粗糙表面形貌对微尺度流动换热的影响

基于分形几何定量描述了多尺度自仿射的粗糙表面形貌,建立了微通道内层流流动换热的理论模型并对表面形貌的影响进行了数值模拟.研究表明,自仿射分形维数直接反映了表面轮廓的不规则度,对于两个具有相同统计粗糙度的轮廓,可能存在不同的分形维数;与常规尺度通道不同,雷诺数、粗糙高度和粗糙表面分形维数都对微通道内层流流动换热有着重要影...     

基于康托尔分形微通道流动与传热的模拟

高密度、 小体积和高集成的电子元器件散热困难, 易造成过早失效, 采用微通道换热器可以实现小体积内高热流的散热, 但流动阻力很大. 为了保证传热效果, 降低流动阻力, 本文提出了一种新型的微通道结构并对其流动与传热特性进行了数值模拟. 首先研究了微通道形状和结构, 模拟结果表明: 进出口截面宽高比为0.8 的矩形微通道的换热效果最好; 并在此基础上提出一种康托尔分型凹槽结构, 研究了有无康托尔分形以及不同分形级数对流动与传热性能的影响, 综合对比发现: 第二级康托尔分形模型 N2 既能保证热阻显著降低, 又能相比阵列结构降低压降, 具有明显的换热优势; 最后对这种康托尔分形结构的凹槽形状, 尺寸及不同方向上的分形进行研究, 结果表明梯形凹槽的下上表面长度比b/a 为0.6 、 流动方向分形比fx 为1 .25 和通道高度方向分形比fy 为1 .5 时换热流动性能最佳.     

The Relation Between Elastic and Total Scatterings from Fractals

The ratio of the elastic and total scattering intensities η(q) = I:(q)/I_t²(q) is studied for fractals of dimension range widely. The results show that it oscillatorily decays with a quantity qR_o where q is the absolute value of the momentum transfer q and R_o the average distance between the nearest neighbor sites of scatters in fractal objects. The locations of valleys and peaks of η are only dependent on fractal dimensions. However, the dependence is very beak and η is almost a constant varying in the range of only several percent for widely different fractal dimensions.     

多孔介质热导率的数值计算

通过数值模拟得出面积分形维数和孔隙率相同,而孔隙结构不同的分形多孔介质的导热特性是不相同的.说明仅仅依靠孔隙率和分形维数两个参数无法有效确定多孔介质的热物理性质,寻找新的表征孔隙结构的参数是必要的.同时也说明了前人所得出的关于多孔介质的热物性的解析表达式具有一定的局限性和不确定性.     

基于分形理论的多孔介质导热系数研究

本文根据分形理论,对多孔介质几何结构进行了描述,计算出了不同孔隙率多孔介质简化模型的剖面面积分布分形维数d,并利用分形维数结合土壤导热模型推出了土壤的有效导热系数表达式,计算结果表明,该方法是符合客观实际的．     

Laplacian growth and diffusion limited aggregation: different universality classes

It had been conjectured that diffusion limited aggregates and Laplacian growth patterns (with small surface tension) are in the same universality class. Using iterated conformal maps we construct a one-parameter family of fractal growth patterns with a continuously varying fractal dimension. This family can be used to bound the dimension of Laplacian growth patterns from below. The bound value is higher than the dimension of diffusion limited aggregates, showing that the two problems belong to two different universality classes.     

Fractal properties of aggregates of metal nanoclusters on solid surface

AFM images are used to determine and analyze fractal characteristics (cluster fraction dimension and lacunarity) of aggregates of Au and Ag nanoclusters on metal films of the same metal produced with the aid of thermal vacuum deposition on mica surface. A fractal dimension of 1.6 that corresponds to typical samples with relatively uniform distribution of nanoclusters on the film surface is in agreement with the mean value calculated from experimental data of Belko et al., who studied the fractal dimension of Au nanoclusters on a different dielectric (quartz) surface. When a compact single aggregate of Au nanoclusters is formed on a certain active center or defect, the fractal cluster dimension decreases to 1.4. The experimental data are compared with the results of existing theoretical models of association of nanoclusters in 2D systems.     

Fractal properties of acoustic location responses

The fractal dimension of reflected ultrasonic signals in steel slabs with wittingly introduced defects is analyzed. The dependence of the fractal dimension on the defect size is demonstrated. The resolving power of a method used to estimate the fractal dimension of acoustic location responses and its applicability in practical flaw detection are considered.     

