Behavior of a Cylindrical Drop under Multi-Frequency Vibration

The behavior of an inviscid-fluid drop surrounded by a different fluid under the action of multi-frequency vibration is investigated. The second-order effects in the vibration amplitude are studied. A superharmonic resonance is registered. The stability of the forced oscillations with respect to small perturbations is studied. The condition of the onset of parametric resonance is found. An average drop shape is investigated. The two-frequency case is considered as a particular case of multi-frequency vibration.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, 2005, pp. 18–28.Original Russian Text Copyright © 2005 by Alabuzhev and Lyubimov.     

Plasma in a high-frequency electric field with a reflective condition on the boundary

An analytical solution is obtained for the linearized problem of the behavior of a collisional gas plasma in a half-space in an external alternating electric field. It is assumed that the electrons are mirror-reflected from the plasma boundary. The solution is used for finding the screened field. The case of an external field frequency close to the plasma frequency is investigated separately.     

硅微机械谐振陀螺仪的非线性分析

给出了硅微机械谐振陀螺仪的结构,介绍了硅微机械谐振陀螺仪的工作原理,详细推导并给出了陀螺仪的输出频率和标度因数非线性的计算公式;基于影响谐振陀螺仪标度因数的参数,分析了由谐振器的振幅和梳齿静电驱动力引起的硅微机械谐振陀螺仪的非线性特性,给出了振动幅度与谐振频率关系的表达式.实验结果表明,陀螺仪的整体性能主要取决于谐振器振动幅度的稳定性.     

Nonlinear Longitudinal Vibrations of Transversally Polarized Piezoceramics: Experiments and Modeling

Nonlinear behavior of piezoceramics at strong electric fields is a well-known phenomenon and is described by various hysteresis curves. On the other hand, nonlinear vibration behavior of piezoceramics at weak electric fields has recently been attracting considerable attention. Ultrasonic motors (USM) utilize the piezoceramics at relatively weak electric fields near the resonance. The consistent efforts to improve the performance of these motors has led to a detailed investigation of their nonlinear behavior. Typical nonlinear dynamic effects can be observed, even if only the stator is experimentally investigated. At weak electric fields, the vibration behavior of piezoceramics is usually described by constitutive relations linearized around an operating point. However, in experiments at weak electric fields with longitudinal vibrations of piezoceramic rods, a typical nonlinear vibration behavior similar to that of the USM-stator is observed at near-resonance frequency excitations. The observed behavior is that of a softening Duffing-oscillator, including jump phenomena and multiple stable amplitude responses at the same excitation frequency and voltage. Other observed phenomena are the decrease of normalized amplitude responses with increasing excitation voltage and the presence of superharmonics in spectra. In this paper, we have attempted to model the nonlinear behavior using higher order (quadratic and cubic) conservative and dissipative terms in the constitutive equations. Hamilton's principle and the Ritz method is used to obtain the equation of motion that is solved using perturbation techniques. Using this solution, nonlinear parameters can be fitted from the experimental data. As an alternative approach, the partial differential equation is directly solved using perturbation techniques. The results of these two different approaches are compared.     

一类强非线性机械基础系统的亚谐振动解析解

建立了机械基础动力系统的强非线性动力学模型，利用能量法对该系统的周期解进行了解析研究，确定了系统动态参数满足周期解的条件、系统的周期解以及解的稳定性判别式。发现了亚谐振动，并给出了系统在满足周期解条件下的一组参数对应的主振动、1／3亚谐振动和1／5亚谐振动。最后利用数值积分方法计算了系统在给定条件下的主振动及亚谐振动解，考察了解析解的正确性。     

The band gap and transmission characteristics investigation of local resonant quaternary phononic crystals with periodic coating

