The application of Hölder exponent to traffic congestion warning

In this paper, we applied multifractal modeling techniques to analyze the traffic data collected from the Beijing Yuquanying. The results indicated that multifractal characteristics obviously exist in the traffic system; the degree of fractality of these traffic data tends to increase as the traffic system becomes congested; the Hölder exponent that measures the local rate of fractality may be used as indicators to predict the presence of the traffic congestion.     

聚丙烯酰胺/醋酸铬与聚丙烯酰胺/酚醛胶态分散凝胶的纳米颗粒自组织分形结构

采用原子力显微镜 ,分别对无机交联体系聚丙烯酰胺 Cr3+ 和有机交联体系聚丙烯酰胺 酚醛胶态分散凝胶的微观结构进行了显微图像分析 .发现无论是在有机还是无机交联体系中 ,也无论聚丙烯酰胺和交联剂浓度如何变化 ,在微米尺度上最终形成的都是具有自相似性的树枝状分形图像 ,在更小尺度上则发现单个小树杈分形体都是由纳米级的颗粒紧密堆积而成 .在所研究的胶态分散凝胶体系中 ,树枝状分形结构的形成及其具体的形态取决于聚丙烯酰胺的浓度 ,而交联剂的有无及其多少只对树枝状凝胶分形的几何形态产生一定影响 .实验结果还表明纳米级 (≤ 10 0nm)的胶体颗粒构成的分形结构的凝胶其弹性模量G′比微米级的高出一个数量级 .且粒子尺度越小 ,则凝胶的力学稳定性越强     

Some aspects of diffusion: fluctuations in reaction diffusion,and geometric influences in nonuniform media

Summary We deal with two diffusion problems: Space-integrated conserved entities characterizing very fast - diffusion - controlled reactions, such as time lags, etc. are universal. They are given by relationships which do not reflect the failure of the mean field hydrodynamic equations. We present another application which does not reflect this failure, for determining the surface flux via a diffusion controlled reaction producing a colored product. Another anomalous diffusion process we considered is transport through cellular materials whose cell sizes are highly nonuniform. We have analyzed the effects of extreme nonuniformity by considering fractal-like models of cellular solids. The diffusion current through these models can exhibit anomalous time-dependencies which are not predicted by the diffusion equation. In particular, it is shown that the initial diffusion current can be characterized by a power-law dependence on the time. Furthermore, the exponent of the power law is given in terms of the distribution of cell sizes in the fractal-like cellular solid.     

Rate processes on fractals: Theory,simulations, and experiments

Heterogeneous kinetics are shown to differ drastically from homogeneous kinetics. For the elementary reaction A + A products we show that the diffusion-limited reaction rate is proportional tot ^– h[A]² or to [A]^x, whereh=1- d _s/2, X=1+2/d _s =(h-2)(h-1), andd _s is the effective spectral dimension. We note that ford = d _s =1, h =1/2 andX = 3, for percolating clustersd _s = 4/3,h = 1/3 andX = 5/2, while for dust ds <1, 1 >h > 1/2 and >X > 3. Scaling arguments, supercomputer simulations and experiments give a consistent picture. The interplay of energetic and geometric heterogeneity results in fractal-like kinetics and is relevant to excitation fusion experiments in porous membranes, films, and polymeric glasses. However, in isotopic mixed crystals, the geometric fractal nature (percolation clusters) dominates.     

分形理论及其在高分子科学中的应用

介绍了分形的基本概念，分形维数的定义及计算方法，讨论了近年来分形理论在高分子科学研究方面的一些应用，内容主要包括高分子溶液、高分子材料的磨损，断裂及界面，高分子结晶过程、导电高分子等。     

Dissipative structures formed in the course of drying the colloidal crystals of silica spheres on a cover glass

Macroscopic and microscopic dissipative structural patterns formed in the course of drying the deionized aqueous colloidal crystal suspensions of silica spheres (diameter: 103 nm) on a cover glass have been observed. Spoke-like and ring-like patterns are formed in the macroscopic scale; the former is the crack in the sphere film and the latter is the hill accumulated with spheres formed around the outside edge. The neighbored inter-spoke angle, thickness of the film, and other morphological parameters have been discussed as a function of sphere concentration, concentration of sodium chloride, and the inclined angle of the cover glass. Fractal patterns of the mud cracks are observed in the microscopic scale. Capillary forces between spheres at the air-liquid surface and the relative rates between the water flow at the drying front and the convection flow of spheres are important for the pattern formation. Electronic Publication     

表面分散过程的分形研究

盐类和氧化物等活性组分在一定条件下,可在高比表面载体上自发分散。研究这些过程对多相催化剂、吸附剂的制备过程理解和控制无疑是重要的。这类分散过程已被系统地研究,并提出了单层分散模型,对CuCl_2/γ-Al_2O_3、HgCl_2/活性炭等多种体系,测定了单层分散阈值。表面化学习惯上理解为就是二维的化学。早在1931年Tayor就指出表面是不均匀的,但这种不均匀性是作为对理想二维表面的修正而引入的,如TLK模型。表面科学的这些基本概念其数学基础是欧基里德几何学,其物理背景是晶体结构,不规则性就是指晶体结     

Drying dissipative structures of the aqueous suspensions of monodisperse bentonite particles

Macroscopic and microscopic dissipative structural patterns formed in the course of drying the fractionated and monodisperse bentonite particles (plate-like in their shape) in aqueous deionized suspension and in the presence of NaCl have been studied on a cover glass. The patterns coexisted with the broad ring of the hill accumulated with the particles and with the round hills are formed around the outside edges of the film and in the center, respectively, in the macroscopic scale. By the addition of NaCl the pattern shifts from the broad ring to the round hill in the center. The spoke-like cracks, which have been observed for the suspensions of the spherical particles so often hitherto, are not observed at all for the bentonite suspensions. The characteristic convection flow of the particles and the interactions among the particles and substrate are important for the macroscopic pattern formation. Wrinkled, branch-like and/or star-like fractal patterns are observed in the microscopic scale. These patterns are determined mainly by the electrostatic and polar interactions between the particles and/or between the particle and the substrate in the course of drying.     

聚甲基丙烯酸甲酯/聚醋酸乙烯酯共混相分离过程的标度行为与逾渗结构

本文用激光光散射和光学显微镜方法研究了聚甲基丙烯酸甲酯/聚醋酸乙烯酯共混体系不稳相分离过程最大散射强度I_m(t,T)和相应波矢q_m(t,T)随时间变化规律及相区的逾渗结构.实验结果表明:I_m(T,t)和q_m(t,T)与时间t满足简单的标度关系I_m(t,T)～t~β,q_m(t,T)～t~(-α),且标度关系β=3α成立.揭示了相态结构的分维特征.给出了计算相态结构分维数的简便方法,其分维数D值约为1.64±0.03.与逾渗模型给出的D值接近.