Lyapunov Modes and Time-Correlation Functions for Two-Dimensional Systems

The relation between the Lyapunov modes (delocalized Lyapunov vectors) and the momentum autocorrelation function is discussed in two-dimensional hard-disk systems. We show numerical evidence that the smallest time-oscillating period of the Lyapunov modes is twice as long as the time-oscillating period of momentum autocorrelation function for both square and rectangular two-dimensional systems with hard-wall boundary conditions.Comment: 9 pages, 4 figure

Lyapunov spectra of periodic orbits for a many-particle system

The Lyapunov spectrum corresponding to a periodic orbit for a two dimensional many particle system with hard core interactions is discussed. Noting that the matrix to describe the tangent space dynamics has the block cyclic structure, the calculation of the Lyapunov spectrum is attributed to the eigenvalue problem of a 16x16 reduced matrices regardless of the number of particles. We show that there is the thermodynamic limit of the Lyapunov spectrum in this periodic orbit. The Lyapunov spectrum has a step structure, which is explained by using symmetries of the reduced matrices.Comment: 16 pages, 4 incorporated postscript figure

Time-oscillating Lyapunov modes and auto-correlation functions for quasi-one-dimensional systems

The time-dependent structure of the Lyapunov vectors corresponding to the steps of Lyapunov spectra and their basis set representation are discussed for a quasi-one-dimensional many-hard-disk systems. Time-oscillating behavior is observed in two types of Lyapunov modes, one associated with the time translational invariance and another with the spatial translational invariance, and their phase relation is specified. It is shown that the longest period of the Lyapunov modes is twice as long as the period of the longitudinal momentum auto-correlation function. A simple explanation for this relation is proposed. This result gives the first quantitative connection between the Lyapunov modes and an experimentally accessible quantity.Comment: 4 pages, 3 figure

Lyapunov modes for a nonequilibrium system with a heat flux

We present the first numerical observation of Lyapunov modes (mode structure of Lyapunov vectors) in a system maintained in a nonequilibrium steady state. The modes show some similarities and some differences when compared with the results for equilibrium systems. The breaking of energy conservation removes a zero exponent and introduces a new mode. The transverse modes are only weakly altered but there are systematic changes to the longitudinal and momentum dependent modes.Comment: 9 pages, 7 figure

Denoising and Edge Classification of Color Image

目前彩色图像处理系统用于各种目的，从为后续处理而获取场景到提取图像的特征，这些处理系统通常需要依赖滤波操作抑制噪声，从而避免了噪声影响系统核心功能的缺陷。 降噪是本文重点讨论的一个图像处理应用。如果图像是为了视觉观察，那么噪声会降低图像的质量，它潜在的价值也因此受到限制。如果图像是为了数据分析，那么噪声通常会影响系统的性能。因此降噪-从含有噪声的图像数据中估计原图像信息的过程-是图像处理过程一个很重要的部分。 本文研究讨论了目前最常用的几种彩色图像降噪算法，并在模糊相似群体降噪算法的基础上，提出了基于边缘检测的模糊相似群体的彩色图像降噪算法。通过仿真实验，该算法不仅改善了降噪效果，同时保存...Color image processing systems have a variety of applications, ranging from scenes capturing for posterity to image processing for feature extraction. These systems often rely on filtering operations to suppress noise to avoid the drawback that would inhibit the central function of the system. Noise remove is one of the main applications discussed in this paper. If an image is destined for human ...学位：工学硕士院系专业：信息科学与技术学院自动化系_控制理论与控制工程学号：2322007115284

Hopping dynamics for localized Lyapunov vectors in many-hard-disk systems

The dynamics of the localized region of the Lyapunov vector for the largest Lyapunov exponent is discussed in quasi-one-dimensional hard-disk systems at low density. We introduce a hopping rate to quantitatively describe the movement of the localized region of this Lyapunov vector, and show that it is a decreasing function of hopping distance, implying spatial correlation of the localized regions. This behavior is explained quantitatively by a brick accumulation model derived from hard-disk dynamics in the low density limit, in which hopping of the localized Lyapunov vector is represented as the movement of the highest brick position. We also give an analytical expression for the hopping rate, which is obtained us a sum of probability distributions for brick height configurations between two separated highest brick sites. The results of these simple models are in good agreement with the simulation results for hard-disk systems.Comment: 28 pages, 13 figure