多孔颗粒材料内孔表面分维测算及与保水性能的关系

为考察多孔颗粒材料内孔表面分形特征及与其保水性能的关系,构建了多孔颗粒物内孔表面分维测算数学模型,并基于高精度扫描电子显微镜系统测算了4种多孔颗粒样品的内孔表面分维,测量了材料保水性能。结果表明:多孔颗粒的内孔表面的分维值介于2.088 2~2.193 5之间,且分形拟合曲线相关系数大于0.98,强的相关性说明内孔表面具有显著的分形特征。进一步研究发现,多孔颗粒材料保水性能与其内孔表面分维呈负相关。     

用投影轮廓分维中位维表征颗粒群粗糙度的研究

为了表征颗粒群粗糙度,本文中构建了单颗粒投影轮廓分维数学模型,并以高精度数字光学显微系统为基础,测算了5种颗粒样品的单颗粒投影轮廓分维。结果表明,5种颗粒样品的单颗粒投影轮廓分维均值从小到大依次为:柴油汽车排气管沉积颗粒、碳黑颗粒、粉煤灰颗粒、石灰性褐土颗粒、河流沉积土壤颗粒。首次提出了"中位维"的概念以表征颗粒群粗糙度,计算了颗粒样品的中位维,其大小排序与投影轮廓分维均值一致,验证了将"中位维"作为表征颗粒群粗糙度的合理性。     

水泥粉体粒度分布分维与其流动性的关系研究

为研究水泥粉体粒度分布分维与流动性的相关性,本文中将粒度分布分维作为表征水泥粉体的粒度分布特征,用图像分析法测算了5种水泥颗粒样品的粒度分布分维,5种水泥样品粒度分布分维值处于2.1006～2.2931之间;并用卡尔指数法测量了水泥样品的流动系数,考察了水泥粉体粒度分布分维及其与粉体流动性的关系,研究表明:水泥粉体粒度分布分维与其流动性呈线性负相关性。     

粉碎能耗与粒度分布指数的相关性

利用分形和分维数基本概念,导出粉粒度分布的分维数和分裂比、粉碎概率互相存在的简单关系,从能耗与颗粒表面分维数相关出发,推出单位体积粉碎能耗与粒度分布的值指数的相关性;同时推出单位体积粉碎能耗的分维数.当粉碎粒度分布的分维数近似小于0.89时,粉碎能耗呈现自然分形的特征.     

PP/纳米碳酸钙复合材料冲击强度与断口表面分维关系的研究

应用脂肪酸、钛酸酯偶联剂分别对纳米级碳酸钙(Nano-CaCO3)进行表面处理,并用熔融共混法制备PP/Nano-CaCO3复合材料.在室温条件下,测量PP/Nano-CaCO3复合材料的V型缺口冲击强度.采用投影覆盖法测算复合材料的冲击断口表面分维,考察断口表面分维与复合材料冲击强度的关系.结果表明,断口表面分维在2.3673～2.4120之间,相关系数均大于0.95,强的相关性说明断口表面分形特性显著;复合体系冲击强度与断口表面分维之间近似呈指数函数关系.     

大气降尘轮廓投影分形与来源辨识

选取燃煤锅炉、道路扬尘、汽车燃油不完全燃烧产生的颗粒、土壤颗粒等4种颗粒,利用数字显微和图像处理技术,求取降尘颗粒轮廓投影曲线的分形维数,并根据实际采样情况,求取降尘部分源颗粒的轮廓投影曲线分形维数,根据分形维数间的关系对比分析后判断降尘颗粒的来源。结果表明:将大气降尘轮廓投影曲线分形维数值作为降尘颗粒来源的辨析参数是可行的,将轮廓投影曲线的分形维数值和投影轮廓的其他几何特征参数相互结合可以得到很好的判断结果。     

