基于复合胞化空间的图胞映射方法

为了提高计算的准确性和效率,通过引入复合胞化空间概念,构建了一种迭代的图胞映射方法.该方法能够对任意感兴趣的空间区域进行细化处理,细化过程采用代数运算完成不会额外增加计算机内存且能保持细化前后图动力系统性质不变.为了便于计算机实施,也给出了相应的有效算法.通过对典型例子Henon映射的应用分析,证实了该方法的有效性. 关键词： 图胞映射方法 迭代方法 Henon映射     

量子态在两体和k体下基于min相对熵的量子关联测度

量子关联作为量子力学的奇特资源已经被应用在很多方面,相对熵作为研究量子关联的关键概念之一,总是被用来度量物理系统状态所包含的不确定性.本文在已知min相对熵的一些基本性质的前提下,分别提出了在两体和k体分划下基于min相对熵的关联测度的定义.除此之外,本文证明了该定义满足量子关联测度的一些基本性质,包括非负性、在酉算子操作下保持不变性以及在完全正的保迹线性映射(CPTP)下的单调性.介绍了量子信道的概念,并且讨论了量子信道对k体分划下基于min相对熵的关联测度的影响.通过提出新的关联测度以及证明量子信道对该测度的影响,能够更好刻画物理系统状态所包含的不确定性.     

图胞映射的一种改进方法

通过引入新的概念,提出了图胞映射动力系统中瞬态胞的新的分类方法,基于新的分类方法研究了动力系统中不变流形的胞映射逼近问题;并结合计算机的计算速度与内存特点,建立了完成上述压缩分类的有效算法.通过对典型算例Henon映射的应用分析,证实了该方法的有效性. 关键词： 图胞映射方法 不变流形 Henon映射     

混沌伪随机序列的谱熵复杂性分析

为了准确分析混沌伪随机序列的结构复杂性,采用谱熵算法对Logistic映射、Gaussian映射和TD-ERCS系统产生的混沌伪随机序列复杂度进行了分析.谱熵算法具有参数少、对序列长度N(惟一参数)和伪随机进制数K鲁棒性好的特点.采用窗口滑动法分析了混沌伪随机序列的复杂度演变特性,计算了离散混沌系统不同初值和不同系统参数条件下的复杂度.研究表明,谱熵算法能有效地分析混沌伪随机序列的结构复杂度;在这三个混沌系统中,TD-ERCS系统为广域高复杂度混沌系统,复杂度性能最好;不同窗口和不同初值条件下的混沌系统复杂度在较小范围内波动.为混沌序列在信息安全中的应用提供了理论和实验依据.     

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     

高精度数字全息显微衍射层析成像

采用样品转动结构的光学衍射层析技术存在"苹果核频谱缺失"的问题,为此,本文提出傅里叶衍射映射正约束迭代算法以恢复缺失频谱,实现高精度折射率层析成像.首先基于光学衍射层析成像原理,采用带有样品转动装置的数字全息显微成像系统记录下360°视角内各个角度的显微全息图,计算得到每个角度的复振幅像分布;然后运用傅里叶衍射映射和正约束迭代相结合的衍射层析成像算法,计算得到样品内部折射率的三维分布.实验结果表明,该方法能有效地恢复缺失频谱,高精度地测量微小样品内部的折射率三维分布.     

CORDIC迭代法快速计算LED显示屏色域边界

针对色域映射过程中快速并精确地计算出任意映射线与色域边界交点坐标的问题,提出一种基于改进的CORDIC算法的迭代逼近求解方法。该方法利用CIE LUV颜色空间的特性可沿映射线逼近边缘交点。无需边界搜索和插值计算过程,可大量节省存储器资源和计算时间,并具有较高的计算精度和广泛的适用性。文章详细分析了算法的计算原理、精度和速度,并以LED显示屏为例,在D65标准光源下进行边界拟合并做出误差分析。实验结果表明:12次迭代运算后,拟合边界非常光滑,最大色差值仅为0.16,计算500个映射线交点的总计算时间约为1 s。与插值类计算方法相比,最大色差值降低了2.15,计算时间从10 s降低到1 s,速度提高了近10倍。     

图胞映射的一种改进方法

通过引入新的概念，提出了图胞映射动力系统中瞬态胞的新的分类方法，基于新的分类方法研究了动力系统中不变流形的胞映射逼近问题；并结合计算机的计算速度与内存特点，建立了完成上述压缩分类的有效算法.通过对典型算例Henon映射的应用分析，证实了该方法的有效性.     

