无机材料科学中的分形特性

本文讨论了无机材料科学中存在的自相似分形特性．在一定尺度范围内，许多材料具有统计的自相似分形几何，其静态几何性质可用分形几何的质量标度指数Ｄ──分形维数来描述．由分形几何造成对经典欧几里德几何表征动力学性质的偏离，可用指数Ｄｉ──分形子维数来描述．Ｄ和Ｄｉ是分形结构的两个重要参数，且Ｄｆ≤Ｄ≤ｄ．     

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．     

一维随机成核生长模型的边界效应

通过计算机模拟，研究周期边界与固定边界对一维随机成生长模型的聚集生长图形形状及相应的分形维数的影响。     

一个关于分形的教学实验 --对大学物理实验课程创新的探索

设计了一个分形（粘性指进）的教学实验，让学生通过动手操作和计算机模拟得出各种粘性指进分形图形，并测量分形维数．从而使他们对目前活跃、有特色的科学概念——分形有所认识，有所学习．     

分形在物理学中的应用

 一、分形理论的基本内容分形是对没有特征长度但有某种意义下的自相似性的形体和结构的总称。分形体系是具有无标度性的自相似结构。自相似结构可用分形维数来表示,这个维数可以是分数,或是一个连续变化的数。分形维数是描述分形的重要参数,有多种定义和计算方法。一般地,如把一个Ｄ维几何物体的尺寸放大Ｌ倍,就得到ＬＤ个原来的几何图像。令ＬＤ=Ｋ,则有Ｄ=ｌｎＫｌｎＬ上式可作为豪斯道夫维数的定义,并且能毫无困难地推广到非整数的范围。分形几何中的主要角色是由传统数学中的“病态”结构所扮演的,如科契曲线、谢尔品斯基海绵等,它们都具有严格的自相似结构,属于有规分形。     

空温式翅片管气化器结霜模型及数值模拟

以分形理论的DLA模型为基础,建立了空温式翅片管气化器深冷表面上霜晶生长的二维模型,模拟了深冷表面上的霜晶生长过程.采用计盒维数法对模拟出的霜晶生长图像进行了分形维数的计算,结果表明深冷表面上霜晶的分形维数较一般冷表面上的分形维数大,从而说明深冷表面上的霜晶具有更加复杂的结构,充满空间的能力更大.这对进一步理解空温式深...     

科赫分形基底上受限固-固模型动力学标度行为的数值研究

为分析基底结构对离散生长模型动力学性质的影响, 本文在随机游走指数十分接近而分形维数和谱维数均不相同的科赫格子和科赫曲线分形基底上对受限固-固(restricted solid-on-solid)模型的生长过程进行数值模拟研究. 通过分析表面宽度和饱和表面极值高度的统计行为发现: 随机游走的动力学指数能够对饱和粗化表面的动力学行为起主要贡献. 尽管分形基底具有不同的分形维数和谱维数, 但是在两种分形基底上得到了在误差范围内相同的粗造度指数. 两种分形基底上饱和表面相对生长高度极大(小)值分布分别可以很好的塌缩在一起, 且很好的满足Asym2Sig函数分布.     

阴极电极形状对电解沉积生长影响的实验研究

利用ZnSO4溶液,通过电解Zn沉积实验研究了不同形状的阴极对电解沉积生长的影响,并将Zn沉积物生长图片导入计算机程序计算了该沉积物的分形维数。结果显示,阴极电极的形状对电解沉积生长有较大影响,影响了沉积物生长的过程及其形状,但并不影响凝聚物的分形维数,沉积物均具有分形结构。     

分形聚集逾渗性质的计算机模拟

提出3种模型——小尺寸随机逐次成核生长模型和二维及三维代代聚集生长模型,在不同的近邻条件下和不同尺寸的网格中,通过蒙特卡罗模拟,系统地研究了一维、二维和三维分形聚集的逾渗性质.计算结果显示,分形聚集的逾渗阈值仅取决于空间维数和近邻条件,与模型的网格大小无关,是分形系统固有的临界属性;生长概率等于逾渗阈值时,聚集体可以无限生长并保持分形维数恒定,此时的分形维数只是空间维数的线性函数.     

固体薄膜中的分形生长

简要报道了作者近年来用离子束方法研究固体薄膜中分形生长现象的部分结果。例如，首次用离子束辐照使非晶态向晶态转变，在临界点观察到析出的Ｎｉ－Ｍｏ晶体的多核心凝素；离子束界面混合形成的类似于晶格动物的不连续分叉树形结构；磁相互作用对分形凝聚过程及其分形维数的影响；离子注入下与化合物形成相关的类ＤＬＡ结构等。     

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。     

Fractal signature methods for profiling of processed surfaces

A new approach to surface profiling of structural materials that evolves from the concept of fractal signature is put forward. This approach has been developed and advantageously applied for acquisition of low-contrast targets. It is based on the fractal theory, and fractal signatures and fractal dimensions (which are intimately related to both the object’s topology and evolutionary processes in dynamic systems) are used as estimating parameters. The experimental data obtained prove the existence of fractal clusters on the processed surface microrelief. Quantitative characterization of these clusters is given.     