准分子激光加工表面微观形貌的分维表征研究

准分子激光加工表面的分形特征的研究未见有报道，文章论述了准分子激光加工的表面可以是分形表面，计算了准分子激光加工某些陶瓷表面轮廓的分维D，并把表面分维Ds与Da值和均方根σ值进行了对照，指出了它们之间的对应关系由它们各自的定义所决定。     

亚微米级扁椭球颗粒群的散射特性

采用T矩阵方法计算亚微米级扁椭球随机取向分布颗粒群的散射特性,研究消光截面、散射截面、吸光截面、单散射反照率、非对称因子以及散射矩阵元素与颗粒的大小、折射率、长短轴比之间的关系。结果表明,随颗粒粒径增大,消光截面、散射截面、吸光截面、非对称因子都单调增加,散射相函数F11的角分布曲线特征可以区分颗粒的大小;颗粒越偏离球形,颗粒对入射光的衰减效率越低,后向散射光强越强,在轴比不大时,前向50°内的F22/F11值可以区分颗粒的形状;折射率变化主要是对后向散射光的分布产生影响,实部、虚部的变化可分别通过F34/F11的角分布曲线、F12/F11的第一个峰值来体现。     

F1离子固化剂加固试验黄土机理及强度特性研究

为研究F1离子固化剂对黄土的加固效果和固化机理,利用不同掺量的F1离子固化剂加固试验黄土.从黏土颗粒表面化学入手,利用CBR试验、三轴压缩试验、SEM电镜扫描以及IPP6.0比表面/微孔隙分析软件,对F1离子固化剂加固试验黄土的CBR值、膨胀特性、强度参数和固化前后土体微观结构的变化规律进行了研究.结果表明:F1固化剂可减小土颗粒表面结合水膜的厚度,使土颗粒间的距离(或体积)减小、引力增大,在碾压时形成排列更加紧密、团聚体更大的层状堆叠结构,使得土体的孔隙面积百分比和形态分布分维数减小,土颗粒间的黏结强度、剪切强度、密实度和稳定性增强;在试验黄土中加入0.3 L/m3(最佳掺入比)的F1溶液后,其摩擦角和黏聚力分别增大了1.17倍和1.55倍;F1固化剂通过离子交换作用占据了黏土颗粒表面的阴离子点位,阻碍了其对水分子的吸附,大幅减小了黏土颗粒的膨胀变形;F1固化剂具有绿色环保、加固效果良好等优点,在黄土地区土体填筑工程中有广阔的应用前景.     

共聚物稳定Al2O3悬浮液及沉积物分形特性的研究

采用ζ电位和沉降实验研究了丙烯酸-丙烯酸酯共聚物对Al2O3表面特性及其悬浮液稳定性的影响.发现共聚物的加入使其等电点向低pH方向移动,且可显著改善浆料的稳定性,共聚物最佳用量为2wt%.研究表明:沉积物表面形貌具有分形特征,且形貌分维值Df的大小与分散剂用量有一定关系.     

Fractal Characteristics and Prediction of Ti-15-3 Alloy Recrystallized Microstructure

Grain shape of the hot deforming alloy is an important of material. The fractal theory was applied to analyze index to character the microstructure and performance the recrystallized microstructure of Ti-15-3 alloy after hot deformation and solution treatment. The fractal dimensions of recrystallized grains were calculated by slit island method. The influence of processing parameters on fractal dimension and grain size was studied, It has been shown that the shapes of recrystallized grain boundaries are self-similar, and the fractal dimension varies from 1 to 2. With increasing deformation degree and strain rate or decreasing deformation temperature, the fractal dimension of grain boundaries increased and the grain size decreased. So the fractal dimension could characterize the grain shape and size. A neural network model was trained to predict the fractal dimension of recrystallized microstructure and the result is in excellent agreement with the experimental data.     