基于混沌映射的图像快速加密改进算法

针对当前的三维混沌映射加密算法存在安全性不高,加密速度慢以及密钥空间小等不足,提出了一种新的三维混沌映射图像加密算法;首先利用快速置乱方法置乱初始图像,以改变像素位置;利用三维Chen系统结合像素值变换函数所生成初始外部密钥迭代三维混沌映射,得到一个序列,由此根据混淆机制对置乱图像像素值进行混淆;改变外部密钥,再迭代计算三维混沌映射,得到三元一维伪随机数组,借助密钥流机制量化该数组,得到新数组,由此根据扩散机制对混淆后的像素进行扩散处理;采用酷睿3.5 GHz双核CPU的PC机和MATLAB仿真平台,输入256×256的明文图像实验,置乱100次所用时间为78.67 s,在灰度平面内其相关性约为-0.001 652,表明该算法高度安全,密钥空间巨大,加密速度快,用于图像快速加密是可行、有效的。     

不连续导电模式DC-DC变换器的倍周期分岔机理研究

根据一般迭代映射的倍周期分岔定理,从数学上论证了电压型不连续导电模式(DCM) Boost和Buck变换器中倍周期分岔现象产生条件,由此揭示了DC-DC变换器中倍周期分岔现象发生的机理,完善了该类变换器倍周期分岔分析的理论和方法. 关键词： 倍周期分岔 迭代映射 Lyapunov 指数 施瓦茨导数     

c=3, N=2 超共形场论的Z2 Orbifold-Prime模型

讨论了二维环面上中心荷c=3, N=2 的超共形场论. 特别给出该理论的配分函数. 进一步,为了产生新的模型,回顾了一般的orbifold方法. 然后构造了模不变的Z2 Orbifold-Prime模型.     

Two results concerning asymptotic behavior of solutions of the Burgers equation with force

We consider the Burgers equation with an external force. For the case of the force periodic in space and time we prove the existence of a solution periodic in space and time which is the limit of a wide class of solutions ast . If the force is the product of a periodic function ofx and white noise in time, we prove the existence of an invariant distribution concentrated on the space of space-periodic functions which is the limit of a wide class of distributions ast .     

Lyapunov exponent for chaotic 1D maps with uniform invariant distribution

Some properties of iterative functions of 1D chaotic maps that provide uniform invariant distribution are formulated. A method for synthesizing strictly nonlinear maps with uniform invariant distribution is demonstrated. The Lyapunov exponents for such maps are analyzed and it is shown that, among the maps with a specified number of full branches, piecewise linear maps with branches characterized by equal moduli of angular coefficients have the maximum Lyapunov exponent.     

Pion correlations and resonance effects in \bar{p}p annihilation to 4\pi^0 at rest

We study correlations in the exclusive reaction at rest with complete reconstruction of the kinematics for each event. The inclusive distribution is fairly flat at small invariant mass of the pion pair while a small enhancement in the double differential distribution is observed for small invariant masses of both pion pairs. Dynamical models with resonances in the final state are shown to be consistent with the data while the stochastic HBT mechanism is not supported by the present findings. Received: 26 February 2002 / Revised version: 22 July 2002 / Published online: 30 August 2002     

