黏性指进的实验与模拟

利用简易装置观察了黏性指进现象,使用照相机拍摄多种黏性指进分形图形,测量了分形维数,并采用数值模拟中的随机模拟演示了黏性指进图形.     

受限分枝无规分形的分维度

提出了受限分枝无规分形的概念．用无规分枝生长的统计方法计算了它的分维．从理论上证明了理想无规分形的分维应在2与4之间．讨论了无规分形的线性度问题，并说明了无规分形体的线性度与物理体系中相互作用的各向异性有关 关键词：     

分形物理进展

本文简要介绍分形的基本概念，综述它在物理学中取得的重要进展．限于篇幅，文中 将略去理论的细节及数学推导，也不涉及分形 在其它领域的应用．     

分形概念及其在材料科学中的应用

本文首先结合几个数学构造分形的例子介绍分形概念，然后对分形在材料科学中的应用作了简要介绍，主要包括：粉体生长中的分形、断裂面的分形、离子注入等非平衡方法产生的分形、表面分形、无机材料中的分形、自旋玻璃中的分形．     

水分子凝聚体系的介孔结构分形学

透射电镜研究表明，4,40-双硬脂酰胺基二苯醚在水中聚集、自组装成缠绕细纤维状聚集体，进而使整个体系形成三维网络结构．水分子被包囊在这个网络结构中，形成一种新型的凝聚体系(水分子凝胶)．水分子凝胶是一种典型的纳米介孔物质，其复杂的微孔结构可以用分形维数D来表征，通过气体吸附方法(孔度法和比表面积法)计算，求得水分子凝胶体系的微孔结构的分形维数为2.1?2.2．对于纤维状三维网络结构的分形表征，通过粘度法和Cayley分形树模型得出分形维数为1.98．由此推测其分形网络形成的过程是一个初始成核-生长-枝化的循环过程．     

基于分形脊波神经网络的遥感图像分类研究

在分形理论和脊波神经网络的基础上，综合利用彩色遥感图像的光谱、纹理和形状特征，提出了一种彩色遥感图像的分类新方法．该方法把彩色图像的蓝、绿、红波段作为3个光谱特征，由分形理论计算的DBC维和多重分形维数作为2个纹理特征，平均不变矩作为1个形状特征，并利用对曲线具有极强方向识别能力的脊波神经网络作为分类器．实验结果表明，提出的彩色遥感图像分类方法具有较高的分类准确率和较强的抗噪音能力．     

沉积岩中的分形及其在石油勘探和开发中的应用

介绍了沉积岩的分形性质，简述了沉积岩中的分形在石油勘探和开发中的应用．     

分形图形与激光全息防伪技术

利用分形图形具有无限可分和比例尺度上的自相似的特征以及可以产生无限变量重复码的特点，通过计算机控制激光双光束干涉光刻成点阵全息光栅，从而形成数字像素全息图．构造出分形图形的迭代函数系统框架，形成丰富多彩，变化多端的分形图形，以此对点阵全息光栅编码，光刻成分形数字像素全息图．     

分形发展三十年

分形发展三十年＠黄田匀￥北京大学物理系，北京大学非线性科学中心分形发展三十年黄田匀（北京大学物理系，北京大学非线性科学中心，北京１００８７１）“分形”作为一门独立的学科，它只有大约３０来年的历史．我们通常都是以芒德布罗（Ｂ．Ｂ．Ｍａｎｄｅｌｂｒｏｔ）发表...     

多相燃烧分形模型及其实验研究

本文提出了多相燃烧的分形模型．模型中认为在多相燃烧中内部孔洞体积与表面积存在分维指数关系，而且反应面积的增长为两种分形增长模式的叠加．结合孔洞合并的因素得到了描述煤多相反应速率的分形模型．该模型描述的反应速率先增加后减少的规律与实验结果十分相符．对五个煤种和其中两个煤焦样品进行了试验研究，在两个不同升温速率下得出的试验数据与理论计算相符．     

FRACTAL PATTERN GROWTH OF METAL ATOM CLUSTERS IN ION IMPLANTED POLYMERS

The fractal and multi-fractal patterns of metal atoms are observed in the surface layer and cross section of a metal ion implanted polymer using TEM and SEM for the first time. The surface structure in the metal ion implanted polyethylene terephthalane (PET) is the random fractal. Certain average quantities of the random geometric patterns contain self-similarity. Some growth origins appeared in the fractal pattern which has a dimension of 1.67. The network structure of the fractal patterns is formed in cross section, having a fractal dimension of 1.87. So it can be seen that the fractal pattern is three-dimensional space fractal. We also find the collision cascade fractal in the cross section of implanted nylon, which is similar to the collision cascade pattern in transverse view calculated by the TRIM computer program. Finally, the mechanism for the formation and growth of the fractal patterns during ion implantation is discussed.     

