A ring-cavity for a quadrupled Nd-Yag lasera

Summary A new high-powered ultraviolet laser system is proposed. The system doubles the infrared light from a Nd-Yag laser mode-locked at 100 MHz, injects this light into a storage-ring cavity to accumulate a high power in the visible and then doubles this into the ultraviolet at 2600 ?. The power levels anticipated at this wavelength are much larger than those of commercially available c.w. lasers. The new system can have a far-reaching impact in basic research and, even more so, in a great many industrial applications.     

BBOⅠ类相位匹配光参量放大中群速失配的补偿

描述了在BBOⅠ类相位匹配的飞秒光参量放大（OPA）中，利用非共线结构和倾斜抽运光的脉 冲波面来完全补偿三波群速失配的方法.理论计算了三波群速匹配时，非共线角、相位匹配 角、抽运光的脉冲波面倾斜角随信号光波长的变化，并分析了对抽运光光斑尺寸的要求和对 空间走离长度的影响.结果表明，利用该方法不仅能够实现最大的参量带宽，而且能够完全 补偿飞秒OPA中三波的群速失配.此外，选取合适的抽运光光斑尺寸和非线性晶体的长度对提 高参量增益也至关重要. 关键词： 群速匹配 非共线相位匹配 脉冲波面倾斜 飞秒光参量放大     

Solitary waves in the Madelung's fluid: Connection between the nonlinear Schrödinger equation and the Korteweg-de Vries equation

An investigation to deepen the connection between the family of nonlinear Schr?dinger equations and the one of Korteweg-de Vries equations is carried out within the context of the Madelung's fluid picture. In particular, under suitable hypothesis for the current velocity, it is proven that the cubic nonlinear Schr?dinger equation, whose solution is a complex wave function, can be put in correspondence with the standard Korteweg-de Vries equation, is such a way that the soliton solutions of the latter are the squared modulus of the envelope soliton solution of the former. Under suitable physical hypothesis for the current velocity, this correspondence allows us to find envelope soliton solutions of the cubic nonlinear Schr?dinger equation, starting from the soliton solutions of the associated Korteweg-de Vries equation. In particular, in the case of constant current velocities, the solitary waves have the amplitude independent of the envelope velocity (which coincides with the constant current velocity). They are bright or dark envelope solitons and have a phase linearly depending both on space and on time coordinates. In the case of an arbitrarily large stationary-profile perturbation of the current velocity, envelope solitons are grey or dark and they relate the velocity u₀ with the amplitude; in fact, they exist for a limited range of velocities and have a phase nonlinearly depending on the combined variable x-u_{0 s} (s being a time-like variable). This novel method in solving the nonlinear Schr?dinger equation starting from the Korteweg-de Vries equation give new insights and represents an alternative key of reading of the dark/grey envelope solitons based on the fluid language. Moreover, a comparison between the solutions found in the present paper and the ones already known in literature is also presented. Received 20 February 2002 and Received in final form 22 April 2002 Published online 6 June 2002     

Stability of testing hypotheses

The stability of testing hypotheses is discussed. Differing from the usual tests measured by Neyman-Pearson lemma, the regret and correction of the tests are considered. After the decision is made based on the observationsX ₁,X ₂, ⋅⋅⋅,X _n, one more piece of datumX _n+1 is picked and the test is done again in the same way but based onX ₁,X ₂, ⋅⋅⋅,X _n,X _n+l There are three situations: (i) The previous decision is right but the new decision is wrong; (ii) the previous decision is wrong but the new decision is right; (iii) both of them are right or both of them are wrong. Of course, it is desired that the probability of the occurrence of (i) is as small as possible and the probability of the occurrence of (ii) is as large as possible. Since the sample size is sometimes not chosen very precisely after the type I error and the type II error are determined in practice, it seems more urgent to consider the above problem. Some optimal plans are also given. Project supported by the National Natural Science Foundation of China and the Doctoral Programme Foundation.     