Radial drift invariant in long-thin mirrors

In omnigenous systems, guiding centers are constrained to move on magnetic surfaces. Since a magnetic surface is determined by a constant radial Clebsch coordinate, omnigeneity implies that the guiding center radial coordinate (the Clebsch coordinate) is a constant of motion. Near omnigeneity is probably a requirement for high quality confinement and in such systems only small oscillatory radial banana guiding center excursions from the average drift surface occur. The guiding center radial coordinate is then the leading term for a more precise radial drift invariant I _r , corrected by oscillatory “banana ripple” terms. An analytical expression for the radial invariant is derived for long-thin quadrupolar mirror equilibria. The formula for the invariant is then used in a Vlasov distribution function. Comparisons are first made with Vlasov equilibria using the adiabatic parallel invariant. To model radial density profiles, it is necessary to use the radial invariant (the parallel invariant is insufficient for this). The results are also compared with a fluid approach. In several aspects, the fluid and Vlasov system with the radial invariant give analogous predictions. One difference is that the parallel current associated with finite banana widths could be derived from the radial invariant.     

Effect of shallow water internal waves on ocean acoustic striation patterns

Contour plots of underwater acoustic intensity, mapped in range and frequency, often exhibit striations. It has been claimed that a scalar parameter 'beta', defined in terms of the slope of the striations, is invariant to the details of the acoustic waveguide. In shallow water, the canonical value is β=1. In the present paper, the waveguide invariant is modelled as a distribution rather than a scalar. The effects of shallow water internal waves on the distribution are studied by numerical simulation. Realizations of time-evolving shallow water internal wave fields are synthesized and acoustic propagation simulated using the parabolic equation method. The waveguide invariant distribution is tracked as the internal wave field evolves in time. Both random background internal waves and more event-like solitary internal waves are considered.     

Algebraic decay in self-similar Markov chains

A continuous-time Markov chain is used to model motion in the neighborhood of a critical invariant circle for a Hamiltonian map. States in the infinite chain represent successive rational approximants to the frequency of the invariant circle. For the case of a noble frequency, the chain is self-similar and the nonlinear integral equation for the first passage time distribution is solved exactly. The asymptotic distribution is a power law times a function periodic in the logarithm of the time. For parameters relevant to the critical noble circle, the decay proceeds ast ^–4.05.     

Third adiabatic invariant and the collisionless distribution function of particles in a tokamak

It has been shown that the distribution function of an ensemble of particles with a given energy in a collisionless regime in a tokamak is formed as a function primarily of the third adiabatic invariant, particularly in the near-axis region. In the periphery of the plasma column, the contribution of the toroidal component of the canonical momentum/longitudinal adiabatic invariant to the distribution function becomes noticeable. The coordinate dependence of the ensemble distribution function in the velocity space is determined predominantly by the trajectories of charged particles.     

Effect of shallow water internal waves on ocean acoustic striation patterns

Abstract

Contour plots of underwater acoustic intensity, mapped in range and frequency, often exhibit striations. It has been claimed that a scalar parameter ‘beta’, defined in terms of the slope of the striations, is invariant to the details of the acoustic waveguide. In shallow water, the canonical value is β=1. In the present paper, the waveguide invariant is modelled as a distribution rather than a scalar. The effects of shallow water internal waves on the distribution are studied by numerical simulation. Realizations of time-evolving shallow water internal wave fields are synthesized and acoustic propagation simulated using the parabolic equation method. The waveguide invariant distribution is tracked as the internal wave field evolves in time. Both random background internal waves and more event-like solitary internal waves are considered.     

Infinite invariant density determines statistics of time averages for weak chaos

Weakly chaotic nonlinear maps with marginal fixed points have an infinite invariant measure. Time averages of integrable and nonintegrable observables remain random even in the long time limit. Temporal averages of integrable observables are described by the Aaronson-Darling-Kac theorem. We find the distribution of time averages of nonintegrable observables, for example, the time average position of the particle, x[over ˉ]. We show how this distribution is related to the infinite invariant density. We establish four identities between amplitude ratios controlling the statistics of the problem.