两个周期激励下Duffing-van der Pol系统的混沌瞬态和广义激变

运用广义胞映射图方法研究两个周期激励作用下Duffing-van der Pol系统的全局特性.发现了系统的混沌瞬态以及两种不同形式的瞬态边界激变, 揭示了吸引域和边界不连续变化的原因. 瞬态边界激变是由吸引域内部或边界上的混沌鞍和分形边界上周期鞍的稳定流形碰撞产生.第一种瞬态边界激变导致吸引域突然变小, 吸引域边界突然变大; 第二种瞬态边界激变使两个不同的吸引域边界合并成一体.此外, 在瞬态合并激变中两个混沌鞍发生合并, 最后系统的混沌瞬态在内部激变中消失. 这些广义激变现象对混沌瞬态的研究具有重要意义. 关键词： 广义胞映射图方法 Duffing-van der Pol 混沌瞬态 广义激变     

一类新的边界激变现象:混沌的边界激变

混沌吸引子的激变是一类普遍现象.借助于广义胞映射图论(generalized cell mapping digraph)方法发现了嵌入在分形吸引域边界内的混沌鞍,这个混沌鞍由于碰撞混沌吸引子导致混沌吸引子完全突然消失,是一类新的边界激变现象,称为混沌的边界激变.可以证明混沌的边界激变是由于混沌吸引子与分形吸引域边界上的混沌鞍相碰撞产生的,在这种情况下,当系统参数通过激变临界值时,混沌吸引子连同它的吸引域突然消失,同时这个混沌鞍也突然增大 关键词： 广义胞映射 有向图 激变 混沌鞍     

常微分方程系统中内部激变现象的研究

应用广义胞映射图论方法研究常微分方程系统的激变.揭示了边界激变是由于混沌吸引子与 在其吸引域边界上的周期鞍碰撞产生的,在这种情况下,当系统参数通过激变临界值时,混 沌吸引子连同它的吸引域突然消失,在相空间原混沌吸引子的位置上留下了一个混沌鞍.研 究混沌吸引子大小(尺寸和形状)的突然变化,即内部激变.发现这种混沌吸引子大小的突然 变化是由于混沌吸引子与在其吸引域内部的混沌鞍碰撞产生的,这个混沌鞍是相空间非吸引 的不变集,代表内部激变后混沌吸引子新增的一部分.同时研究了这个混沌鞍的形成与演化. 给出了对永久自循环胞集和瞬态自循环胞集进行局部细化的方法. 关键词： 广义胞映射 有向图 激变 混沌鞍     

非自治分数阶Duffing系统的激变现象

对一个非自治分数阶Duffing系统的激变现象进行了研究.首先介绍了一种研究分数阶非线性系统全局动力学的数值方法,即拓展的广义胞映射方法 (EGCM).该方法是基于分数阶导数的短记忆原理,并结合了广义胞映射方法和改进的预估校正算法,根据胞空间的特点,将胞尺寸作为截断误差的参考值,以此得到了一步映射时间的估算公式.用EGCM方法分别研究了分数阶Duffing系统随分数阶导数的阶数和外激励强度变化发生的边界激变和内部激变.并基于此,将激变拓展定义为混沌基本集与周期基本集之间的碰撞,其中混沌基本集包括混沌吸引子,边界上的混沌集合以及吸引域内部的非混沌吸引子的混沌集合.所得结果进一步说明了EGCM方法对于分析分数阶系统全局动力学的有效性.     

