Early transient responses of multi-span stepped single-walled carbon nanotubes using the method of reverberation ray matrix

The early transient responses of multi-span stepped single walled carbon nanotubes (SWCNTs) under impact loadings are studied by the method of reverberation ray matrix (MRRM). The dynamics model of the carbon nanotubes is established in the Fourier phase space on the basis of the nonlocal Timoshenko beam model. The wave solutions of SWCNTs with arbitrary boundary conditions are obtained by the wave method. The reverberation ray matrix of the multi-span stepped SWCNTs is the product of scattering, phase and permutation matrices, which can be determined by the impact loadings, continuous conditions and boundary conditions. The early transient responses can be calculated by the inverse Fourier transform of the sum of initial ray groups. It can be found that the early transient displacement response in the very short time subjected to the impact loading is very small, while the transient transverse shear strain becomes large in the very short time. The influences of nanotubes span number, nanotubes type and boundary conditions on the early transient responses of multi-span stepped SWCNTs are investigated.     

GENERALIZED FRACTIONAL TRACE VARIATIONAL IDENTITY AND A NEW FRACTIONAL INTEGRABLE COUPLINGS OF SOLITON HIERARCHY

Based on fractional isospectral problems and general bilinear forms, the gener-alized fractional trace identity is presented. Then, a new explicit Lie algebra is introduced for which the new fractional integrable couplings of a fractional soliton hierarchy are derived from a fractional zero-curvature equation. Finally, we obtain the fractional Hamiltonian structures of the fractional integrable couplings of the soliton hierarchy.     

一类非线性偏微分方程组的直接解法

根据Hopf-Cole变换法和试探函数法的基本思想,引入一个变换,并把它应用于求解(2+1)维破裂孤子方程组、(2+1)维Nizhnik-Novikov-Vesslov方程组和(2+1)维Broer-Kaup方程组,得到了这三个方程组的许多新的解析解,包括孤波解和奇异行波解.该方法也适用于其它方程组.     

向列相液晶中强非局域空间光孤子的实验观察

通过实验对向列相液晶中的非局域空间光孤子的传输进行了研究。理论上基于非线性的液晶孤子传输方程,采用高斯形式的试探解,得到了孤子传输的解析解,以及对液晶中的非局域孤子和Snyder等提出的强非局域孤子模型的结果进行了比较。实验上,观察了空间光孤子在向列相液晶中的传输,找到了不同束宽下空间光孤子的临界功率。比如束宽为2μm时临界功率为2.0mW。观察了向列相液晶中空间光孤子的弛豫过程,并注意到液晶分子的响应时间长达几秒钟,液晶中的孤子形成速度较慢。     

差分相移键控色散管理孤子多扰动系统的相位抖动

差分相移键控(DPSK)调制方式和色散管理孤子传输方式的结合能抵制噪声和非线性损伤,在高速(40 Gbit/s以上)多信道系统中具有突出的优点。采用变分法分析了多波长信道的放大自发辐射(ASE)噪声、信号间的非线性串扰(ISI)等多种扰动因素引起差分相移键控色散管理孤子系统的均方根相位抖动,给出了扰动的作用区域以及各扰动的大小。研究发现,放大自发辐射引起的抖动与传输距离成三次方的关系,而交叉相位调制(XPM)引起的抖动与距离近似成线性关系。通过优化选择色散管理图强度范围1.5~3.5,各种扰动得到了抑制,而以放大自发辐射扰动抑制为最大,此时要远低于交叉相位调制引起的抖动,然后分别是交叉相位调制-放大自发辐射扰动和交叉相位调制,从而波分复用系统主要来自于增加信道数这一客观限制。     

梯度折射率非局域介质中空间孤子振荡行为研究

应用等效粒子近似方法研究了光学空间孤子在带有局域和非局域非线性横向非均匀介质中的传输动力学行为.发现孤子在传播过程中横向的周期性振荡.折射率调制幅度和波导的归一化宽度决定了振荡周期的大小.介质的非局域对振荡振幅有着较小的影响.模拟了孤子传输过程,所得数值结果与理论分析符合很好.此外,模拟传输还发现多孤子束缚态能够在这个模型中稳定传播.这种振荡特性或许可以应用于光学路由器、转换器、开关等.     

计算流管声场的三维有限元数值模型

发展了一种三维有限元数值模型和计算方法来对矩形流管声场进行整体的计算.与以往的二维方法相比,此种数值方法不仅全面反映了矩形流管内声波的传播情况,而且提高了网格精度,从而大大扩展了对铺设有声衬的流管的计算领域.结果表明,该数值模型是有效和准确的,与其它方法和文献的计算结果吻合得非常好.同时,在大大增加计算量的同时,也对程序代码进行了优化工作,提高了计算效率.     

A study of the effect of step excrescences and free‐stream disturbances on boundary layer stability

In this work, a study of the mechanism by which free‐stream acoustic and vorticity disturbances interact with a boundary layer flow developing over a flat plate featuring a step excrescence located at a certain distance from a blunt leading edge is included. The numerical tool is a high‐fidelity implicit numerical algorithm solving for the unsteady, compressible form of the Navier–Stokes equations in a body‐fitted curvilinear coordinates and employing high‐accurate compact differencing schemes with Pade‐type filters. Acoustic and vorticity waves are generated using a source term in the momentum and energy equations, as opposed to using inflow boundary conditions, to avoid spurious waves that may propagate from boundaries. The results show that the receptivity to surface step excrescences is largely the result of an overall adverse pressure gradient posed by the step, and that the free‐stream disturbances accelerate the generation of instabilities in the downstream. As expected, it is found that the acoustic disturbance interacting with the surface imperfection is more efficient in exciting the Tollmien–Schlichting waves than the vorticity disturbance. The latter generates Tollmien–Schlichting waves that are grouped in wave packets consistent with the wavelength of the free‐stream disturbance. Copyright © 2015 John Wiley & Sons, Ltd.     

Wave propagation in fluid-conveying viscoelastic single-walled carbon nanotubes with surface and nonlocal effects

In this paper, the transverse wave propagation in fluid-conveying viscoelastic single-walled carbon nanotubes is investigated based on nonlocal elasticity theory with consideration of surface effect. The governing equation is formulated utilizing nonlocal Euler-Bernoulli beam theory and Kelvin-Voigt model. Explicit wave dispersion relation is developed and wave phase velocities and frequencies are obtained. The effect of the fluid flow velocity, structural damping, surface effect, small scale effects and tube diameter on the wave propagation properties are discussed with different wave numbers. The wave frequency increases with the increase of fluid flow velocity, but decreases with the increases of tube diameter and wave number. The effect of surface elasticity and residual surface tension is more significant for small wave number and tube diameter. For larger values of wave number and nonlocal parameters, the real part of frequency ratio raises.