中厚度圆浮板自由振动的一个解析解

本文提出了常水深环境下中厚度圆浮板自由振动的一个解析解.分析中考虑了板横向剪切变形的影响和横截面转动惯性效应,利用空气中中厚度圆板的振型叠加和势流理论,导得了浮板系统频率方程的解析式.由此可看出Y.Tanaka得到的圆形薄浮板的解是本文的特例.最后数值计算还给出了水深和钢缆刚度与频率的关系曲线.并指出了h/a在什么范围可以略去剪切变形和转动惯量的影响.     

Direct modeling of flow of FENE fluids

Direct simulations of macromolecular fluids are carried out for flows between parallel plates and in expanding and contracting channels. The macromolecules are modeled as FENE dumbbells with soft disks or Lennard-Jones dumbbell-dumbbell interactions. The results are presented in terms of profiles and contour plots of velocity, pressure, temperature, density, and flow fields. In addition the data for potential energy, shear stress, and the normal components of the stress tensor are collected. In general, an excellent agreement is found between the simulated profiles and the well-known flow structures, such as flow separation and formation of viscous eddies, indicating that micro-hydrodynamics is a viable tool in linking macroscopic phenomena with the underlying physical mechanisms. The simulations are performed in the Newtonian regime, for medium-size systems comprising up to 3888 dumbbells. This number is sufficiently large to control boundary and particle number effects. The flow is induced by gravity. The traditional stochastic (thermal) and periodic boundary conditions are employed. Also, diffusive boundary conditions, which could include a stagnant fluid layer and repulsive potential walls, are developed. The scaling problems, which are related to the application of a large external force in a microscopic system (of the size of the order 100 Å), result in extreme pressure and temperature gradients. In addition, the viscosity and thermal conductivity coefficients obtained from velocity and temperature profiles of the channel flow are presented. These results are confirmed independently from modeling of Couette flow by the SLLOD equations of motion and from the Evans algorithm for thermal conductivity.     

Gemini表面活性剂烷烃尾链在吸附和聚集过程中的疏水协同效应(英文)

以表面张力法测定了系列Gemini表面活性剂m-6-m以及对应单体表面活性剂CmTABr的临界胶束浓度(cmc)和降低水表面张力20mN·m-1需要的浓度(pC20).比较这些参数表明m-6-m胶束化和在界面吸附的能力均强于CmTABr,这被归结为Gemini表面活性剂烷烃尾链间的疏水协同效应.与不对称Gemini表面活性剂12-6-m比较,对称的Gemini结构更有利于表面活性剂的聚集和吸附.     

投影的约化极小模和空间的夹角

Let M and N be nonzero subspaces of a Hilbert space H, and PM and PN denote the orthogonal projections on M and N, respectively. In this note, an exact representation of the angle and the minimum gap of M and N is obtained. In addition, we study relations between the angle, the minimum gap of two subspaces M and N, and the reduced minimum modulus of （I - PN）PM,     

液态结构与性质关系Ⅱ——Mg-9Al熔体的运动黏度及与熔体微观结构的关系

采用坩埚扭摆振动法测量Mg-9Al熔体的运动黏度,得到890—1190 K温区内高精度的黏度-温度关系曲线ν(T),发现升温过程中黏度随温度升高发生异常变化,当温度升高至1000—1075 K时,黏度由快速增大转变为逐渐减小,即发生转折变化;在随后的降温和第二次升温过程中,黏度随温度变化呈指数规律单调递增(减),符合Arrhenius方程式.在实验研究基础上,采用剩余键结构模型和"平均原子集团"演变行为的计算模型讨论Mg-9Al熔体的黏度与微观结构之间的相关性,结果表明:类关键词： 合金熔体 结构与黏度相关性 剩余键结构 平均原子集团模型     

Emergent cooperation amongst competing agents in minority games

We study a variation of the minority game. There are N agents. Each has to choose between one of two alternatives every day, and there is a reward to each member of the smaller group. The agents cannot communicate with each other, but try to guess the choice others will make, based only on the past history of the number of people choosing the two alternatives. We describe a simple probabilistic strategy using which the agents, acting independently, and trying to maximize their individual expected payoff, still achieve a very efficient overall utilization of resources, and the average deviation of the number of happy agents per day from the maximum possible can be made O(N^?), for any ?>0. We also show that a single agent does not expect to gain by not following the strategy.     

The Rasmussen invariants and the sharper slice-Bennequin inequality on knots

Rasmussen introduced a knot invariant based on Khovanov homology theory, and showed that this invariant estimates the four-genus of knots. We compare his result with the sharper slice-Bennequin inequality for knots. Then we obtain a similar estimate of the Rasmussen invariant for this inequality.     

Nonaxiomatisability of equivalences over finite state processes

This paper considers the existence of finite equational axiomatisations of behavioural equivalences over a calculus of finite state processes. To express even simple properties such as μxE = μxE[E/x] some notation for substitutions is required. Accordingly, the calculus is embedded in a simply typed lambda calculus, allowing such schemas to be expressed as equations between terms containing first order variables. A notion of first order trace congruence over such terms is introduced and used to show that no finite set of such equations is sound and complete for any reasonable equivalence finer than trace equivalence. The intermediate results are then applied to give two nonaxiomatisability results over calculi of regular expressions.