Duffing-van der Pol振子随机分岔的全局分析

应用广义胞映射方法研究了参激和外激共同作用的Duffing-van der Pol振子的随机分岔.以 系统参数通过某一临界值时，如果系统的随机吸引子或随机鞍的形态发生突然变化，则认为 系统发生随机分岔为定义，分析了参激强度和外激强度的变化对于随机分岔的影响.揭示了 随机分岔的发生主要是由于系统的随机吸引子与系统的随机鞍碰撞产生的.分析表明，广义 胞映射方法是分析随机分岔的有力工具，这种全局分析方法可以清晰地给出随机分岔的发生 和发展. 关键词： 随机分岔 全局分析 广义胞映射方法 随机吸引子 随机鞍     

一类含非黏滞阻尼的Duffing单边碰撞系统的激变研究

以一类含非黏滞阻尼的Duffing单边碰撞系统为研究对象, 运用复合胞坐标系方法, 分析了该系统的全局分岔特性. 对于非黏滞阻尼模型而言, 它与物体运动速度的时间历程相关, 能更真实地反映出结构材料的能量耗散现象. 研究发现, 随着阻尼系数、松弛参数及恢复系数的变化, 系统发生两类激变现象: 一种是混沌吸引子与其吸引域内的混沌鞍发生碰撞而产生的内部激变, 另一种是混沌吸引子与吸引域边界上的周期鞍(混沌鞍)发生碰撞而产生的常规边界激变(混沌边界激变), 这两类激变都使得混沌吸引子的形状发生突然改变. 关键词： 非黏滞阻尼 Duffing碰撞振动系统 激变 复合胞坐标系方法     

含指数项广义平方映射的分岔和吸引子

由平方映射延伸构造出了一类含指数项的广义平方映射,并由一维映射通过一次耦合项得到了二维映射.利用一参数分岔图、二参数动力学行为分布图、映射迭代曲线和吸引子相图等方法对这类广义平方映射进行了分析和仿真.研究结果表明：一维广义平方映射分布在一个单位区域内的,有着与单峰平方映射相类似的非线性动力学现象;而二维广义平方映射则存在Hopf分岔和锁频等现象,有着复杂多变、形状奇异的极限环和混沌吸引子. 关键词： 广义平方映射 分岔 迭代曲线 吸引子     

椭圆旋轮线

一条光滑曲线在另一条光滑曲线上无滑动滚动,滚动曲线上一点的轨迹就是广义旋轮线.利用弧长坐标,给出了广义旋轮线的轨迹方程.对于椭圆,画出了椭圆旋轮线轨迹.     

广义色散Camassa-Holm模型的奇异孤子

引进一类广义色散Camassa-Holm模型，对其做奇异性分析.通过改进的WTC-Kruskal算法，证明该模型在Painlevé意义下可积，得到了它的一组Painlevé-Bcklund系统和Bcklund变换.应用Maple进行代数运算，得到了丰富的规则(regular)孤子和一类奇异(singular)孤子，扭结(kink)孤子,紧孤子(compacton)和反紧孤子(anti-compacton).特别地，推导出一类在扭结孤子的中间区域包含有一列周期尖点(cuspon)波的奇异结构.在这些规则的孤子系统的基础上，对可积广义系统应用Bcklund变换，得到三类奇异孤子，分别是具有驼峰结构的周期爆破波，具有爆破波结构的扭结孤子和紧孤子. 关键词： 广义Camassa-Holm 模型 周期尖点波 紧孤子 周期爆破波     

气相爆轰波在分叉管中传播现象的数值研究

数值研究气相爆轰波在分叉管中的传播现象.用二阶附加半隐龙格-库塔法和5阶WENO格式求解二维欧拉方程,用基元反应描述爆轰化学反应过程,得到了密度、压力、温度、典型组元质量分数场及数值胞格结构和爆轰波平均速度.结果表明:气相爆轰波在分叉管中传播,分叉口左尖点的稀疏波导致诱导激波后压力、温度急剧下降,诱导激波和化学反应区分离,爆轰波衰减为爆燃波(即爆轰熄灭).分离后的诱导激波在垂直支管右壁面反射,并导致二次起爆.畸变的诱导激波在水平和垂直支管中均发生马赫反射.分叉口上游均匀胞格区和分叉口附近大胞格区的边界不是直线,其起点通常位于分叉口左尖点上游或恰在左尖点.水平支管中马赫反射三波点迹线始于右尖点下游.分叉口左尖点附近的流场中出现了复杂的旋涡结构、未反应区及激波与旋涡作用.旋涡加速了未反应区的化学反应速率.反射激波与旋涡作用并使旋涡破碎.反射激波与未反应区作用,加速其反应消耗,并形成一个内嵌的射流.数值计算得到的波系演变和胞格结构与实验定性一致.     

