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。     

分形理论在光谱识别中的应用

分形理论是研究一类不规则、混乱复杂,但其局部和整体具有相似性体系的科学。分形维数是分形理论中用于描述对象的不规则度和自相似性的基本度量。文章以符合朗伯-比尔定律的光谱信号为研究对象,在概述分形几何基本原理的基础上,提出了以分形维数作为光谱识别特征的方法,运用相空间重构得出了光谱信号的分形维数,通过对光谱信号的分形维数进行比较,达到识别不同光谱的目的,最后举例对该方法进行了说明。     

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.     

Implications of an extended fractal hydrodynamic model

Considering that the motions of the particles take place on continuous but non-differentiable curves, i.e. on fractals with constant fractal dimension, an extended scale relativity model in its hydrodynamic version is built. In this approach, static (particle in a box and harmonic oscillator) and time-dependent (free particle etc.) systems are analyzed. The static systems can be associated with a coherent fractal fluid (of superconductor or of super-fluid types behavior), whose particles are moving on stationary trajectories. The complex speed field of the fractal fluid proves to be essential: the zero value of the real (differentiable) part specifies the coherence of the fractal fluid, while the non-zero value of the imaginary (non-differentiable or fractal) part selects, through some “quantization” relations, the “stationary” trajectories (that may correspond to the observables from quantum mechanics) of the fractal fluid particles. Moreover, the momentum transfer in the fractal fluid is achieved only through the fractal component of the complex speed field. The free time-dependent systems can be associated with an incoherent fractal fluid, and both the differentiable and fractal components of complex speed field are inhomogeneous in fractal coordinates due to the action of a fractal potential. It exist momentum transfer on both speed components and the “observable” in the form of an uniform motion is generated through a specific mechanism of “vacuum” polarization induced by the same fractal potential. The analysis on the fractal fluid specifies conductive properties in the case of movements synchronization both on differentiable and fractal scales, and convective properties in the absence of synchronization.     

Fractal Analysis of Mobile Social Networks

Fractal and self similarity of complex networks have attracted much attention in recent years.The fractal dimension is a useful method to describe the fractal property of networks.However,the fractal features of mobile social networks(MSNs) are inadequately investigated.In this work,a box-covering method based on the ratio of excluded mass to closeness centrality is presented to investigate the fractal feature of MSNs.Using this method,we find that some MSNs are fractal at different time intervals.Our simulation results indicate that the proposed method is available for analyzing the fractal property of MSNs.     

火灾烟雾颗粒凝并分形特性研究

火灾烟雾颗粒因布朗运动由初期的主粒子凝并形成大颗粒的凝团结构，其外形呈现出分形特征，根据分形理论对火灾烟雾颗粒凝团结构进行分析研究，采用场发射扫描电镜对多种材料的烟雾颗粒图像进行测试，通过对烟雾凝团图像进行处理，获得了火灾探测中常见的多种材料的分形维数和分形系数，给出了烟雾颗粒的主粒子粒径，并对其影响因素进行了对比分析，为火灾烟雾探测中颗粒凝并分形特性研究提供有益的探索. 关键词： 火灾 烟雾 颗粒 凝并 分形     

Small-angle scattering from fat fractals

A number of experimental small-angle scattering (SAS) data are characterized by a succession of power-law decays with arbitrarily decreasing values of scattering exponents. To describe such data, here we develop a new theoretical model based on 3D fat fractals (sets with fractal structure, but nonzero volume) and show how one can extract structural information about the underlying fractal structure. We calculate analytically the monodisperse and polydisperse SAS intensity (fractal form factor and structure factor) of a newly introduced model of fat fractals and study its properties in momentum space. The system is a 3D deterministic mass fractal built on an extension of the well-known Cantor fractal. The model allows us to explain a succession of power-law decays and respectively, of generalized power-law decays (GPLD; superposition of maxima and minima on a power-law decay) with arbitrarily decreasing scattering exponents in the range from zero to three. We show that within the model, the present analysis allows us to obtain the edges of all the fractal regions in the momentum space, the number of fractal iteration and the fractal dimensions and scaling factors at each structural level in the fractal. We applied our model to calculate an analytical expression for the radius of gyration of the fractal. The obtained quantities characterizing the fat fractal are correlated to variation of scaling factor with the iteration number.     

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.     

Boundary Fractal Dimensions from Sections of a Particle Profile

The fractal dimension of particles is commonly evaluated from complete particle boundaries. In this work, a study has been made of the self-similar nature of complete and incomplete boundary profiles of a range of morphologically different copper powders. Boundary images were captured from SEM micrographs of particle boundaries at a range of magnifications up to nearly 14000X. An algorithm was developed to compute the fractal dimension of boundary segments. This algorithm was tested against the Koch Island fractal, and was found to give excellent estimates of the fractal dimension. For the particle system studied, the boundary fractal was found to be sensitive to magnification with appreciable drops in value at high magnification. This demonstrates that the particles studied did not have true fractal boundaries and the use of fractal theory to study particle surface roughness must be used with caution.     

High Efficient Tunable Fractal Axicon Based on LCoS

Based on the Cantor function and phase modulation, a tunable fractal axicon is formed on a liquid crystal on silicon （LCoS） with an improved generating method. It has higher focusing efficiency in higher fractal stage and approaches to 100% theoretically. The on-axis intensity keeps its fractal structure unchanged in operation of fractal stages. The tunability of the axicon is demonstrated by tune fractal stage from 1 to 3 and focal length from 0.8 m to 1 m. We also provide details of theoretical analyses and experimental results.     