Diffraction Fields of Fractally Bounded Apertures

Experimental study is performed of optical diffractions by two-dimensional, self-similar mass and surface fractal apertures as well as mass fractal apertures bounded by surface fractals. Self-similar intensity distributions are observed in the Fraunhofer diffraction fields from surface and mass fractal apertures. Power law decays in average intensities of the diffraction patterns are also investigated for the mass, surface and combined fractal apertures in connection with the fractal dimensions of the objects.     

Experimental determination of Hurst exponent of the self-affine fractal patterns with optical fractional Fourier transform

The extension of ordinary Fourier transform to the fractional Fourier transform (FRFT) was first accomplished by Namias in 1980. He gave a complete mathematical definition and discussed the eigenfunction of the transform. Using a system of lenses Lohmann et al.[1] first successfully realized the FRFT optically and designed the single lens mode and double lens mode for the realization of the FRFT of continuously variable fractional order. The concept of fractals was first proposed by Man…     

煤多相燃烧分形增长模型的初步研究

本文运用分形理论对煤的多相燃烧过程进行了探索性研究。根据分形动力学的概念认为；煤的多相燃烧中，反应面积的分形增长有DLC模式和KLC模式，一般情况是这两种模式的迭加。模型还引入了孔洞的合并及煤种的影响因素，初步提出了较有通用意义的燃烧模型。该模型把对碳焦的表面分形与燃烧速率的计算结合起来初步揭示了碳焦结构对燃烧过程的影响。     

Localized Excitations of (2+1)-Dimensional Korteweg-de Vries System Derived from a Periodic Wave Solution

With the aid of an improved projective approach and a linear variable separation method,new types of variable separation solutions (including solitary wave solutions,periodic wave solutions,and rational function solutions)with arbitrary functions for (2 1)-dimensional Korteweg-de Vries system are derived.Usually,in terms of solitary wave solutions and rational function solutions,one can find some important localized excitations.However,based on the derived periodic wave solution in this paper,we find that some novel and significant localized coherent excitations such as dromions,peakons,stochastic fractal patterns,regular fractal patterns,chaotic line soliton patterns as well as chaotic patterns exist in the KdV system as considering appropriate boundary conditions and/or initial qualifications.     

分形介质的传热与传质分析(综述)

本文论述了分形介质的分形理论和数学基础,并简要综述了用分形理论和方法研究分形介质的传热与传质特性(如多孔介质的渗透率、热导率以及池核态沸腾换热)方面目前所取得的研究进展,最后扼要展望了用分形理论和方法进一步研究分形介质的传热与传质的可能的若干课题和方向。     

New Fractal Localized Structures in Boiti-Leon-Pempinelli System

A novel phenomenon that the localized coherent structures of a (2 1)-dimensional physical model possess fractal behaviors is revealed. To clarify the interesting phenomenon, we take the (2 1)-dimensional Boiti-Leon Pempinelli system as a concrete example. Starting from an extended homogeneous balance approach, a general solution of the system is derived. From which some special localized excitations with fractal behaviors are obtained by introducing some types of lower-dimensional fractal patterns.     

New Fractal Localized Structures in Boiti-Leon-Pempinelli System

A novel phenomenon that the localized coherent structures of a (2 1)-dimensional physical model possess fractal behaviors is revealed. To clarify the interesting phenomenon, we take the (2 1)-dimensional Boiti Leon-Pempinelli system as a concrete example. Starting from an extended homogeneous balance approach, a general solution of the system is derived. From which some special localized excitations with fractal behaviors are obtained by introducin gsome types of lower-dimensional fractal patterns.     

树状分形结构形成过程的实验研究

对大量金属小球在强电场作用下运动形态的演化全过程用联机摄像装置进行了实时拍摄,通过用Sandbox方法计算其稳定状态的分维数,系统地研究了分维数随电压的变化关系.结果表明：在一定电压范围内金属小球聚集体通过自组织过程形成稳定的树状分形结构,其分维数随外加电压的增加而减小.该结果对研究耗散结构的形成机理和外界动力对耗散结构的形貌影响具有参考价值. 关键词： 分形生长 自组织过程 树状结构 分维数