Parameter vertex method and its parallel solution for evaluating the dynamic response bounds of structures with interval parameters

In this article, we propose a parameter vertex method to determine the upper and lower bounds of the dynamic response of structures with interval parameters, which can be regarded as an extension of the matrix vertex method proposed by Qiu and Wang. The matrix vertex method requires considerable computation time and encounters the dependency problem in practice, thereby limiting its application in engineering. The proposed parameter vertex method can avoid the dependency problem, and the number of possible vertex combinations in the proposed method is significantly less than that in the matrix vertex method. The parameter vertex method requires that each matrix element in the dynamic differential equation is monotonic with respect to the uncertain parameter, and that the dynamic response reaches its extreme value when the uncertain parameter is at its endpoint. To further reduce the runtime, both vertical and transversal parallel algorithms are introduced and integrated into the parameter vertex method to improve its computational efficiency. Two numerical examples are presented to demonstrate the proposed method combined with both parallel algorithms. The performances of the two parallel algorithms are thoroughly studied. The parameter vertex method combined with parallel algorithm can be used for large-scale computing.     

On inclusive gluon jet production off the nucleus in perturbative QCD

In the perturbative QCD approach single and double inclusive cross-sections for gluon production off the nucleus are studied by the relevant reggeized gluon diagrams. Various terms corresponding to emission of gluons from the triple pomeron vertex are found. Among them the term derived by Kovchegov and Tuchin emerges as a result of the transition from the diffractive to effective high-energy vertex. However it does not exhaust all the vertex contributions to the inclusive cross-section. In the double inclusive cross-section a contribution violating the naive AGK rules is found in which one gluon is emitted from the vertex and the other from one of the two pomerons below the vertex. But then this contribution is subdominant at high energies and taking it into account seems to be questionable.Received: 6 March 2005, Revised: 5 May 2005, Published online: 8 June 2005     

A new type of global bifurcation in Hénon map

A simple branch of solution on a bifurcation diagram, which begins at static bifurcation and ends at boundary crisis (or interior crisis in a periodic window), is generally a period-doubling cascade. A domain of solution in parameter space, enclosed by curves of static bifurcation and that of boundary crisis (or the interior of a periodic window), is the trace of branches of solution. A P-n branch of solution refers to the one starting from a period-n (n≥1) solution, and the corresponding domain in parameter space is named the P-n domain of solution. Because of the co-existence of attractors, there may be several branches within one interval on a bifurcation diagram, and different domains of solution may overlap each other in some areas of the parameter space. A complex phenomenon, concerned both with the co-existence of attractors and the crises of chaotic attractors, was observed in the course of constructing domains of steady state solutions of the Hénon map in parameter space by numerical methods. A narrow domain of period-m solutions firstly co-exists with (lies on) a big period-n (m≥3n) domain. Then it enters the chaotic area of the big domain and becomes period-m windows. The co-existence of attractors disappears and is called the landing phenomenon. There is an interaction between the two domains in the course of landing: the chaotic area in the big domain is enlarged, and there is a crisis step near the landing area.     

一类粗锐复合结构光子晶体的完全带隙研究

通过研究发现粗锐组合的二维复式结构光子晶体的完全带隙宽度和带隙结构随结构粗锐尺寸灵敏地改变. 而其粗锐复合结构的复合错位对带隙宽度影响不大. 对二维复式正方格子和二维复式三角格子的研究结果表明：二维复式正方格子的粗锐尺寸选择恰当时其完全带隙的带宽可大于１8％. 二维复式三角格子中的粗锐尺寸选取可导致出现单、双完全带隙两种情况. 本文给出了反映其变化规律的关系曲线. 关键词： 光子晶体 光子能隙 复式结构     

