一类谐波激励相对转动非线性动力系统的稳定性与近似解

建立具有一般非线性弹性力、广义摩阻力和谐波激励的一类相对转动非线性动力系统的动力学方程. 对相对转动非线性自治系统进行定性分析,通过构造Lyapunov函数研究自治系统奇点的稳定性. 运用多尺度法求解谐波激励下非自治系统在几种不同共振响应下的近似解,同时分析了主振系统稳态运动的稳定性. 关键词： 相对转动 非线性动力系统 Lyapunov函数 稳定性     

Fidelity for States of Spin- \frac{1}{2} Particles Moving in a Traversable Wormhole Spacetime

Fidelity for states of spin- particles moving in a static spherically symmetric traversable wormhole spacetime is discussed. When the centroid of the corresponding wave packet moves along a specified path in the gravitational field, both acceleration and gravity cause to transform the state of the particle. For circular orbits of the centroid coinciding the throat of wormhole, the fidelity between initial and final states of the whole system as well as the fidelity of the spin parts of the states are equal to the unity. This means that, the error in quantum communication diminishes on such a paths. For fixed elapsed proper time and angular momentum of the centroid, there always exists one circular orbit with determined radius on which the fidelity of spin parts is minimum. The fidelity for wave packets moving along a radial geodesic toward the throat of wormhole is also discussed. In this case, the centroid traverses the wormhole and reaches to the other side, with a perfect fidelity for the spin parts, though the fidelity for the states of the whole system is not perfect.     

基于模场自积增强检测的光纤声光旋转传感器

介绍了一种应变不敏感的基于模场自积增强检测的光纤声光旋转传感器.通过调节加载到光纤声致光栅上的微波频率能使双模光纤输出高纯度LP_(11)模式.采用自积增强算法显著提高传感分辨比例,改善探测速度,实现对环境旋转角度变化的动态监测.传感器在0°—180°的测量范围内,角度最大测量误差范围小于11%;在轴向应变为100—1500με之间对应变不敏感.     

铷原子气体自旋噪声谱的测量与改进

利用自主设计并制作的基于现场可编程门阵列的实时傅里叶变换采集卡(FFTsDAC),采用线偏振光检测碱金属铷原子气样品中的自旋随机涨落(即自旋噪声谱).详细讨论了背景噪声以及自旋噪声随探测光光强的变化关系,证实了自旋噪声来自于系统中自旋的随机涨落.对比了两种FFTsDAC(8 bit采样的FFTsDACl和12 bit采样的FFTsDAC2)的测量性能,分析了影响实验信噪比的因素.FFTsDAC2具有更高的测量效率和采样深度以及更长的单次采样时间,因而具有更高的信噪比和更好的频率分辨率,与数值模拟的结果一致.     

Multifarious injection chamber for molecular structure study (MICOSS) system: development and application for serial femtosecond crystallography at Pohang Accelerator Laboratory X‐ray Free‐Electron Laser

The multifarious injection chamber for molecular structure study (MICOSS) experimental system has been developed at the Pohang Accelerator Laboratory X‐ray Free‐Electron Laser for conducting serial femtosecond crystallography. This system comprises several instruments such as a dedicated sample chamber, sample injectors, sample environment diagnostic system and detector stage for convenient distance manipulation. Serial femtosecond crystallography experiments of lysozyme crystals have been conducted successfully. The diffraction peaks have reached to ～1.8 Å resolution at the photon energy of 9.785 keV.     

Equilibrium structure in the presence of internal rotation: A case study of cis-methyl formate