基于显微CT图像的岩芯孔隙分形特征

采用国内自主开发的高分辨率显微CT设备,对岩芯样本进行图像采集,运用数字图像分析方法获得图像中的岩芯孔隙目标,并以此为基础重建三维模型。然后基于分形理论,分别从二维图像和重建的三维模型角度计算孔隙的分形维数。最后,再采用基于多孔介质的分形模型对岩芯孔隙分形特征进行验证,得出岩芯的二维分形维数和三维分形维数之间的差值均值为1.000 3,最大偏差为0.004,很好地满足多孔介质分形模型中关于二维和三维分形维数的关系。     

Fractal Analysis of Surface Roughness of Particles in Porous Media

A fractal dimension for roughness height （RH） is introduced to characterize the degree of roughness or disorder of particle surface characters which significantly influence physical-chimerical processes in porous media. An analytical expression for the fractal dimension of RH on statistically self-similar fractal surfaces is derived and is expressed as a function of roughness parameters. The specific surface area （SSA） of porous materials with spherical particles is also derived, and the proposed fractal model for the SSA of particles with rough surfaces is expressed as a function of fractal dimension for RH and fractal dimension for particle size distribution, relative roughness of particle surface, and ratio of the minimum to the maximum particle diameters of spherical particles.     

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.     

基于分形特征的复杂背景下扩展目标检测

 将分形面积度量和分形拟合误差相结合,提出一种复杂背景下扩展目标检测方法。运用分形面积度量进行目标和背景的边缘检测,并结合扩展目标特性确定目标所在区域范围,实现初检。计算原始图像各像素分形拟合误差特征,并运用概率松弛迭代法进行分形特征增强,利用增强特征进一步抑制初检结果中的自然背景。最后运用数学形态学操作剔除背景粘连,实现扩展目标精确检测。实验结果表明:该方法能够有效、可靠地检测复杂背景下的扩展目标,并能较好保持目标的外形轮廓。     

Influences of Fractal Substrate Structures on Dynamic Scaling Behaviors of Etching Model

The Etching model on various fractal substrates embedded in two dimensions was investigated by means of kinetic Mento Carlo method in order to determine the relationship between dynamic scaling exponents and fractal parameters. The fractal dimensions are from 1.465 to 1.893, and the random walk exponents are from 2.101 to 2.578.It is found that the dynamic behaviors on fractal lattices are more complex than those on integer dimensions. The roughness exponent increases with the increasing of the random walk exponent on the fractal substrates but shows a non-monotonic relation with respect to the fractal dimension. No monotonic change is observed in the growth exponent.     

应用分形理论探讨炸药的撞击感度

 根据分形几何的周长-面积公式及线性回归原理,对TATB等六种炸药样品的落锤试验的分幅图像进行了图像处理和分形维数计算。从中发现,越钝感的炸药样品,分形维数越大。因此,可以认为,用炸药样品的分形维数来鉴别撞击感度是基本可行的。     

Mapping physical problems on fractals onto boundary value problems within continuum framework

In this Letter, we emphasize that methods of fractal homogenization should take into account a loop structure of the fractal, as well as its connectivity and geodesic metric. The fractal attributes can be quantified by a set of dimension numbers. Accordingly, physical problems on fractals can be mapped onto the boundary values problems in the fractional-dimensional space with metric induced by the fractal topology. The solutions of these problems represent analytical envelopes of non-analytical functions defined on the fractal. Some examples are briefly discussed. The interplay between effects of fractal connectivity, loop structure, and mass distributions on electromagnetic fields in fractal media is highlighted. The effects of fractal connectivity, geodesic metric, and loop structure are outlined.     

Radiation of some fractal structures

The fractal properties of a candle flame and fractal discharges are considered. The fractal concept is applied to ball lightning.     

Characterization of Synthetic-Coal Char Particles using fractal dimension analysis

The development and change of surface ruggedness in chars was studied at conditions typical in a pulverized coal furnace. The fractal dimension, a measure of surface ruggedness, of chars was measured using physisorption techniques. By adjusting the temperature encountered (1173 to 1773 K) and residence time (0.1 to 1.5 s) of the synthetic coal (sized to 46–106 μm diameter), chars at different stages of combustion were prepared in a laminar flow (drop-tube) furnace. The particles were quickly cooled and quenched in an inert atmosphere. The samples were examined using a scanning electron microprobe, and their fractal dimensions were determined using gas physisorption. The adsorption data were used to test if the char surface was fractal on a molecular scale, to determine the fractal dimension, and to quantify changes in the fractal dimension during combustion. The fractal dimension of the unburned synthetic coal was approximately 2. The fractal dimension increased as high as 2.85 as the carbon matrix burned away and exposed mineral moieties. However, as combustion continued the carbon burned completely away leaving a mineral fly ash particle with a fractal dimension as low as 2.47.     

Fractal Aggregation Under Rotation

By means of the Monte Carlo simulation, a fractal growth model is introduced to describe diffusion-limited aggregation (DLA) under rotation. Patterns which are different from the classical DLA model are observed and the fractal dimension of such clusters is calculated. It is found that the pattern of the clusters and their fractal dimension depend strongly on the rotation velocity of the diffusing particle. Our results indicate the transition from fractal to non-fractal behavior of growing cluster with increasing rotation velocity, i.e. for small enough angular velocity ω; thefractal dimension decreases with increasing ω;, but then, with increasing rotation velocity, the fractal dimension increases and the cluster becomes compact and tends to non-fractal.