纳米流体对流换热机理分析

考虑在纳米流体中纳米颗粒做布朗运动引起的对流换热, 基于纳米颗粒在纳米流体中遵循分形分布, 本文得到纳米流体对流换热的机理模型. 本解析模型没有增加新的经验常数, 从该模型发现纳米流体池沸腾热流密度是温度、纳米颗粒的平均直径、 纳米颗粒的浓度、纳米颗粒的分形维数、沸腾表面活化穴的分形维数、基本液体的物理特性的函数. 对不同的纳米颗粒浓度和不同的纳米颗粒平均直径与不同的实验数据进行了比较, 模型预测的结果与实验结果相吻合. 所得的解析模型可以更深刻地揭示纳米流体对流换热的物理机理.     

a-Ge/Au双层膜退火后分形区的形成

本文用透射电子显微镜观察了a-Ge/Au双层膜在不同退火温度后出现的分形区域,并计算了它们的分数维数。100℃退火时,触发分形结晶区的成核位较少,形成良好的具有无规分叉、自相似的分形区,分数维数为1.785±0.01。200℃退火时,成核位迅速增加,除了分数维数为:1.818±0.008的分形区外,还出现孤立的无枝叉结构的岛状区域。300℃退火时,只出现尺寸很不相同的两种岛状区域,对上述枝叉伏、岛状区域的出现以及a-Ge膜的晶化和Au膜缩聚之间的关系进行了讨论。 关键词：     

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.     

花簇分形无标度网络中节点影响力的区分度

大量研究表明分形尺度特性广泛存在于真实复杂系统中, 且分形结构显著影响网络上的传播动力学行为. 虽然复杂网络的节点传播影响力吸引了越来越多学者的关注, 但依旧缺乏针对分形网络结构的节点影响力的系统研究. 鉴于此, 本文基于花簇分形网络模型, 研究了分形无标度结构上的节点传播影响力. 首先, 对比了不同分形维数下的节点影响力, 结果表明, 当分形维数很小时, 节点影响力的区分度几乎不随节点度变化, 很难区分不同节点的传播影响力, 而随着分形维数的增大, 从全局和局域角度都能很容易识别网络中的超级传播源. 其次, 通过对原分形网络进行不同程度的随机重连来分析网络噪声对节点影响力区分度的影响, 发现在低维分形网络上, 加入网络噪声之后能够容易区分不同节点的影响力, 而在无穷维超分形网络中, 加入网络噪声之后能够区分中间度节点的影响力, 但从全局和局域角度都很难识别中心节点的影响力. 所得结论进一步补充、深化了基于花簇分形网络的节点影响力研究, 研究结果对实际病毒传播的预警控制提供了一定的理论借鉴.     

Fractal dimensions in perceptual color space: a comparison study using Jackson Pollock's art

The fractal dimensions of color-specific paint patterns in various Jackson Pollock paintings are calculated using a filtering process that models perceptual response to color differences (L*a*b* color space). The advantage of the L*a*b* space filtering method over traditional red-green-blue (RGB) spaces is that the former is a perceptually uniform (metric) space, leading to a more consistent definition of "perceptually different" colors. It is determined that the RGB filtering method underestimates the perceived fractal dimension of lighter-colored patterns but not of darker ones, if the same selection criteria is applied to each. Implications of the findings to Fechner's "principle of the aesthetic middle" and Berlyne's work on perception of complexity are discussed.     

X分形晶格上Gauss模型的临界性质

采用实空间重整化群变换的方法,研究了2维和d(d>2)维X分形晶格上Gauss模型的临界性质.结果表明:这种晶格与其他分形晶格一样,在临界点处,其最近邻相互作用参量也可以表示为K=bqiqi(qi是格点i的配位数,bqi是格点i上自旋取值的Gauss分布常数)的形式;其关联长度临界指数v与空间维数d(或分形维数df)有关.这与Ising模型的结果存在很大的差异. 关键词： X分形晶格 重整化群 Gauss模型 临界性质     

分数维结构有机物体系中的发光

本文介绍了分数维结构和激子渗透概念,概述了分数维结构有机物体系中能量传递和发光动力学研究的基本现状。     

高速铁路轮轨滚动噪声的分形描述及分形维估计

提出基于分形分析的轮轨滚动噪声研究方法,研究了不同尺度下轮轨滚动噪声增量的统计特性,证明轮轨滚动噪声具有分形特性,可由分形布朗运动描述。在此基础上,利用分形布朗运动的小波系数方差与分形维的幂律关系估计了轮轨滚动噪声的分形维,并估计了以裂纹扩展为代表的钢轨伤损声发射信号的分形维,对比研究发现:轮轨滚动噪声分形维本身具有随机性,不同车速下的轮轨滚动噪声分形维估计以1.5666为均值随机分布在小于2的小区间内;分形维是轮轨滚动噪声的固有特征,与车速无关,不同车速的轮轨滚动噪声可由统一的分形布朗运动模型描述;裂纹扩展信号与轮轨滚动噪声不同,其分形维估计大于2,不满足分形布朗运动模型的要求,但分形维可作为二者的区别特征。研究提取了轮轨滚动噪声的分形维作为固有特征,为高速轮轨滚动噪声描述及轮轨伤损检测提供了有效的分析方法。      

