GLOBAL EXISTENCE, UNIFORM DECAY AND EXPONENTIAL GROWTH FOR A CLASS OF SEMI-LINEAR WAVE EQUATION WITH STRONG DAMPING

In this paper, we consider the nonlinearly damped semi-linear wave equation associated with initial and Dirichlet boundary conditions. We prove the existence of a local weak solution and introduce a family of potential wells and discuss the invariants and vacuum isolating behavior of solutions. Furthermore, we prove the global existence of solutions in both cases which are polynomial and exponential decay in the energy space respectively, and the asymptotic behavior of solutions for the cases of potential well family with 0相似文献   

OSCILLATION CRITERIA FOR SECOND ORDER NONLINEAR DYNAMIC EQUATIONS WITH p-LAPLACIAN AND DAMPING

This paper concerns the oscillation of solutions of the second order nonlinear dynamic equation with p-Laplacian and damping（r（t）φ（x^△（t））^△＋p（t）φα（x^△α（t）＋q（t）f（xδ（t））=0on a time scale T which is unbounded above. Sign changes are allowed for the coefficient functions r, p and q. Several examples are given to illustrate the main results.     

Effects of the symmetry energy slope on the axial oscillations of neutron stars

The impact of symmetry energy slope L on the axial w-mode oscillations is explored, where the range of the con- strained slope L of symmetry energy at saturation density is adopted from 25 MeV to 115 MeV while keeping the equation of state （EOS） of symmetric nuclear matter fixed. Based on the range of the symmetry energy slope, a constraint on the frequency and damping time of the wi-mode of the neutron star is given. It is found that there is a perfect linear relation between the frequency and the stellar mass for a fixed slope L, and the softer symmetry energy corresponds to a higher frequency. Moreover, it is confirmed that both the frequencies and damping times have a perfect universal scaling behavior for the EOSs with different symmetry energy slopes at saturation density.     

一类带阻尼项的二阶强迫脉冲微分方程的区间振动准则

研究了一类带阻尼项的二阶强迫脉冲微分方程的区间振动性质,利用广义Riccati变换、不等式技巧,建立了对该类方程的El-Sayed型和Kameneve型新的振动准则.结果改进和推广了最近文献中的一些相应结论.     

多层隔震结构地震作用取值的解析分析法

为建立多层隔震结构等效静态抗震设计法,对该结构基于规范反应谱的最大地震效应及其等效静态地震作用取值的解析分析法进行了系统研究。首先运用实振子解耦法,将非对称非经典隔震结构响应精确分解为系列标准振子位移与速度响应的线性组合;继而根据随机振动频域法和响应方差与最大响应平方成正比的性质,将结构位移的响应方差及最大响应平方精确分解为系列标准振子位移与速度响应方差及反应谱平方的线性组合,精确获得了隔震结构基于规范加速度谱的最大地震效应;最后基于静态效应与最大动态效应的等效准则,给出了基于最大位移响应的等效地震作用的新定义及其取值的解析计算法,使新定义的地震作用精确满足等效准则,并通过算例,验证了所提出方法的正确性。所建立的方法基于响应精确解耦和方差精确分解以及等效准则精确满足,属精确解析法,具有一般性,较基于响应近似解耦和方差近似分解以及等效准则近似满足的现有地震作用(即最大惯性力)计算方法更科学合理。     

适应复杂外形的三维粘性混合网格生成算法

提出一类适应复杂外形的粘性混合网格生成算法。表面网格由前沿推进三角形曲面网格程序获得,边界层布置各向异性的三棱柱体网格,远物面区域采用Delaunay方法生成四面体网格。针对模型的复杂几何特征,综合采用了各种网格处理技术,以保证边界层网格的质量,并避免算法失效问题。网格实例及计算结果表明了本文算法的实用性及和效性。     

Damping in a Squeezed Bath and Its Time Evolution through the Complete Class of Gaussian Quasi-Distributions

By virtue of the thermo-entangled states representation of the density operator and using the dissipative interaction picture, we solve the master equation of a driven damped harmonic oscillator in a squeezed bath. We show that the essential part of the dynamics can be expressed by the convolution of the initial Wigner function with a special kind of normalized Gaussian in the phase space and relate the dynamics with the change of Gaussian ordering of the density operator.     

带非线性阻尼项的三维可压缩欧拉方程组的整体解

研究了三维空间中带非线性阻尼项的可压缩欧拉方程组的初值问题.利用能量估计和傅立叶分析的方法,在初值是常状态附近的一个H~3∩L~1中的小扰动时获得了初值问题的解整体存在,并得到了解在大时间的L~2,L~∞衰减率分别为t~(-3/4),t~(-3/2),将线性阻尼的情形推广到了非线性阻尼的情形.     

Dynamic steering beams for efficient force measurement in optical manipulation

An efficient and inexpensive method that uses a glass plate mounted onto a motorized rotating stage as a beam-steering device for the generation of dynamic optical traps is reported.Force analysis reveals that there are drag and trapping forces imposed on the bead in the opposite directions,respectively,in a viscous medium.The trapped bead will be rotated following the beam’s motion before it reaches the critical escape velocity when the drag force is equal to the optical trapping force.The equilibrium condition facilitates the experimental measurement of the drag force with potential extensions to the determination of the viscosity of the medium or the refractive index of the bead.The proposed technique can easily be integrated into conventional optical microscopic systems with minimum modifications.     

复杂结构冲击声合成及实验验证

以复杂结构受击振动响应的时域计算为目的, 讨论了结构阻尼的计算方法, 给出一种用于冲击声合成的综合数值方法, 并进行了实验验证. 首先, 考虑到阻尼是影响瞬态振动时变特性的重要因素, 详细讨论了两种模态阻尼的计算方法; 其次, 对阻尼板的受击振动和声辐射进行了时域仿真, 并与时域有限差分法的计算结果进行对比, 显示出两种声音合成方法的计算结果具有高度的一致性; 最后, 针对有限长圆柱壳的受击振动, 将合成声与实验录音进行了对比研究. 结果表明, 合成声与实际录音的时域包络、频谱结构以及衰减趋势基本一致, 证明了采用数值方法进行冲击声合成的有效性. 关键词： 声音合成 模态阻尼 冲击声 数值方法