Real Solutions of the First Painlevé Equation with Large Initial Data

We consider three special cases of the initial value problem of the first Painlevé (PI) equation. Our approach is based on the method of uniform asymptotics introduced by Bassom et al. A rigorous proof of a property of the PI solutions on the negative real axis, recently revealed by Bender and Komijani, is given by approximating the Stokes multipliers. Moreover, we build more precise relation between the large initial data of the PI solutions and their three different types of behavior as the independent variable tends to negative infinity. In addition, some limiting form connection formulas are obtained.     

A new condition for solvable groups

A subgroup H of G is called complemented in G if there exists a subgroup K of G such that $G=HK$ and $H\cap K=1$. The aim of this paper is to prove the following: A finite group G is solvable if and only if its Sylow 3-, 5- and 7-subgroups are complemented in G.     

Rogue waves in baroclinic flows

We investigate an AB system, which can be used to describe marginally unstable baroclinic wave packets in a geophysical fluid. Using the generalized Darboux transformation, we obtain higher-order rogue wave solutions and analyze rogue wave propagation and interaction. We obtain bright rogue waves with one and two peaks. For the wave packet amplitude and the mean-flow correction resulting from the self-rectification of the nonlinear wave, the positions and values of the wave crests and troughs are expressed in terms of a parameter describing the state of the basic flow, in terms of a parameter responsible for the interaction of the wave packet and the mean flow, and in terms of the group velocity. We show that the interaction of the wave packet and mean flow and also the group velocity affect the propagation and interaction of the amplitude of the wave packet and the self-rectification of the nonlinear wave.     

经方量化归经研究中的向量矩阵应用

在经方量化归经研究中发现,药物组成的归经量化问题,若以五维向量表示更能体现其药物的归经方向和归经比例.利用向量矩阵分析方法给出了方剂归经量化的一种全新的量化模型体系,并以此研究方剂归经的量化规律及其应用特点.     

Dynamics of milling processes with variable time delays

A milling-process model with a variable time delay associated with each cutting tooth is presented in this article. The source of this variable time delay is the feed rate. The effect of the feed motion on the entry cutting angle, the exit cutting angle, and the amplitude of feed mark is also discussed. Loss-of-contact effects are also considered. The system dynamics is described by a set of delay differential equations with periodic coefficients and variable time delays. A semi-discretization scheme is presented for analyzing the stability of periodic orbits of this system. The analysis provides evidence of period-doubling bifurcations and secondary Hopf bifurcations. Good agreement is found between the numerical results obtained from this work and the results of related experimental studies.     

Stress relaxation of large amplitudes and long timescales in soft thermoplastic and filled elastomers

We propose a model for describing mesoscale relaxation mechanisms in soft thermoplastic elastomers and also in the high-temperature regime of filled rubbers. The model consists of hard spheres embedded in an elastic matrix. It is solved by dissipative particle dynamics. We study the response of the model to deformations of various amplitudes. We show that it displays slow relaxation processes of large amplitudes that are related to irreversible reorganizations at a mesoscopic scale. We characterize these reorganizations as buckling of instabilities that change the local environment of the hard inclusions. Paper presented at the 3rd Annual Rheology Conference, AERC 2006, April 27–29, 2006, Crete, Greece.     

炸药驱动强电流短路开关的研

由于电磁轨道炮和其它强电流装置中短路运行的需要,研制了一种条形炸药驱动的大电流闭合开关。利用爆炸成型技术使金属飞板负电极在炸药部件作用下,大面积地同时切断绝缘薄膜,嵌入另一电极模槽中构成牢固的接触。开关的绝缘强度大于30kV,电感(包括传输线)小于50nH,最大峰值电流达到400kA,闭合接触电阻小于0.1m,动作时间约为14us。对于开关的爆轰,撞击及变形过程进行了一维和二维数值模拟计算,并提出了一个描述爆炸开关行为的经验模型。利用这个模型进行电磁轨道炮整个系统的数值模拟,同实验结果符合较好。     

CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅰ)—BASIC PROPERTIES AND PRELIMINARY RESULTS

The controllability for switched linear system with time-delay in controls was first investigated. The whole work contains three parts. This is the first part, including problem formulation and some preliminaries. Firstly, the mathematical model of switched linear systems with time-delay in control functions was presented. Secondly, the concept of column space, cyclic invariant subspace and generalized cyclic invariant subspace were introduced. And some basic properties, such as separation lemma, were presented. Finally, a basic lemma was given to reveal the relation between the solution set of a centain integral equations and the generalized cyclic invariant subspace. This lemma will play an important role in the determination of controllability. All these definitions and lemmas are necessary research tools for controllability analysis. Contributed by YE Qing-kai Foundation items: the National Natural Science Foundation of China (69925307, 60274001); the National Key Basic Reasearch and Development Program (2002CB312200); the Postdoctoral Program Foundation of China Biography: XIE Guang-ming (1972∼), Doctor (E-mail: xiegming@mech.pku.edu.cn)     

DIRECT NUMERICAL SIMULATIONS ON THE TURBULENT FLOW PAST A CONFINED CIRCULAR CYLINDER WITH THE INFLUENCE OF THE STREAMWISE MAGNETIC FIELDS1)

绕流是托卡马克装置中液态包层内常见的流动形态,对流场与热量分布有着重要的影响.本文通过直接数值模拟(DNS),研究了不同磁场强度下$Re=3900$的圆柱绕流,分析了磁场强度对于湍流尾迹的影响.无磁场情况下,直接数值模拟的结果与前人的实验及模拟结果吻合很好.圆柱下游的尾迹中,随着流向距离的增大, 流向速度剖面逐渐从U型进化呈V型, 并慢慢趋于平缓,这表明尾迹中的流动结构受圆柱影响逐渐减小.圆柱后方两侧的剪切层中,由于Kelvin-Helmholtz不稳定性的影响,可以清晰地看到小尺度剪切层涡的脱落.通过对无磁场的计算结果施加流向磁场,本文计算了哈特曼数($Ha$)分别为20, 40和80的工况,以研究磁场效应对于湍流的影响.结果表明磁场较弱时,流动依然呈三维湍流状态.随着磁场增强, 近圆柱尾流区受磁场抑制明显,回流区被拉长,剪切层失稳位置向下游转移.圆柱后方的涡结构由于受到竖直方向洛伦兹力的挤压作用,随着哈特曼数的增加尾迹区域逐渐变窄.相比于无磁场情况的涡结构,由于磁场的耗散作用,相应的涡结构尺度变小.该研究不仅扩展了现有磁场下湍流运动的参数范围,对于液态包层的设计及安全运行同样具有重要的理论指导意义和工程应用价值.     

BIFURCATIONS OF TRAVELLING WAVE SOLUTIONS FOR GENERALIZED DRINFELD-SOKOLOV EQUATIONS

Ansatz method and the theory of dynamical systems are used to study the traveling wave solutions for the generalized Drinfeld-Sokolov equations. Under two groups of the parametric conditions, more solitary wave solutions, kink and anti-kink wave solutions and periodic wave solutions are obtained. Exact explicit parametric representations of these travelling wave solutions are given.