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     

Fluctuations and scaling in models for particle aggregation

We consider two sequential models of deposition and aggregation for particles. The first model (No Diffusion) simulates surface diffusion through a deterministic capture area, while the second (Sequential Diffusion) allows the atoms to diffuse up to ? steps. Therefore the second model incorporates more fluctuations than the first, but still less than usual (Full Diffusion) models of deposition and diffusion on a crystal surface. We study the time dependence of the average densities of atoms and islands and the island size distribution. The Sequential Diffusion model displays a nontrivial steady-state regime where the island density increases and the island size distribution obeys scaling, much in the same way as the standard Full Diffusion model for epitaxial growth. Our results also allow to gain insight into the role of different types of fluctuations.     

Particle aggregation versus cluster aggregation in high dimensions

We distinguish two different types of irreversible aggregation-accretion of individual particles and successive aggregation of clusters of comparable size. In aggregation of particles which follow trajectories of fractal dimensionD ₁, we show that physical limits on the aggregation rate impose a lower bound on the fractal dimensionD ₀ of the aggregate. Ind-dimensional space,D ₀{d–D}₁ + 1. Thus aggregation of ballistic particles, withD ₁ = 1, is not fractal. By contrast, cluster aggregates appear to attain a finite, limitingD ₀ in high dimensions. We present a soluble model with this property, and argue that it should agree with Sutherland's binary aggregation model in high dimensions. For this model,D ₀ depends continuously on a parameter; the exponent is not universal.     

Williams-watts dielectric relaxation: A fractal time stochastic process

Dielectric relaxation in amorphous materials is treated in a defect-diffusion model where relaxation occurs when a mobile defect, such as a vacancy, reaches a frozen-in dipole. The random motion of the defect is assumed to be governed by a fractal time stochastic process where the mean duration between defect movements is infinite. When there are many more defects than dipoles, the Williams-Watts decaying fractional exponential relaxation law is derived. The argument of the exponential is related to the number of distinct sites visited by the random walk of the defect. For the same reaction dynamics but with more traps than walkers, an algebraically decaying relaxation is found.     

稳恒磁场下金属电沉积枝晶生长的模拟

采用Monte-Carlo模拟方法,给出用于描述稳恒磁场作用下电沉积枝晶生长的模型.该模型综合考虑了外加磁场B,电解溶液浓度和离子在阴极发生还原反应的几率P_s等因素对电沉积过程的影响,模拟得到与实验结果一致的枝晶生长图形.模拟结果表明:团簇的形状和它们的分形维数都与外加磁场B的强弱,即体现在模型中离子的旋转角速度ω的大小有关;随着磁场强度的增加,沉积团簇会从分形向非分形转变;在相对强的外加磁场作用下,较高离子浓度时的沉积物是非分形的;离子在阴极的反应概率P_s越小,随着磁场强度的增加枝晶生长越易趋向非分形.     

薄板热扩散分形生长的环境干扰控制

研究了薄板热扩散中分形生长的控制,给出了生长概率与干扰项之间的数量关系,预测了热扩散分形生长表面在干扰作用区域内的凝聚情况,并随着干扰项的制约而达到控制的目的.其中以三角函数形式的非线性项与定义域为圆域的源项构成的环境干扰项为例,验证了该控制方法的有效性.另外,生长表面的标度维数变化显示了环境干扰项对实际生长复杂度的影响.     

无格点基底表面的杂质分布对分枝状凝聚体的影响

根据含杂质熔融玻璃表面金原子凝聚的实验规律，在原子团簇具有随机的线扩散步长和刚性转动角的特征条件下，建立了含杂质无格点基底表面上改进的杂质限制团簇-团簇(IRCCA)凝聚模型.对团簇的扩散、刚性转动以及凝聚全过程进行了计算机模拟，系统地研究了杂质区域分布情况对分枝状凝聚体诸多特性的影响.结果表明规则分布的杂质对凝聚体生长的影响比随机分布的杂质大，导致杂质规则分布的基底表面上的分枝状凝聚体的数密度更大，分枝状凝聚体的回旋半径，凝聚体平均大小及分形维数更小. 关键词： 薄膜生长 Monte Carlo模拟 分形 杂质     

Multirate diversity strategy of fractal modulation

Previous analyses of fractal modulation were carried out mostly from a signle perspective or a subband,but the analyses from the perspective of multiscale synthesis have not been found yet; while multiscale synthesis is just the essence of the mutlirate diversity which is the most important characteristic of fractal modulation. As for the mutlirate diversity of fractal modulation,previous studies only dealt with the general outspread of its concept,lacked the thorough and intensive quantitative comparison and analysis. In light of the above fact,from the perspective of multiscale synthesis,in this paper we provide a comprehensive analysis of the multirate diversity of fractal modulation and corresponding quantitative analysis. The results show that mutlirate diversity,which is a fusion of frequency diversity and time diversity,pays an acceptable price in spectral efficiency in exchange for a significant improvement in bit error rate. It makes fractal modulation particularly suitable for the channels whose bandwidth and duration parameters are unknown or cannot be predicted to the transmitter. Surely it is clearly of great significance for reliable communications. Moreover,we also attain the ability to flexibly make various rate-bandwidth tradeoffs between the transmitter and the receiver,to freely select the reception time and to expediently control the total bandwidth. Furthermore,the acquisitions or improvements of these fine features could provide support of the technical feasibility for the electromagnetic spectrum control technology in a complex electromagnetic environment.     