The Born-Oppenheimer (BO) equilibrium molecular structure () of cis-methyl formate has been determined at the CCSD(T) level of electronic structure theory using Gaussian basis sets of at least quadruple-ζ quality and a core correlation correction. The quadratic, cubic and semi-diagonal quartic force field in normal coordinates has also been computed at the MP2 level employing a basis set of triple-ζ quality. A semi-experimental equilibrium structure () has been derived from experimental ground-state rotational constants and the lowest-order rovibrational interaction parameters calculated from the ab initio cubic force field. To determine structures, it is important to start from accurate ground-state rotational constants. Different spectroscopic methods, applicable in the presence of internal rotation and used in the literature to obtain “unperturbed” rotational constants from the analysis and fitting of the spectrum, are reviewed and compared. They are shown to be compatible though their precision may be different. The and structures are in good agreement showing that, in the particular case of cis-methyl formate, the methyl torsion can still be treated as a small-amplitude vibration. The best equilibrium structure obtained for cis-methyl formate is: r(C_m-O) = 1.434 Å, r(O-C_c) = 1.335 Å, r(C_m-H_s) = 1.083 Å, r(C_m-H_a) = 1.087 Å, r(C_c-H) = 1.093 Å, r(CO) = 1.201 Å, ∠(COC) = 114.4°, ∠(CCH_s) = 105.6°, ∠(CCH_a) = 110.2°, ∠(OCH) = 109.6°, ∠(OCO) = 125.5°, and τ(H_aCOC) = 60.3°. The accuracy is believed to be about 0.001 Å for the bond lengths and 0.1° for the angles.     

Dynamical structure of peptide molecules: Fourier transform microwave spectroscopy and ab initio calculations of N-methylformamide

Rotational spectra of both trans and cis forms of the N-methylformamide normal as well as deuterated (HCONDCH₃, referred to as N-D) species were observed by Fourier transform microwave spectroscopy in the frequency region from 5 to 118 GHz. Samples were prepared in the form of a beam by a pulsed jet valve maintained at 50 °C and were introduced in a high-vacuum cavity cell, with either Ne or Ar as a carrier gas at a backing pressure of 100 kPa. The observed spectra were analyzed to yield molecular parameters including rotational constants and barrier, V₃, to CH₃ internal-rotation: 53.9 (6) and 301 (4) cm⁻¹ for the trans and cis forms of the normal species, respectively, and 41.9 (6) and 309 (4) cm⁻¹ for the trans and cis forms of the N-D species, respectively. Spectra of four trans isotopologues with ¹³C, ¹⁵N, or ¹⁸O singly-substituted in the internal-rotation A state were observed and analyzed to derive the r_s structure of the trans form. For comparison with the experimental data, ab initio calculations were carried out at MP2/6-31G∗∗ level to derive molecular structure, potential barrier to CH₃ internal rotation, and the energy difference between the cis and trans forms. An extensive coupling was found between the CH₃ internal rotation and N-H out-of-plane bending, suggesting that the potential function for the CH₃ internal-rotation deviates considerably from a simple cos(3α) form. The effects of the V₆ term is briefly discussed.     

Periodic intensity variations on the pulse-train of a passively mode-locked fiber ring laser

We investigate the evolvement of the periodic intensity variations of the pulse-train in a fiber ring laser mode-locked by the nonlinear polarization rotation technique. It is found that the phenomenon of such intensity fluctuations is related to the orientation of the polarization controllers when the pump power is fixed. The numerical results show that the mechanism of the periodic intensity variations is caused by the interaction of the nonlinear polarization rotation and the passive polarizer in the cavity.     

基于非线性偏振旋转效应的多波长掺铥锁模光纤激光器

运用非线性偏振旋转效应实现了一种掺铥锁模多波长光纤激光器.采用环形腔结构,以1 565nm半导体光源为泵浦源,3m长掺铥光纤为增益介质.利用非线性偏振旋转效应进行滤波.当泵浦功率在800mW时,通过调节光纤偏振控制器,激光器出现了被动锁模状态的脉冲输出,脉冲重复频率为3.178MHz,脉冲宽度为617ps.进一步增加泵浦功率,激光器进入多波长输出的工作状态.调节偏振控制器在室温下得到1~5个稳定的波长激光输出,边摸抑制比为40~60dB.     

一类相对转动时滞非线性动力系统的稳定性分析

建立了具有时变刚度、非线性阻尼和谐波激励的一类相对转动时滞非线性动力系统的动力学方程.采用多尺度法推导出时滞动力系统的分岔响应方程,运用奇异性理论研究系统结构稳定性,得到主共振稳态响应方程的转迁集以及不同参数下分岔曲线的拓扑结构.应用Hopf分岔理论讨论了时滞动力系统动态稳定性,给出了系统产生极限环的条件,最后用数值模拟的方法研究了时滞参数对系统极限环幅值的影响。