Prediction of heat transfer of nanofluid on critical heat flux based on fractal geometry

Analytical expressions for nucleate pool boiling heat transfer of nanofluid in the critical heat flux (CHF) region are derived taking into account the effect of nanoparticles moving in liquid based on the fractal geometry theory. The proposed fractal model for the CHF of nanofluid is explicitly related to the average diameter of the nanoparticles, the volumetric nanoparticle concentration, the thermal conductivity of nanoparticles, the fractal dimension of nanoparticles, the fractal dimension of active cavities on the heated surfaces, the temperature, and the properties of the fluid. It is found that the CHF of nanofluid decreases with the increase of the average diameter of nanoparticles. Each parameter of the proposed formulas on CHF has a clear physical meaning. The model predictions are compared with the existing experimental data, and a good agreement between the model predictions and experimental data is found. The validity of the present model is thus verified. The proposed fractal model can reveal the mechanism of heat transfer in nanofluid.     

Fractality of self-grown nanostructured tungsten by He plasma irradiation

Fractal property of the helium irradiated nanostructured tungsten was investigated from the scanning electron microscope (SEM) micrographs, gas adsorption isotherms, and transmission electron microscope (TEM) micrographs. From the SEM micrographs, fractal dimension and the parameter _dmin$d_{\min }$, which characterizes the SEM texture image, were deduced, and the fractal dimension was compared with the one obtained from the gas adsorption isotherms. It was revealed that the fractal dimension obtained from the top view SEM micrographs was significantly lower than that from the adsorption isotherms. From the cross sectional SEM micrographs, two power law relations were identified in two different scales, and the fractal dimension from the adsorption was in between the two fractal dimensions. From the TEM micrographs, it was found that the porosity distribution also has fractal relation with height of the nanostructures when the nanostructures were sufficiently grown.     

KDP晶体单点金刚石车削表面形貌分形分析

 分别使用2维和3维分形方法对单点金刚石车削加工的KDP晶体表面形貌进行了分析，并对表面的3维分形维数和3维粗糙度表征参数进行了比较，分析了二者对表面形貌表征的差异。使用2维轮廓分形方法计算了KDP晶体表面圆周各方向上的分形维数。通过分析得出：3维分形维数与表面粗糙度值成反比关系；使用单点金刚石车削方法加工KDP晶体会形成各向异性特征明显的已加工表面，在一定程度上容易形成小尺度波纹；已加工表面是否具有明显的小尺度波纹特征与表面粗糙度值并无直接关系，但与其表面轮廓分形状态分布密切相关；KDP晶体表面2维功率谱密度与其分形状态具有相近的方向性特征。     

Comparison of fractal analyses methods and fractal dimension for pre-treated stainless steel surfaces and the correlation to adhesive joint strength

The fractal dimensions of six differently mechanically pre-treated stainless steel samples were investigated using five fractal algorithms. The surfaces were analyzed using a profiler, atomic force microscopy (AFM), scanning electron microscopy (SEM) and light microscopy (LM), and thereafter adhesively bonded and tested in single-overlap joints to test their tensile strength. All samples showed different fractal behavior, depending on the microscopic methods and fractal algorithms. However, the overall relation between fractal dimension and tensile strength is qualitatively the same, except for the SEM images. This verifies that tensile strength is correlated to fractal dimension, although only within the length-scale of the profiler and the light microscope (≈0.5–100 μm). The AFM method was excluded in this comparison, since the limitation in the z-direction for the AFM scanner made it difficult to scan the rougher parts of the blasted samples. The magnitude of the surfaces is a parameter not often considered in fractal analysis. It is shown that the magnitude, for the Fourier method, is correlated to the arithmetic average difference, R_a, but only weakly to the fractal dimension. Hence, traditional parameters, such as R_a, tell us very little about the spatial distribution of the elevation data. Received: 22 December 1999 / Accepted: 9 October 2000 / Published online: 9 February 2001