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。     

Correlation and fractal properties of speckles in the extremely deep Fresnel diffraction region

Based on the Kirchhoff approximation and the theoretical analysis of the random light fields,the speckle intensity distributions in the extremely deep Fresnel diffraction region are simulated.The fractal property of the speckles as well as the relation between the speckle intensity distribution and the corresponding random surface is investigated.We design a microscope system to detect experimentally the speckles in the extremely deep Fresnel diffraction region,and the experimental results prove the conclusions drawn from our simulations.     

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.     

Small angle neutron scattering study of pore microstructure in ceria compacts

Ceria powders were prepared by gel combustion process using cerium nitrate and hitherto unexplored amino acids such as aspartic acid, arginine and valine as fuels. The powders have been characterized by X-ray and laser diffraction. Cold pressed compacts of these powders have been sintered at 1250°C for 2 h. Internal pore microstructure of the sintered compacts has been investigated by small angle neutron scattering (SANS) over a scattering wave vector q range of 0.003–0.17 nm⁻¹. The SANS profiles indicate surface fractal morphology of the pore space with fractal dimensionality lying between 2.70 and 2.76.      

互补Sierpinski地毯光栅夫琅和费衍射现象的研究

利用菲涅耳 基尔霍夫光栅衍射原理和傅里叶分析方法，对具有分形结构互补Sierpinski地毯光栅的夫琅和费衍射现象进行了探讨。导出了观察平面上的频谱函数、振幅函数以及光强函数。运用MATLAB软件对该光栅的衍射现象进行了仿真，并绘制出其幅 频特性曲线。结果表明，在各阶光栅的衍射图样中，幅度较大的部分主要集中在接收屏的中心区域，而在偏离中心的区域内，幅度值较小，在较远区域幅度值趋近于零，这说明获得的衍射图样不仅具有衍射光的基本特性，而且都呈现出明显的分形特征。     

分形多孔介质中的热传导

本文将多孔介质视为由骨架和空隙组成的二元混合介质,研究了多孔介质中的热传导过程,发现分形结构中的导热规律与孔隙的分布有关,存在着与实体导热完全不同的特征。计算表明,分形介质中的导热过程除了与基质(骨架)的分形维数有关外,还与基质率以及反映介质中热量传递动态过程有关。     

关于康托集类光栅的实验探究

设计制作了康托集分形衍射光栅,通过对康托集分形光栅3个阶段的夫琅禾费衍射现象的观察,根据惠更斯-菲涅耳原理,得到了一维康托集分形光栅的夫琅禾费衍射光强分布特性.     

粗糙表面形貌对湿润性的影响

采用自仿射分形对粗糙表面形貌进行了定量描述。基于分形粗糙表面形貌,建立了粗糙表面润湿性的理论模型并进行了数值计算,分析讨论了均方根粗糙度和表面分形维数对接触角的影响。研究结果表明,均方根粗糙度对接触角的影响较大,而粗糙表面的分形维数对润湿性的影响则并不明显。     

分形粗糙面合成孔径雷达成像研究

研究了分形粗糙面的成像问题. 分形粗糙面能够较好的逼近真实环境, 采用带限形式的Weierstrass-Mandelbrot函数建立了分形粗糙面几何模型, 对分形粗糙面参数的选取进行了讨论. 对大尺度粗糙面散射问题提出了一种基于大面元的Kirchhoff近似方法, 采用面元模型来计算粗糙面总的后向散射场以及每一个面元的后向散射场, 并对面元的尺寸选取进行了研究, 通过与解析解进行对比证明了该方法的正确性. 在分形理论建立的确定性粗糙面几何模型与面元的Kirchhoff方法获取的散射场的基础上, 采用正侧视条带式成像模式, 并选用距离多普勒算法对不同分形参数的粗糙面进行合成孔径雷达(SAR) 成像模拟, 结果显示从SAR像中可以清晰地观察到不同分形参数对粗糙面几何轮廓的影响. 该研究包括了从环境模型、电磁模型到SAR成像技术在内的完整的分形环境SAR像模拟过程, 仿真结果显示出分形环境的SAR像特点, 这对基于分形理论的自然环境的遥感探测以及参数反演具有一定的理论支撑作用.     

多相燃烧分形模型及其实验研究

本文提出了多相燃烧的分形模型．模型中认为在多相燃烧中内部孔洞体积与表面积存在分维指数关系，而且反应面积的增长为两种分形增长模式的叠加．结合孔洞合并的因素得到了描述煤多相反应速率的分形模型．该模型描述的反应速率先增加后减少的规律与实验结果十分相符．对五个煤种和其中两个煤焦样品进行了试验研究，在两个不同升温速率下得出的试验数据与理论计算相符．     

Polaron effects in cylindrical GaAs/Al_xGa_(1-x)As core-shell nanowires

By the fractal dimension method, the polaron properties in cylindrical GaAs/Al_xGa_(1-x)As core-shell nanowire are explored. In this study, the polaron effects in GaAs/Al_xGa_(1-x)As core-shell nanowire at different values of shell width and aluminum concentration are discussed. The polaron binding energy, polaron mass shift and fractal dimension parameter are numerically worked out each as a function of core radius. The calculation results show that the binding energy and mass shift of the polaron first increase and then decrease as the core radius increases, forming their corresponding maximum values for different aluminum concentrations at a given shell width. Polaron problems in the cylindrical GaAs/Al_xGa_(1-x)As core-shell nanowire are solved simply by using the fractal dimension method to avoid complex and lengthy calculations.     