纹理高阶分形特征在海面舰船目标检测中的应用

针对复杂海面环境下的舰船目标检测，分析了高阶分形特征缝隙在纹理分类中的应用，提出了一种基于分形维与缝隙的目标检测新方法，并利用该方法对海面舰船目标进行了检测。实验结果表明利用纹理分形维与缝隙特征进行海面舰船目标检测，可以取得较单一分形维检测更高的准确率。     

A highly efficient algorithm for the generation of random fractal aggregates

A technique to generate random fractal aggregates where the fractal dimension is fixed a priori is presented. The algorithm utilizes the box-counting measure of the fractal dimension to determine the number of hypercubes required to encompass the aggregate, on a set of length scales, over which the structure can be defined as fractal. At each length scale the hypercubes required to generate the structure are chosen using a simple random walk which ensures connectivity of the aggregate. The algorithm is highly efficient and overcomes the limitations on the magnitude of the fractal dimension encountered by previous techniques.     

一种基于超复数系的数字全息图像生成方法

提出了一种基于超复数系的数字全息图像生成方法，通过定义超复数系，由此构成n维向量空间，然后采用分形迭代方法在n维向量空间中选择不同截面来绘制分形图像，因而能够在高维空间生成分形数字图像序列，并能够制作出具有动态效果和美感的激光全息图。由于分形数字全息图像生成具有较好的参数可控制性和不可逆转性，全盛的防伪标专难以仿制，在激光全息防伪领域有着良好的应用前景。     

Simulation model of the fractal patterns in ionic conducting polymer films

Normally polymer electrolyte membranes are prepared and studied for applications in electrochemical devices. In this work, polymer electrolyte membranes have been used as the media to culture fractals. In order to simulate the growth patterns and stages of the fractals, a model has been identified based on the Brownian motion theory. A computer coding has been developed for the model to simulate and visualize the fractal growth. This computer program has been successful in simulating the growth of the fractal and in calculating the fractal dimension of each of the simulated fractal patterns. The fractal dimensions of the simulated fractals are comparable with the values obtained in the original fractals observed in the polymer electrolyte membrane. This indicates that the model developed in the present work is within acceptable conformity with the original fractal.     

Band structure characteristics of T-square fractal phononic crystals

The T-square fractal two-dimensional phononic crystal model is presented in this article.A comprehensive study is performed for the Bragg scattering and locally resonant fractal phononic crystal.We find that the band structures of the fractal and non-fractal phononic crystals at the same filling ratio are quite different through using the finite element method.The fractal design has an important impact on the band structures of the two-dimensional phononic crystals.     

A box-covering algorithm for fractal scaling in scale-free networks

A random sequential box-covering algorithm recently introduced to measure the fractal dimension in scale-free (SF) networks is investigated. The algorithm contains Monte Carlo sequential steps of choosing the position of the center of each box; thereby, vertices in preassigned boxes can divide subsequent boxes into more than one piece, but divided boxes are counted once. We find that such box-split allowance in the algorithm is a crucial ingredient necessary to obtain the fractal scaling for fractal networks; however, it is inessential for regular lattice and conventional fractal objects embedded in the Euclidean space. Next, the algorithm is viewed from the cluster-growing perspective that boxes are allowed to overlap; thereby, vertices can belong to more than one box. The number of distinct boxes a vertex belongs to is, then, distributed in a heterogeneous manner for SF fractal networks, while it is of Poisson-type for the conventional fractal objects.     

Annihilation on a percolation cluster

The diffusion-controlled reaction A+A = 0 on a percolation cluster (fractal system) is investigated analytically and by means of Monte Carlo simulations. The conclusion about reaction kinetics and particle distribution behaviour obtained by a generalized of the Smoluchovsky theory to fractal systems are confirmed by simulations.     

Transfer across random versus deterministic fractal interfaces

A numerical study of the transfer across random fractal surfaces shows that their responses are very close to the response of deterministic model geometries with the same fractal dimension. The simulations of several interfaces with prefractal geometries show that, within very good approximation, the flux depends only on a few characteristic features of the interface geometry: the lower and higher cutoffs and the fractal dimension. Although the active zones are different for different geometries, the electrode responses are very nearly the same. In that sense, the fractal dimension is the essential "universal" exponent which determines the net transfer.