自仿射分形在高能碰撞多重产生中的应用

当分形体在不同方向的标度规律不同时，它就是自仿射而不是自相似．本文指出，高能多重产生中的分形属于这种情况，并建议了一种用实验检验自仿射性和测量自仿射的特征量──赫斯特指数的方法     

一种基于分形维数聚类的分形图像编码方法

对分形维数进行了探讨 ,提出了用分形维数对domainblocks进行聚类 ,从而达到了快速搜索编码的目的。实验结果表明 :与经典分形方法相比 ,在图像保真度基本接近的前提下 ,编码速度提高了 80倍左右     

双边扩散枝晶生长的定量相场模型

本文针对非对称双边扩散条件下的二元合金枝晶生长,建立了一个包含溶质截流项的定量相场模型．本模型耦合了非线性热力学函数并采用化学势相等的界面条件．通过对相场方程进行二阶的薄界面渐进分析,并结合溶质拖拽模型,推导出相场迁移率和溶质截流项．随后将模型简化为二元稀溶液合金等温枝晶生长的相场模型以对其进行理论验证．通过在各种相场界面厚度条件下进行数值模拟,测试了本模型的数值收敛性．用所建立的模型模拟了Fe-0．15m01％C合金的等温枝晶生长,将相场模拟结果和经典Gibbs—Thomson关系,线性可解性理论以及改进的Lipton—Glicksman—Kurz（LGK）解析模型进行比较,取得了良好的符合．模拟结果表明本模型能有效地消除延拓的界面厚度所导致的界面异常效应,具有良好的定量模拟能力．而且,本模型能够定量地描述从单边扩散到对称扩散的各种固相扩散迁移率条件下的枝晶生长．     

Scaling behavior of surface irregularity in the molecular domain: From adsorption studies to fractal catalysts

For an unexpected variety of solids, the surface topography from a few up to as many as a thousand angstroms is very well described by fractal dimension,D. This follows from measurements of the number of molecules in surface monolayers, as function of adsorbate or adsorbent particle size. As an illustration, we present a first case, amorphous silica gel, whereD has been measured independently by each of the two methods. (The agreement, 3.02±0.06 and 3.04±0.05, is excellent, and the result is modeled by a heavy generalized Menger sponge.) The examples as a whole divide into amorphous and crystalline materials, but presumably all of them are to be modeled as random fractal surfaces. The observedD values exhaust the whole range between 2 and 3, suggesting that there are a number of different mechanisms by which such statistically self-similar surfaces form. We show that fractal surface dimension entails interfacial power laws much beyond what is the source of theseD values. Examples are reactive scattering events when neutrons of variable flux pass the surface (this is of interest for locating fractal substrates that may support adlayer phase transitions); the rate of diffusion-controlled chemical reactions at fractal surfaces; and the fractal implementation of the traditional idea that the active sites of a catalyst are edge and apex sites on the surface.     

分形理论在物理实验教学中应用的探索

综述了作者近年来将分形理论引入基础物理实验教学中的尝试与实践，介绍了分形维数的测定方法及其应用，阐述了教师参与适量的科学研究是实现基础物理实验教学现代化的重要保证。     

Transfer processes in fractal media

An irreversible process in fractal media involves coupling relation between the space and the time. The present note displays how the fractional derivation has to be introduced to describe this effect. As a result the law of the chemical diffusion to a fractal is given.     

硫酸铜电解沉积的分形与电导率研究

用电化学的方法,制备出具有分形结构的金属铜样品,计算了不同电解电压下铜样品的分形维数,并求出其电导率.发现随着电解电压的增大,分形结构的维数趋于增大,而铜样品的电导率减小.     

NaCl稀溶液结晶的分形形态研究

通过光学显微镜观察NaCl稀溶液在玻璃基底上快速蒸发结晶形成了完整的立方晶体、DLA凝聚体和形状复杂的凹凸状结晶3种形貌.对复杂的凹凸状结晶进行分析,认为不完整的NaCl小晶粒构成了一个个微小的生成元,以随机Koch曲线的生长方式自组织地顺次相互连接起来,指出此类结晶符合随机Koch曲线,是远离平衡态下的自组织现象.通过改变观测尺度求维数的方法,得到分形维数是1.15±0.06,与Koch曲线相近.     

基于分形几何边界提取的图像跟踪方法

为了满足现代武器装备对图像跟踪系统的实时性和跟踪可靠性的双重要求，针对武器装备所跟踪目标的特点，将基于分形几何的边界提取方法用于图像跟踪系统，提出了一种基于运动区域和边界图像的目标跟踪方案。文中的边界提取方法不仅能提取出目标的轮廓，还能较好地保留其内部细节，这样通过模板匹配得到的最佳匹配位置更加可靠。同时，基于运动区域的边界提取，尤其是对于远景的目标跟踪大大减少了计算量。此外，在利用边界图像进行匹配的基础上，采用了自适应模板更新策略，目的是尽可能地克服形变、光照等影响，使跟踪过程准确可靠。仿真实验表明，该方法运算量小，能满足武器装备实时性要求。     

Anomalous aggregation of squaraine dyes in confined solutions

Enhanced aggregation of squaraine (SQ) dyes in solution capillary layers in contrast to the monomer behavior of the bulk solutions has been observed through differences in electronic absorption spectra of the capillary and bulk SQ solutions of the same concentration. The spectra of the capillary solutions were also different from spectra of SQ condensed films. The spectral differences were dependent on both chemical structure of the dye used and the solvent. It was found that aggregation was stronger in dimethylformamide (DMFA) capillary solutions when compared to the chloroform capillary solutions where aggregation was negligible. It is proposed that the driven force of the observed phenomena is enhanced adsorption of SQ molecules and formation of a liquid crystalline state of the solution near the liquid/solid interface.