Polarimetric scattering from a two-dimensional improved sea fractal surface

This paper studies the influence of wind parameters and fractal dimension from an improved two-dimensional sea fractal surface on the polarimetric scattering by using facet integration.A two-dimensional improved sea surface simulated is discretized into three matrices of sea surface facets including a height matrix and two slope matrices on orthogonal directions.Based on the Kirchhoff approximation,the polarimetric scattered field is derived in the Cartesian coordinate system by integration of three matrices mentioned above.Finally,the fully polarised radar cross section is numerically simulated and the dependence of the polarimetric scattering on the sea fractal surface,such as the wind speed,the wind direction,as well as the fractal dimension,is discussed in detail.     

The autocorrelation of speckles in deep Fresnel diffraction region and characterizations of random self-affine fractal surfaces

This paper studies the correlation properties of the speckles in the deep Fresnel diffraction region produced by the scattering of rough self-affine fractal surfaces. The autocorrelation function of the speckle intensities is formulated by the combination of the light scattering theory of Kirchhoff approximation and the principles of speckle statistics. We propose a method for extracting the three surface parameters, i.e. the roughness w, the lateral correlation length ξ and the roughness exponent α, from the autocorrelation functions of speckles. This method is verified by simulating the speckle intensities and calculating the speckle autocorrelation function. We also find the phenomenon that for rough surfaces with α= 1, the structure of the speckles resembles that of the surface heights, which results from the effect of the peak and the valley parts of the surface, acting as micro-lenses converging and diverging the light waves.     

Surface influence on the behavior of stabilized zirconia nanoparticles under pressure

The surface state of partially stabilized zirconia with nanoparticles of sizes 10–30 nm after temperature and pressure treatments was investigated by Fourier transform infrared spectroscopy, X-ray diffraction and small-angle X-ray scattering. It is shown that the synthesized nanoparticles are surface fractals and the fractal dimensions non-monotonically change with nanoparticles size change. The martensite tetragonal-to-monoclinic transition of the partially stabilized zirconia nanoparticles under hydrostatic pressure (100–1000 MPa) was investigated. It was shown that the character of the martensite transition in nanoparticles’ system depends on the pressure values. Three ranges of pressures were revealed. It was shown that the stability of martensite tetragonal–monoclinic transition decreases with the increase in size of the nanoparticles only for the pressures range of 300–500 MPa. Below 200 MPa, the character of the martensite transition is extreme and has a maximum for the particle size of 17 nm. In pressure range of 600–1000 MPa, the degree of martensite transition is dependent on the fractal dimension of the surface.     

规则表面形貌的分形和多重分形描述

以6种具有典型特征的生成元构造了6个具有相同rms粗糙度的规则表面,用变分法计算了这些表面的分形维数,结果表明,分形维数可以将具有相同rms粗糙度的表面区分开来,它定量表征了表面的总体形貌。进一步将多重分形的方法应用到对这些表面的分析中,发现多重分形谱可以全面反映表面概率的分布特征。多重分形谱的宽度可以定量表征表面的起伏程度,多重分形谱最大、最小概率子集维数的差别可以统计表面最大、最小概率处的数目比例。 关键词： 粗糙度 分形维数 多重分形谱     

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.     

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。     

具有二维fBm特征的分层介质粗糙面电磁散射的特性研究

运用微扰法研究了平面波入射分层介质粗糙面的电磁散射,推出了不同极化状态下的双站散射系数公式.采用二维fBm分形粗糙面来模拟实际的分层介质粗糙面,结合二维fBm分形粗糙面的功率谱导出了平面波入射二维fBm分形分层介质粗糙面的散射系数计算公式.通过数值计算得到了HH极化下双站散射系数随散射角的变化曲线,讨论了分维、底层介质介电常数、中间介质介电常数和厚度及入射波频率对双站散射系数的影响,得到了二维fBm分形分层介质粗糙面散射系数的分维特征、基本特征、分区特征和随频率变化的特征. 关键词： 电磁散射 二维fBm分形粗糙面 分层介质 微扰法     

分形基底上受限固-固模型动力学性质的数值模拟研究

为了探讨非完整基底结构对生长表面动力学行为的影响,本文在具有相同分形维数而不同谱维数的谢尔宾斯基箭头和蟹状分形基底上对受限固-固(restricted solid-on-solid,RSOS)模型的生长过程进行了大量的数值模拟研究.通过计算表面宽度和饱和表面极值高度的统计行为对生长表面的动力学行为进行了分析.结果表明,分形基底结构对生长表面的动力学行为具有显著的影响.尽管在两种基底上受限固-固模型的表面宽度均表现出很好的动力学标度行为,仍然满足Family-Vicsek标度规律,但由此计算得到的动力学标度指数并不相同.饱和生长表面的极值高度并不能满足三种常用的极值统计分布,即Weibull,Gumbel和Frechet分布,而是能很好地符合Asym2Sig分布.