗侵彻能力问题，根据混凝土在弹体侵彻过程中的介质状态及能量的分配关系，揭示了侵彻近区耗散能量结构与破碎区之间的比例尺度关系。由于近区介质的运动特性变形接近一维应变状态，受力类似于流体动力学状态，据此推导并简化了具有宽广的适用范围的侵彻计算公式，认为侵彻的深度主要由弹体的质量、形状、速度及靶体的强度、密度、断裂韧度、变形波速决定。通过多次的实弹试验，验证了公式的可靠性，得到了RPC的抗侵彻能力是普通混凝土的3倍的结论。     

Uniqueness of positive radial solutions of △u+g(r)u+h(r)u p =0 in Rn

Positive radial solutions of a semilinear elliptic equation u+g(r)u+h(r)u ^p =0, where r=|x|, xR ⁿ , and p>1, are studied in balls with zero Dirichlet boundary condition. By means of a generalized Pohoaev identity which includes a real parameter, the uniqueness of the solution is established under quite general assumptions on g(r) and h(r). This result applies to Matukuma's equation and the scalar field equation and is shown to be sharp for these equations.     

Macroscopic Response of¶Nematic Elastomers via Relaxation of¶a Class of SO(3)-Invariant Energies

We obtain an explicit formula for the relaxation of the free-energy density for nematic elastomers proposed by Bladon, Terentjev&;Warner (Phys. Rev. E 47 (1993), 3838–3840). The proof is based on a characterization of the level sets of the relaxed energy. In particular, the construction uses only laminates within laminates and it identifies those deformations that correspond to simple laminates.     

Group Classification of Equations of the Form y″ = f(x,y)

The problem of classification of ordinary differential equations of the form y = f(x,y) by admissible local Lie groups of transformations is solved. Standard equations are listed on the basis of the equivalence concept. The classes of equations admitting a oneparameter group and obtained from the standard equations by invariant extension are described.     

Laboratory of Solid Lubrication in Lanzhou Institute of Chemical Physics,Chinese Academy of Sciences(A Brief Introduction)

Laboratory of solid lubrication was established in Lanzhou Institute of Chemical Physics, Chinese Academy of Sciences with the ratification of Chinese Academy of Sciences in August 1987. Research Professor Yan Dongsheng, specially invited consultant and the member of the division of Chemistry, Chinese Academy of Sciences, is the honorary director of this laboratory. Associate research professors Xue Qunji and Gu Zeming of Lanzhou Institute of Chemical Physics are the head and the deputy head of this laboratory. The academic committee of the laboratory consists of 18 scientists at home and abroad (cf. appendix 1). Research professor Dang Hongxin, the vice-chairman of Chinese Society of Tribology of CMES, is the head of this committee.     

Some bounded results of θ(t)-type singular integral operators

Let B be a Banach space in UMD with an unconditional basis. The boundedness of the θ(t)-type singular integral operators in L _B ^p (R ⁿ), (1≤p<+∞) and H _B ¹ (R ⁿ) spaces are discussed. Foundation item: the Education Commission of Shandong Province (J98P51) Biography: Zhao Kai (1960-)     

Stability Analysis of Slowly Divergent Swirling Flow(Ⅰ)──Theory

ＳＴＡＢＩＬＩＴＹＡＮＡＬＹＳＩＳＯＦＳＬＯＷＬＹＤＩＶＥＲＧＥＮＴＳＷＩＲＬＩＮＧＦＬＯＷ（Ｉ）──ＴＨＥＯＲＹ＇ＸｉａＮａｎ（夏南）;ＹｉｎＸｉｅｙｕａｎ（尹协远）（ＲｅｃｅｉｖｅｄＪｕｌｙ１９．１９９３．ＣｏｍｍｕｎｉｃａｔｅｄｂｙＴｓａｉＳｈ...     