花岗石抛光表面的粗糙度、分形维数及其关系研究

对两种典型的不同晶粒度的花岗石抛光表面的分形特性和粗糙度特性进行了研究，分析了花岗石抛光表面的分形维数、粗糙度与金刚石磨盘目数的关系，同时也对组成花岗石的重要成分的分形特性及粗糙度做了分析。研究了花岗石抛光表面粗糙度与分形维数的相互关系，并对两者作为花岗石表面质量评价指标的适用性进行了讨论。     

水泥砂浆断面形貌像素点法与投影法分形的计算对比研究

为对比分析像素点覆盖法和投影覆盖法计算水泥砂浆断口分形维数的优缺点,采用这2种方法分别计算水泥砂浆在3种不同养护龄期下的断面分形维数,探索分形维数与抗压强度之间的关系。结果表明,像素点覆盖法计算得到的断口分形维数为2.258 0～2.265 6,相关系数为0.988 6～0.989 3,计算精确度高,数值变化区间小;投影覆盖法计算得到的断口分形维数为2.856 0～2.918 9,相关系数为0.921 4～0.935 2,计算精度较差,但数值变化区间大,有利于实际应用,与抗压强度呈良好相关性。     

整体式载体的分形研究

整体式Al2O3载体结构实测结果表明,虽然不同组分、不同条件下形成的块体具有不同的结构,但孔隙尺寸均满足分形标度律,是一种分形.本文构造了整体式载体分形体,提出了整体式载体的一种分形模型--蜂窝分形体,导出了关联表面积和体积增量的分形表达式,并分析了表面分维数的几何意义.本文在测得载体孔径分布的基础上,利用该模型的表面积与体积增量分形表达式,从压汞法的实验数据,研究了整体式载体分维数:实验得到的比表面积、体积增量及样品制备条件、孔隙尺寸等性能与分维数的关系,与模型提出的结论符合得很好,此方法对优化制备条件与块状载体的性能有重要意义.     

Relationship between Fracture Toughness and Fractal Dimension of Fracture Surface of Steel

The relationship between fracture toughness and fractal dimension of fracture surface was analysed based on a united fractal model of microscopic fracture modes. It was indicated that fracture toughness is a multivariant function of yield strength, microstructural length, fractal dimension of fracture surface and volume fraction of inclusions, other than a monovariant function of fractal dimension of fracture surface. This new fractal model of fracture toughness was verified to fit well with a set of experimental data of a ultrahigh strength steel with equal microstructure and grain size but different volume fraction of inclusion.     

A possible method for retrieval of particle size distribution from its phase function in a fractal tissue model

In problems relating to light propagation in soft biomedical tissues, the tissue is generally modeled as a turbid medium. In one of the often used models, the suspended scatterers have been assumed to be of spherical shape following a fractal size distribution law. This paper studies the relationship between scattering phase function features of tissue and the fractal dimension within the framework of a fractal tissue model. It is demonstrated that witin the framework of this model the measurement of scattering phase function at two or three near-forward angles can be employed to infer fractal dimension of the model tissue. This method for tissue characterization therefore could be a potentially useful method for early detection of cancer of soft tissues.     

Stereological Models Simulation of BaTiO3 Ceramics Grains

The Stereological configuration of the position of BaTiO₃-grains and the influence of grain displacement of contact surfaces is studied in this paper. We add two important conjectures to the recent authors' result that the fractal dimension of the contours of BaTiO₃-ceramics grains is 1.0677699. The function that represents spacial distribution of the intergrains' contacts is not a totally random function but a function that contains an amount of order which makes the fractal dimension lower than D_s < 3. Next is the supported conjecture that the intergrain contact surface has a global shape of minimal surface, while the local shape is fractal which increases the size of the smooth surface and also increases the microcapacity generated at the contact. To simplify calculations, grain shape is approximated by polyhedron, sphere, ellipsoid and a real grain's shape, obtained by the SEM method. Relevant mathematical relations are established that give an approximate size of the intergrains contact area as the function of grains displacement inside the pattern used. The offered method consists of two components: 1) Fractal analysis, which gives the fractal dimension of the grain on the basis of microphotography, 2) Adding the fractal grains surface on Euclidean models—polyhedron, sphere, ellipsoid and the real grain's shape.