1／2亚谐共振──主参数共振情况下非线性振动系统的余维2退化分叉

本文应用Normal Form理论和退化向量场的普适开折理论研究了参数激励与强迫激励联合作用下非线性振动系统的余维2退化分叉,用Melnikov方法讨论了全局分叉的存在性.     

Nonlinear Dynamics of a Cantilever Beam Carrying an Attached Mass with 1:3:9 Internal Resonances

In this paper the nonlinear response of a base-excited slender beam carrying an attached mass is investigated with 1:3:9 internal resonances for principal and combinationparametric resonances. Here the method of normal forms is used to reduce the second order nonlinear temporal differential equation of motion of the system to a set offirst order nonlinear differential equations which are used to find the fixed-point, periodic, quasi-periodic and chaotic responses of the system.Stability and bifurcation analysis of the responses are carried out and bifurcation sets are plotted. Many chaotic phenomena are reported in this paper.     

A centrosymmetric chaos

Symmetry plays an important part in the research of the dynamical behavior of nonlinear system. It is proved in this paper that, for a class of centrosymmetric systems with parametric excitation, chaos behaves in centrosymmetric manner, which implies that chaos need not to be an unsymmetric dynamical state. The project supported by National Natural Science Foundation of China     

具有损伤耦合效应的弹塑性蠕变问题结构分析的变分原理

本文基于连续介质损伤力学中有效应力的概念,研究弹塑性蠕变问题中的损伤耦合,并应用由最优控制理论基本思想发展起来的参变量变分原理建立起用于弹塑性蠕变损伤问题结构分析的变分原理.文中给出了原理的证明.该原理的物理意义明确,表达式简单且规范,容易为数值手段实现.     

Simultaneous combination and 1:3:5 internal resonances in a parametrically excited beam-mass system

The nonlinear dynamics of a base-excited slender beam carrying a lumped mass subjected to simultaneous combination parametric resonance of sum and difference type along with 1:3:5 internal resonances is investigated. Method of normal form is applied to the governing nonlinear temporal differential equation of motion to obtain a set of first-order differential equations which are used to obtain the steady-state, periodic, quasi-periodic and chaotic responses for different control parameters viz., amplitude and frequency of external excitation and damping. Frequency response, phase portraits, time spectra and bifurcation diagram are plotted to visualize the system behaviour with variation in the control parameters. Here, two distinct zones of trivial instability, blue sky catastrophe phenomena, jump down phenomena, simultaneous occurrence of periodic and chaotic orbits, period doubling of the mixed-mode periodic orbits leading to chaos, attractor merging crisis, boundary crisis, type II and on-off intermittencies are observed. Bifurcation diagram is plotted to facilitate the designer to choose a safe operating zone.     

A combined parametric quadratic programming and precise integration method based dynamic analysis of elastic-plastic hardening/softening problems

The objective of the paper is to develop a new algorithm for numerical solution of dynamic elastic-plastic strain hardening/softening problems. The gradient dependent model is adopted in the numerical model to overcome the result mesh-sensitivity problem in the dynamic strain softening or strain localization analysis. The equations for the dynamic elastic-plastic problems are derived in terms of the parametric variational principle, which is valid for associated, non-associated and strain softening plastic constitutive models in the finite element analysis. The precise integration method, which has been widely used for discretization in time domain of the linear problems, is introduced for the solution of dynamic nonlinear equations. The new algorithm proposed is based on the combination of the parametric quadratic programming method and the precise integration method and has all the advantages in both of the algorithms. Results of numerical examples demonstrate not only the validity, but also the advantages of the algorithm proposed for the numerical solution of nonlinear dynamic problems. The project supported by the National Key Basic Research Special Foundation (G1999032805), the National Natural Science Foundation of China (19872016, 50178016, 19832010) and the Foundation for University Key Teacher by the Ministry of Education of China