The Micro-Theory of Ultra-Short Pulse Propagating in Nonlinear Fiber

The modified quantum nonlinear Schrodinger equation of ultra-short pulse propagating in fiber is derived using dispersion relation and the Hamiltonian of the transmission system. The derived equation is solved with linearization approximation, and modulation instability is analyzed. The equation is also solved with Hartree approximation. The results indicate that pulse power, loss and self-steeping effect change the critical frequency, the maximum gain and the gain spectrum range, but the third order dispersion has no effect on modulation instability. The expectation value of optical field is average of a set of modified classical solitons, and higher order terms change the amplitude, pulse position and phase of soliton.     

The stress driven instability in elastic crystals: Mathematical models and physical manifestations

Summary Equilibrium equations and stability conditions for the simple deformable elastic body are derived by means of considering a minimum of the static energy principle. The energy is supposed to be sum of the volume (elastic) and the surface terms. The ability to change relative positions of different material particles is taken into account, and appropriate natural definitions of the first and second variations of the energy are introduced and calculated explicitly. Considering the case of negligible magnitude of the surface tension, we establish that an equilibrium state of a nonhydrostatically stressed simple elastic body (of any physically reasonable elastic energy potential and of any symmetry) possessing any small smooth part of free surface is always unstable with respect to relative transfer of the material particles along the surface. Surface tension suppresses the mentioned instability with respect to sufficiently short disturbances of the boundary surface and thus can probably provide local smoothness of the equilibrium shape of the crystal. We derive explicit formulas for critical wavelength for the simplest models of the internal and surface energies and for the simplest equilibrium configurations. We also formulate the simplest problem of mathematical physics, revealing peculiarities and difficulties of the problem of equilibrium shape of elastic crystals, and discuss possible manifestations of the above-mentioned instability in the problems of crystal growth, materials science, fracture, physical chemistry, and low-temperature physics.     

On the Criteria of Instability for Electrochemical Systems

Both cyclic-voltammetry-based and impedance-based experimental criteria that have been developed recently for the oscillatory electrochemical systems are critically appraised with two typical categories of oscillators.Consistent conclusions can be drawn by the two criteria for the category of oscillators that involve the coupling of charge transfer mainly with surface steps(e.g.ad-and desorption)such as in the electrooxidation of C1 organic molecules.Whereas,impedance-based criterion is not applicable to the category of oscillators that involve the coupling of charge transfer mainly with mass transfer(e.g.diffusion and convection) such as in the Fe(CN)6^3- reduction accompanying periodic hydrogen evolution.The reason is that the negative impedance cannot include the feedback information of convection mass transfer induced by the hydrogen evolution.However,both positive and negative nonlinear feedbacks,i.e., the diffusion-limited depletion and convection-enhanced replenishment of the Fe(CN)6^3- surface concentration,that coexist between the bistability,i.e.,Fe(CN)6^3- reduction with and without hydrogen evolution at lower and higher potential sides respectively,are all reflected in the crossed cyclic voltammogram(CCV).It can be concluded that the voltammetry-based criterion(in time domain)is more intuitive,less time-consuming and has a wider range of applications than the impedancebased one (in frequency domain).     

带背景激波系的凹腔流动特性研究

凹腔作为超燃冲压发动机的一种火焰稳定器受到广泛关注,凹腔剪切层与背景激波系的相互作用影响凹腔火焰稳定器的性能。为深入分析背景激波系对凹腔流动的影响,设计了长深比为13.3的闭式凹腔,将凹腔模型前缘激波和风洞上壁面干扰激波作为背景激波系,在Ma=2的直连式风洞中开展了背景激波系与凹腔剪切层的相互作用的试验,采用高速纹影系统对瞬态流场进行了捕捉,重点关注背景激波系和凹腔剪切层的动态变化特性。采用纹影序列的本征正交分解来研究流场中的主要相干结构,采用快速傅里叶变换和连续小波变换对流场的频率域特征进行了分析。结果表明：在背景激波与剪切层相互作用下,激波结构产生大尺度振荡,凹腔内流动结构产生小尺度脉动。通过对激波位置的傅里叶变换分析,发现激波振荡的主导频率集中在90～400 Hz的范围内。通过对纹影图像的空间傅里叶变换分析,发现5 kHz以下的流场振荡主要由激波振荡引起,5 kHz以上的流场脉动主要由凹腔内流动结构引起。     

扩展裂纹缺陷评定方法的优化研究

裂纹扩展的缺陷评定方法,越益受到了人们的重视,美国ＥＰＲＩ提出的“裂纹 推力图”方法,虽然准确合理,但方法偏于繁复,尚难于向工程界推广。清华大学力学 研究所曾先后提出几种评定方法,以期使评定过程得以简化。在此基础上,文章提出 “相容应力增量”法作为优化方法,它将使全部评定过程大为简化,从而为扩展裂纹的 缺陷评定方法向工程界推广创造便利条件。     

Negative-mass instability at nonsymmetrical perturbations

The negative-mass (space-charge) instability is studied within the model of a flat thin electron beam moving along the stationary uniform magnetic field in the case of nonsymmetrical perturbations. It is shown that due to the phenomenon of "phase mixing" of electron bunches the instability increments are small for perturbations with spatial scales smaller than the Larmor diameter.     

竖壁下降液膜受热流动的不稳定性分析

利用液膜自由表面的温度随波动变化的关系,从理论上分析了饱和液膜在竖壁上受热流动因温度不均而存在表面张力波动的流动不稳定性,讨论了波数,雷诺数,壁面和液膜温差的影响。     

考虑空洞演化效应的金属超塑性变形理论

根据金属超塑性变形时一般出现严重空洞化的特点,对金属板料超塑性变形时的屈服准则、空洞长大模型、材料损伤动力学方程、起塑性极科的受拉（包括双向受拉）失稳过程和先稳时的成形极限计算方法,起塑性极科成形极限图的预测以及自由胀形和充模胀形等具体起塑成形工艺考虑空洞演化效应的工艺计算与分析等问题进行了系统全面的研究．从而形成了考虑空洞演化效应的金属起塑性变形理论体系。对考虑空洞演化效应的金属起塑性变形理论中的基本问题作了扼要介绍。     

Effect of surfactants on the stability of thin liquid film flow on a rotating disk

The effect of surfactants on surface instabilities of thin liquid film flow on a rotating disk was studied at different flow rates Q (0.5相似文献   

On the origin of dynamic instability of molecular systems

The vibronic origin of dynamic instability of molecular systems considered earlier, is here given a more complete and rigorous treatment. It is shown that the nonvibronic contribution to the curvature of the adiabatic potential arising due to nuclear displacements under fixed electronic density distribution, is always positive, and hence the only reason for dynamic instability is the pseudo Jahn-Teller effect. For some examples of special interest (planar equilateral NH₃, planar square CH₄ and linear H ₃ ⁺ ) the molecular excited states, responsible for the instability of the ground state, are revealed by means of ab initio calculations.