In this article, the investigation of the Lamb wave propagation in two-dimensional phononic crystals (PCs) composed of an array of periodic coating on a thin plate is presented. Compared with the traditional PCs usually consist of cylindrical scatters with uniform coatings in their exterior structure, the newly exterior coating structures with periodic alternant arrangement of two different materials are proposed. The band structures are calculated using finite element method. We discover that a complete band gap can be exhibited at low frequency. Furthermore, for a finite PCs plate, the computed transmission and resonance spectra shown an evident resonance nature which can be directly related to formation of the low-frequency gaps. The effects of different material parameters and arrangement mode of coating on the acoustic energy transmission and attenuation are also studied. Finally, the experimental transmission spectrum of the periodic coating PCs are also presented and compared with the numerical results. This study will provide useful support to the design of tuning band gaps and isolators in the low-frequency range.     

EPR,ENDOR and optical spectroscopy of Yb3+ ion in KZnF3 single crystals

The paramagnetic center of tetragonal symmetry formed by the Yb³⁺ ion in the KZnF₃ crystal has been studied using methods of EPR, ENDOR and optical spectroscopy. The location of the impurity ion and the structural model of the complex differing from the model of the Yb³⁺ center in KMgF₃ have been established. The empirical scheme of the energy levels of the Yb³⁺ ion has been found. The parameters of its interaction with the crystal electrostatic field and the hyperfine interaction with ligands of the nearest environment have been determined. The parameters of the crystal field were used for the analysis of the distortions of the crystal lattice in the vicinity of Yb³⁺. The parameters of the transferred hyperfine interaction have been calculated for the distances between Yb³⁺ and F⁻ ions of the nearest environment obtained taking into account the found distortions. They are in good agreement with the experimental values.     

Assessment of DFT functionals with fluorine–fluorine coupling constants†

Density functional theory (DFT) calculations of nuclear magnetic resonance (NMR) spin–spin coupling constants (SSCCs) provide an important contribution for understanding experimentally observed values. It is known that calculated SSCCs using DFT methods correlate well with those experimentally measured. Unlike most of SSCCs, in fluorine compounds, fluorine–fluorine SSCC J_FF shows that the Fermi contact (FC) term is not dominant, particularly for J_FF in polyfluorinated organic molecules. In order to devise a DFT approach that would correctly reproduce the variation of SSCCs within a series of fluorine compounds, we test several DFT-based approaches, using different exchange and correlation functionals. Isotropic contributions to NMR fluorine–fluorine coupling constants (FC, spin-dipolar, SD, paramagnetic spin-orbit, PSO, and diamagnetic spin-orbit, DSO) have been calculated. Results show that DFT methods give appropriate values for ⁿJ_FF (n = 4 to 7), while for geminal and vicinal J_FF present large deviations from experimental values. For the latter SSCCs (²J_FF and ³J_FF), the four contributions (FC, SD, PSO and DSO) are analysed as a function of the local and nonlocal exchange in 1,1- and 1,2-difluoroethylene. Although FC term is not dominant for these SSCCs, the variation of this contribution with exchange is remarkable. On the other hand, SD and PSO contributions can be suitably computed without and with exact exchange, respectively.     

CdTe量子点-铜酞菁复合体系荧光共振能量转移的研究

以波长为780 nm、重复频率为76 MHz、脉宽为130 fs的飞秒激光作为激发光源, 采用超快时间分辨光谱技术研究了CdTe量子点-铜酞菁复合体系的荧光共振能量转移. 实验结果表明, 在780 nm的双光子激发条件下, 复合体系中CdTe量子点的荧光寿命随着铜酞菁溶液浓度的增加而减少, 荧光共振能量转移效率增加. 同时也研究了激发功率对荧光共振能量转移效率的影响. 结果表明, 随着激发光功率的增加, 复合体系溶液中CdTe量子点的荧光寿命增加, 荧光共振能量转移效率减小, 其物理机理是因为高激发功率下的热效应和由双光子诱导的高阶激发态的跃迁. 当激发光功率为200 mW时, 双光子荧光共振能量转移效率为43.8%. 研究表明CdTe量子点-铜酞菁复合体系是非常有潜力的第三代光敏剂.