Semilinear wave models with friction and viscoelastic damping

In this paper, we study the global (in time) existence of small data solutions to the Cauchy problem for the semilinear wave equation with friction, viscoelastic damping, and a power nonlinearity. We are interested in the connection between regularity assumptions for the data and the admissible range of exponents p in the power nonlinearity.     

Second-order random wave solutions for interfacial internal waves in N-layer density-stratified fluid

This paper studies the random internal wave equations describing the density interface displacements and the velocity potentials of N-layer stratified fluid contained between two rigid walls at the top and bottom. The density interface displacements and the velocity potentials were solved to the second-order by an expansion approach used by Longuet-Higgins （1963） and Dean （1979） in the study of random surface waves and by Song （2004） in the study of second- order random wave solutions for internal waves in a two-layer fluid. The obtained results indicate that the first-order solutions are a linear superposition of many wave components with different amplitudes, wave numbers and frequencies, and that the amplitudes of first-order wave components with the same wave numbers and frequencies between the adjacent density interfaces are modulated by each other. They also show that the second-order solutions consist of two parts： the first one is the first-order solutions, and the second one is the solutions of the second-order asymptotic equations, which describe the second-order nonlinear modification and the second-order wave-wave interactions not only among the wave components on same density interfaces but also among the wave components between the adjacent density interfaces. Both the first-order and second-order solutions depend on the density and depth of each layer. It is also deduced that the results of the present work include those derived by Song （2004） for second-order random wave solutions for internal waves in a two-layer fluid as a particular case.     

一类机器人系统的最优控制

本文通过把结构阻尼系数当作控制变量来讨论一类弹性机器人系统的最优控制问题 ,并利用Banach空间几何性质证明了最优控制元的存在唯一性     

The generation of three-dimensional internal waves and attendant boundary layers in a viscous continuously stratified fluid. Construction of an analytical solution

An analytical solution of a linearized problem of the emission of periodic internal waves by part of a plane which oscillates with a small amplitude in an arbitrary direction in a viscous exponentially stratified fluid is constructed. Solutions of the dispersion equation are given for all positions of the emitting surface (arbitrary, vertical, horizontal, and critical when one of the beam propagation directions is collinear with the emitting surface). The possibility of transition to the case of a uniform fluid, which is important for applications, is analyzed.     

全内反射荧光显微术应用于单分子荧光的纵向成像

利用这种显微术中激发场的纵向强度呈指数衰减的分布特性，测得的荧光强 度将强烈依赖渗透深度（强度衰减到1/e时的距离），从而快速直接的确定单分子荧光 团间的纵向间隔、每个荧光团的纵向绝对位置和荧光团的半径大小，即实现荧光分子三维分 布的重构.在整个重构的过程中，只需要改变一次入射角的大小，即只需探测两幅荧光分子 的全内反射成像. 关键词： 全内反射荧光显微术 纵向重构     

Oscillation theorems for differential equations with a nonlinear damping term

In this paper, we are concerned with a class of nonlinear second-order differential equations with a nonlinear damping term. Passage to more general class of equations allows us to remove a restrictive condition usually imposed on the nonlinearity, and, as a consequence, our results apply to wider classes of nonlinear differential equations. Two illustrative examples are considered.     

A thermodynamic approach with internal variables using Lagrange formalism. Part I: General framework

We present some reflections on the application of the Lagrangian formalism for continuous media locally uniform subjected to internal irreversible evolutions. The Lagrangian density, defined as the time derivative of a non-equilibrium thermodynamic potential, [Thermodynamics of Relaxation Processes using Internal variables within a Lagrange-formalism. P. Germain’s Anniversary Volume 2000. Contiuum Thermomechanics: the Art and Science of Modeling Matter’s Behaviour, 2000], contains all the symmetry properties of the system. The generalised Lagrange co-ordinates correspond to the state and internal variables of the time derivative of the generalised Gibbs potential. The latter being used within the framework of the De Donder’s method, must also account for the memory effect of the physical medium.This first part is devoted to the thermodynamic framework called the distribution of non-linear relaxations approach (DNLR) developed by C. Cunat on the basis of the generalised Gibbs’ relation.     

快冷Fe_(71)Al_(29)合金中的两个内耗峰

用一个计算机控制的倒扭摆研究了快冷Fe71 Al2 9合金中的两个内耗峰 .在快冷的Fe71 Al2 9样品中分别在 180℃(P1 ) ,340℃ (P2 )和 5 10℃ (P3)出现了内耗峰 ,而在慢冷的Fe71 Al2 9样品中只发现了P3峰 .快冷样品中的P1 和P2峰在从 6 5 0℃冷却下来的测量过程中或在 35 0℃经过较长时间的时效后消失 ,其峰高随时效时间的增加而下降 ,直至消失 .P1 和P2 峰都有弛豫特征 ,它们的激活能分别为 :H1 =1.0 3± 0 .0 8eV(P1 峰 ) ;H2 =1.6 4± 0 .0 5eV(P2 峰 ) .P1 峰被认为是无序合金中Al原子在四面体点阵内的最近邻运动所引起 ,P2 峰则是无序合金中Al原子在四面体点阵内的次近邻运动所引起     

微波谐振腔Q值对磁激子振幅不稳定态阈值的影响

基于Safonov和Yamazaki所发展的激励自旋波非线性辐射衰减的理论［J. MMM. 161 (1996 ) 275］, 考虑磁激子与磁激子以及磁激子与光子的两种非线性相互作用过程，计算了微波谐振腔Q值对磁激子振幅不稳定态阈值的影响，结果与实验数据基本一致. 关键词： 磁激子 谐振器 铁磁体     

Two-dimensional numerical calculation of the flow field about a scoop inlet by the piecewise linear method

The piecewise linear method (PLM) based on time operator splitting is used to solve the unsteady compressible Euler equations describing the two-dimensional flow around and through a straight wall inlet placed stationary in a rapidly rotating supersonic flow. The PLM scheme is formulated as a Lagrangian step followed by an Eulerian remap. The inhomogeneous terms in the Euler equations written in cylindrical coordinates are first removed by Sod's method and the resulting set of equations is further reduced to two sets of one-dimensional Lagrangian equations, using time operator splitting. The numerically generated flow fields are presented for different values of the back pressure imposed at the downstream exit of the inlet nozzle. An oblique shock wave is formed in front of the almost whole portion of the inlet entrance, the incoming streamlines being deflected towards the higher pressure side after passing through the oblique shock wave and then bending down to the lower pressure side. A reverse flow appears inside the inlet nozzle owing to the recovery pressure of the incoming streams being lower than the back pressure of the inlet nozzle.