源于G.I.Taylor工作的现代经典物理学

一位科学家的工作提供了一门完整课程的素材,涉及从流体动力学稳定性、湍流到流体电动力学、微生物的运动．     

I.I.Glass教授来华访问

加拿大多伦多大学宇航研究所(UTIAS)著名空气动力学家I.I.Glass教授偕夫人应中国力学学会中国气动力研究与发展中心等单位邀请于1985年4月30日至5月31日第二次来我国访问。Glass教授先后在中国科学院力学研究所,北京航空学院,中国气动力研究与发展中心,西北工业大学,中国科技大学,南京航 ...     

纪念流体力学家G.K.Batchelor

英国皇家协会会员,英国剑桥大学Ｇ．Ｋ．Ｂａｔｃｈｅｌｏｒ教授（１９２０～２０００）不幸于２０００年３月３０日晚逝世,享年８０岁．他与帕金森氏病进行了顽强的抗争．４月１０日中午,他的同仁和亲友在剑桥火葬场举行了简单的葬礼,只有鲜花．对他生活和工作的纪念将在剑桥的Ｔｒｉｎｉｔｙ学院保留到夏季． Ｂａｔｃｈｅｌｏｒ教授生于 １９２０年 ３月 ８日,就读于墨尔本大学（ＢＳｃ, ＭＳｃ）,剑桥大学（ＰｈＤ）;在墨尔本 ＣＳＩＲ航空部工作 ４年后到剑桥大学跟随 Ｇ．Ｉ． Ｔａｙｌｏｒ工作,任数学讲师（１９４１～１９…     

THE LAW OF THE ITERATED LOGARITHM OF RANDOM WEIGHTING APPROXIMATION FOR MEAN ERROR──NON.I.I.D.SITUATION

For the dislribulion if mean error under independent but not identicallydislribuled conditions. its approximating dislribution whose precision reach O(√lnlnn/n) is obtained.     

AN ANALYTICAL SOLUTION OF G.I.TAYLOR’S THEORY OF PLASTIC DEFORMATION IN IMPACT OF CYLINDRICAL PROJECTILES AND ITS IMPROVEMENT

The theory of plastic deformation in the impact of cylindrical projec-tiles on rigid targets was first introduced by G.I.Taylor(1948).The importance of this theorg lies in the fact that the dgnamic yieldstrength of the materials can be determined from the measurement ofthe plastic deformation of flat-ended cylindrical projectiles.Fromthe experimental results.we find that the dynamic gield strengthis independent of impact velocity.and that it is higher than the sta-tic yield strength in general,and several times higher than the sta-tic yield strength in certain cases.This gives an important founda-tion for the studg of elastoplastic impact problems in qeneral.How-ever,it is well known that the complexity of differential equationsin Taylor’s theory compelled us to use the troublesome numerical so-lution.In this paper,the analgtical solution of all the equationsin Taylor’s theory is given in parametrical form and the results arediscussed in detail.In the latter part of this paper,the method of calculatio     

AN ANALYTICAL SOLUTION OF G. I. TAYLOR’S THEORY OF PLASTIC DEFORMATION IN IMPACT OF CYLINDRICAL PROJECTILES AND ITS IMPROVEMENT

The theory of plastic deformation in the impact of cylindrical projectiles on rigid targets was first introduced by G. I. Taylor(1948)^[1]. The importance of this theory lies in the fact that the dynamic yield strength of the materials can be determined from the measurement of the plastic deformation of flat-ended cylindrical projectiles. From the experimental results^[2] we find that the dynamic yield strength is independent of impact velocity, and that it is higher than the static yield strength in general, and several times higher than the static yield strength in certain cases. This gives an important foundation for the study of elastoplastic impact problems in general. However, it is well known that the complexity of differential equations in Taylor’s theory compelled us to use the troublesome numerical solution. In this paper, the analytical solution of all the equations in Taylor’s theory is given in parametrical form and the results are discussed in detail.In the latter part of this paper, the method of calculation of impulse of impact is improved by considering the processes of radial’ movement of materials. The analytical solution of the improved theory shows that it gives better agreement with the experimental results than that of original Taylor’s theory.     

??Batchelor??????????——————??????????????????G.K.Batchelor??????????????

没有想到 这是30年前的旧事. 1979年10月我第一次走出国门,来到这世界科学的圣地--剑桥大学.我们可说是改革开放政策的第一批受益者.事情决定在更早,那是在1978年的夏天,中美两国还没有建交.我们通过了国家的英语考试,组织上决定以公费公派的访问学者身份送我出国进修.我那时在中国科学院安徽光学精密机械研究所工作,研究激光在大气中传输时由大气湍流对激光光束引起的种种湍流效应.     

L.A.S. and Negative Schwarzian Derivative Do Not Imply G.A.S. in Clark’s Equation

It has been conjectured that a locally attracting equilibrium of Clark’s equation \(x_{n+1}=\alpha x_n + (1-\alpha )h(x_{n-k})\) is also globally attracting whenever h is a unimodal or decreasing map with negative Schwarzian derivative. The main aim of this paper is to show that the conjecture is false when \(k\ge 3\). This is done by studying the (Neimark–Sacker) bifurcation at the parameter \(\alpha \) where the locally attracting equilibrium of the equation becomes unstable. Our results, on the other hand, reinforce the validity of the conjecture in the cases \(k=1,2\).     

The Γ-Limit of the Two-Dimensional Ohta–Kawasaki Energy. I. Droplet Density

This is the first in a series of two papers in which we derive a Γ-expansion for a two-dimensional non-local Ginzburg–Landau energy with Coulomb repulsion, also known as the Ohta–Kawasaki model, in connection with diblock copolymer systems. In that model, two phases appear, which interact via a nonlocal Coulomb type energy. We focus on the regime where one of the phases has very small volume fraction, thus creating small “droplets” of the minority phase in a “sea” of the majority phase. In this paper we show that an appropriate setting for Γ-convergence in the considered parameter regime is via weak convergence of the suitably normalized charge density in the sense of measures. We prove that, after a suitable rescaling, the Ohta–Kawasaki energy functional Γ-converges to a quadratic energy functional of the limit charge density generated by the screened Coulomb kernel. A consequence of our results is that minimizers (or almost minimizers) of the energy have droplets which are almost all asymptotically round, have the same radius and are uniformly distributed in the domain. The proof relies mainly on the analysis of the sharp interface version of the energy, with the connection to the original diffuse interface model obtained via matching upper and lower bounds for the energy. We thus also obtain an asymptotic characterization of the energy minimizers in the diffuse interface model.     

Craft––a plastic-damage-contact model for concrete. I. Model theory and thermodynamic considerations

A framework is described for the development of a thermodynamically consistent plastic directional-damage-contact model for concrete. This framework is used as a basis for a new model, named Craft, which uses planes of degradation that can undergo damage and separation but which can regain contact according to a contact state function. The thermodynamic validity of the resulting model is considered in detail, and is proved for certain cases and demonstrated numerically for others. The model has a fully integrated plasticity component that uses a smooth triaxial yield surface and frictional hardening–softening functions. A new type of consistency condition is introduced for simultaneously maintaining both local and global constitutive relationships as well as stress transformation relationships. The introduction of contact theory provides the model with the ability to simulate the type of delayed aggregate interlock behavior exhibited by fully open crack surfaces that subsequently undergo significant shear movement. The model has been implemented in a constitutive driver program as well as a finite element program. The model is assessed against a range of experimental data, which includes data from uniaxial tension tests with and without unloading–reloading cycles, tests in which cracks are formed and then loaded in shear, and uniaxial, biaxial and triaxial compression tests.