声学时间尺度下活塞效应的数值模拟研究

流体在气液临界点附近热平衡重新建立的时间大大缩短,这主要依赖于“活塞效应”对能量输运的加速作用,它本质上是一种热声波动作用。本文从基本控制方程组出发,通过数值求解流体动力学控制方程组,对声学时间尺度上超临界CO2中的动量和能量输运过程展开研究,结果表明流体温度空间分布不遵循经典傅里叶导热模型,其随时间的演化过程呈现明显...     

时间尺度上具阻尼项的二阶半线性时滞动力方程的振动准则(Ⅱ)

本文讨论一类具阻尼项的二阶半线性时滞动力方程解的振动性质, 利用广义Riccati 变换和不等式技巧. 在一定条件下, 建立了四个新的振动准则, 改进和推广了已知的一些结果.     

Landau-Zener-Stiickelberg interference in a multi-anticrossing system

We propose a universal analytical method of studying the dynamics of a multi-anticrossing system subjected to driving by a single large-amplitude triangle pulse, within a time scale smaller than the dephasing time. Our approach can explain the main features of the Landau-Zener St/ickelberg interference patterns recently observed in a tripartite system ]Nature Communications 1 51 （2010）]. In particular, we focus on the effect of the size of the anticrossing on interference and compare the calculated interference patterns with numerical simulations. In addition, a Fourier transform of the patterns can extract the information about the energy level spectrum.     

A multifractal model for linking Lagrangian and Eulerian velocity structure functions

A multifractal model is developed to connect the Lagrangian multifractal dimensions with their Eulerian counterparts. We propose that the characteristic time scale of a Lagrangian quantity should be the Lagrangian time scale, and it should not be the Eulerian time scale which was widely used in previous studies on Lagrangian statistics. Using the present model, we can obtain the scaling exponents of Lagrangian velocity structure functions from the existing data or models of scaling exponents of Eulerian velocity structure functions. This model is validated by comparing its prediction with the results of experiments, direct numerical simulations, and the previous theoretical models. The comparison shows that the proposed model can better predict the scaling exponents of Lagrangian velocity structure functions, especially for orders larger than 6.     

一般时间尺度上时滞脉冲系统的双测度稳定性

讨论了一般时间尺度上时滞脉冲系统的双测度稳定性问题.我们引进了一个新的概念即一般时间尺度上时滞脉冲系统的(h_0,h)稳定性.利用Lyapunov函数法和分析法得到了一般时间尺度上时滞脉冲系统解的双测度稳定性判据.最后给出了一个例子以说明本文结论的有效性.     

时间尺度上具阻尼项的二阶半线性时滞动力方程振动性的新结果

本文讨论一类具阻尼项的二阶半线性时滞动力方程解的振动性质, 利用广义Riccati 变换和不等式技巧, 在一定条件下, 建立了4 个新的振动准则, 其结果改进和推广了已知的一些结果.     

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.     

时间尺度上具阻尼项的二阶半线性时滞动力方程的振动准则

利用广义Riccati变换和不等式技巧,研究了一类具阻尼项的二阶半线性时滞动力方程解的振动性质,在一定条件下,建立了四个新的振动准则,其结果不仅推广和改进了已知的一些结果,而且在时间尺度上统一了具阻尼项的二阶半线性时滞微分方程和差分方程解的振动性质.     

时间尺度上三阶Emden-Fowler动力方程的振动准则

运用Riccati 变换技术, 研究了时间尺度T上三阶Emden-Fowler时滞动力方程 (a(t)(r(t)x^? (t))^? ) ^?+p(t)x^γ(τ(t)) = 0 的振动性, 这里γ>0是正奇数的比, a, r, p是定义在T上的正的实值rd -连续函数. 得到一些新的振动结果, 推广和丰富了已有文献中的结论. 另外, 还给出了几个例子说明主要结果的合理性.