An ?-Deformed Virasoro Algebra as Hidden Symmetry of the Restricted sine-Gordon Model

As the Yangian double with center, which is deformed from affine algebra by the additive loop parameter ?, we get the commutation relation and the bosonization of quantum ?-deformed Virasoro algebra. The corresponding Miura transformation, the associated screening operators and the BRST charge have been studied. Moreover, we also construct the bosonization for type Ⅰ and type Ⅱ intertwiner vertex operators. Finally, we show that the commutation relations of these vertex operators in the case of p^′ = γ, p = γ - 1 and ? = π actually give the exact scattering matrix of the restricted sine-Gordon model.     

On the inclusive gluon jet production from the triple pomeron vertex in the perturbative QCD

Single and double inclusive cross-sections for gluon jet production from within the triple pomeron vertex are studied in the reggeized gluon technique in the QCD with N_c→∞. It is shown that to satisfy the AGK rules the vertex has to be fully symmetric in all four reggeized gluons which form the two final pomerons. The single inclusive cross-sections are found for different cuttings of the triple pomeron vertex. They sum to the expression obtained by Kovchegov and Tuchin in the color dipole picture. The found double inclusive cross-sections satisfy the AGK rules.     

Duffing单边碰撞系统的混沌鞍合并激变

以典型的Duffing单边碰撞系统为研究对象,对系统中的混沌鞍进行了细致的分析.研究表明,系统的混沌鞍同样存在合并激变,合并激变是由连接两个混沌鞍的周期鞍的稳定流形与不稳定流形相切所诱发,相切使得边界上的混沌鞍与内部的混沌鞍发生碰撞而突然合并为一个较大的边界混沌鞍.混沌鞍的合并激变行为最终会诱导混沌吸引子的合并激变发生. 关键词： Duffing碰撞系统 混沌鞍 周期鞍 稳定与不稳定流形     

Anderson impurity model: Double occupancy contribution to the magnetic susceptibility

After solving the single Anderson impurity model (SIAM) within the non-crossing approximation with a finite Coulomb repulsion, U, and vertex corrections (NCAf²v), we focus on the magnetic susceptibility. Using the same diagrammatic expansion the susceptibility can be dressed with two factors, namely, the double state occupancy and the vertex corrections. In this work we analyse the effect of double occupancy on the dynamic and static susceptibility as a function of U and on the degeneracy of the total impurity angular moment, S.     

Kinks and d-waves from phonons: The intermediate coupling story

I present results from an approach that extends the Eliashberg theory by systematic expansion in the vertex function; an essential extension at large phonon frequencies, even for weak coupling. In order to deal with computationally expensive double sums over momenta, a dynamical cluster approximation (DCA) approach is used to incorporate momentum dependence into the Eliashberg equations. First, I consider the effects of introducing partial momentum dependence on the standard Eliashberg theory using a quasi-local approximation; which I use to demonstrate that it is essential to include corrections beyond the standard theory when investigating d-wave states. Using the extended theory with vertex corrections, I compute electron and phonon spectral functions. A kink in the electronic dispersion is found in the normal state along the major symmetry directions, similar to that found in photo-emission from cuprates. The phonon spectral function shows that for weak coupling Wλ<ω₀, the dispersion for phonons has weak momentum dependence, with consequences for the theory of optical phonon mediated d-wave superconductivity, which is shown to be 2nd order in λ. In particular, examination of the order parameter vs. filling shows that vertex corrections lead to d-wave superconductivity mediated via simple optical phonons. I map out the order parameters in detail, showing that there is significant induced anisotropy in the superconducting pairing in quasi-2D systems.     

Gluon production on two centers and the effective action approach

Application of the effective action formalism is studied for processes in which the reggeons may split. It is shown that the gluon production on two centers is described by the contribution of the Reggeon-to-two-Reggeons-plus-Particle vertex supplemented by certain singular contributions from the double gluon exchange. The rules for longitudinal integrations are established from the comparison to perturbative QCD amplitude. Convenient expressions for application to the inclusive gluon production are derived.