Hysteretic Θ(S) Curve Prediction: Comparison of Two Models

The prediction of the first-order wetting and drying scanning curves is attempted by two different methods. These are: Mualem model II and Poulovassilis and Kargas (P–K). Model II by Mualem was chosen deliberately as the most appropriate. Experimental (S) data obtained in the laboratory for a sand mixture and a real soil were used for the comparison. Moreover, data presented originally by Poulovassilis (1970) were also used for the same purpose. It is shown that the P–K method gives better results than Mualems model II. Some remarks on Mualems model are also included.     

力学史杂谈(八)、(九)

力学史杂谈（八）、（九）武际可（北京大学力学与工程科学系，北京１００８７１）（八）力学家之间的首创权之争摘要介绍一些著名力学家之间关于首创权的争议．关键词万有引力，胡克定律，卡门涡街人类愈是文明、进步，人们给予历史上的大科学家、大文化名人的尊敬愈多些...     

力学史杂谈(一)—(三)

力学史杂谈（一）—（三）武际可（北京大学力学与工程科学系，１００８７１）（一）汉语中“力学”一词考源摘要本文通过历史回顾，说明汉语中“力学”一词的来源．关键词力学，重学将西文Ｍｅｃｈａｎｉｃｓ一词译为“力学”是何人开始的呢？这人不是力学家，也不是自然...     

力学史杂谈(八)、(九)

力学史杂谈（八）、（九）武际可（北京大学力学与工程科学系，北京１００８７１）（八）力学家之间的首创权之争摘要介绍一些著名力学家之间关于首创权的争议．关键词万有引力，胡克定律，卡门涡街人类愈是文明、进步，人们给予历史上的大科学家、大文化名人的尊敬愈多些...     

力学史杂谈(四)、(五)

本文简要说明古代力学与天文学密不可分的关系     

力学史杂谈(六)、(七)

介绍力学和数学的密切关系，并说明中国力学的落后同数学没有相应的几何有关     

Effects of tension on vortex-induced vibration(ⅥⅤ) responses of a long tensioned cylinder in uniform flows

The effects of tension on vortex-induced vibration(ⅥⅤ) responses for a tension-dominated long cylinder with an aspect ratio of 550 in uniform flows are experimentally investigated in this paper. The results show that elevated tension suppresses fluctuations of maximum displacement with respect to flow velocity and makes chaotic ⅥⅤ more likely to appear. With respect to periodic ⅥⅤ, if elevated tension is applied, the dominant vibration frequency in the in-line(IL) direction will switch from a fundamental vibration frequency to twice the value of the fundamental vibration frequency, which results in a ratio of the dominant vibration frequency in the IL direction to that in the cross-flow direction of 2.0. The suppression of the elevated tension in the fluctuation of the maximum displacement causes the axial tension to become an active control parameter for the ⅥⅤ maximum displacement of a tension-dominated long riser or tether of an engineering structure in deep oceans. However,the axial tension must be optimized before being used since the high dominant vibration frequency due to the elevated tension may unfavorably affect the fatigue life of the riser or tether.     

Symmetric Representation of Stress and Strain in the Stroh Formalism and Physical Meaning of the Tensors L, S, L(θ) and S(θ)

The Stroh formalism for two-dimensional deformation of an anisotropic elastic material does not give the stress _ij explicitly in a symmetric form. It does not give an explicit expression for the strain _ij at al. Mantic and Paris [1] have recently derived an explicit symmetric representation of stress. We present here a new and elementary derivation that is more straight forward and transparent. The derivation does not require consideration of the surface traction or the normalization of the Stroh eigenvectors. The new derivation also provides an explicit symmetric representation of strain. Moreover, it allows us to deduce two of the three Barnett–Lothe tensors L, S [2] and the associated tensors L ( ), S ( ) [3], resulting in a physical interpretation of these tensors and the component ( L S )₂₁.     

VECTOR ANALYSIS OF SPATIAL MECHANISM—(Ⅳ)Dynamics of Spatial Mechanisms

The standard dynamical problems of the previous four Spatialmechanisms are here solved by the method of vector equations.Theprocedure is completely independent of the transfer matrices dueto the changes of reference frame from one connecting pair to thenext,as used by Yang and Bagci.