Relationship of energy to geometry in brittle fracture

Numerous investigators have noticed that there is a relationship between the energy of branching and the energy of initiation during a fracture event in materials that fail in a brittle manner. Usually, this is measured in terms of the stress intensities, i.e., K_B/K_c. The ratio has been reported between 3 and 4, implying a constant value. However, data suggests that it is a constant for a material, but not a universal constant. The fractal dimension of the fracture surface is related to the critical stress intensity factor. It is a measure of the tortuosity of the fracture surface. We show that the K_B/K_C ratio is directly related to the square root of the fractal dimensional increment, indicating a relationship between the energy of crack propagation and the tortuosity of the fracture surface.     

Bubble size fractal dimension,gas holdup,and mass transfer in a bubble column with dual internals

As the scale of residual oil treatment increases and cleaner production improves in China, slurry bubble column reactors face many challenges and opportunities for residual oil hydrogenation technology. The internals development is critical to adapt the long-term stable operation. In this paper, the volumetric mass transfer coefficient, gas holdup and bubble size in a gas–liquid up-flow column are studied with two kinds of internals. The gas holdup and volumetric mass transfer coefficient increase by 120% and 42% when the fractal dimension of bubbles increases from 0.56 to 2.56, respectively. The enhanced mass transfer processing may improve the coke suppression ability in the slurry reactor for residual oil treatment. The results can be useful for the exploration of reacting conditions, scale-up strategies, and oil adaptability. This work is valuable for the design of reactor systems and technological processes.     

储层岩石孔隙结构的分形研究

储层岩石的孔隙空间具有良好的分形特征，孔隙结构的分形维数可以定量描述孔隙结构的复杂程度和非均质性。应用分形几何的原理，对低渗透储层岩石的孔隙结构进行了研究。建立了毛管压力和孔隙大小概率密度分布的分形几何模型。并根据毛管压力曲线资料计算了孔隙结构的分形维数和孔径大小概率密度分布。计算结果表明，用该方法研究孔隙结构不仅简单易行，而且精度很高。     

岩石断裂演化过程元胞自动机模型的研究

提出了一种研究岩石断裂演化过程的元胞自动机模型。通过大量模拟发现，岩石断裂演化过程是岩石内部微裂隙萌生、扩展、聚集和贯通的的过程，大量微裂隙的集体行为具有特定的规律。在岩石断裂演化过程中，微裂隙的空间分布是一个分级维形态的生长过程，岩石内完整岩石微元的空间分布是一个降维过程。岩石断裂隙化过程是一个确定性和随机性统一的过程，其中的分形物理机制是研究的关键。     

细骨料混凝土细观断裂试验研究

用带扫描电镜的电液伺服试验系统对细骨料混凝土进行了断裂试验，拍摄到了不同荷栽水平下裂纹扩展过程的SEM图像。对应于荷载水平，对这些断裂过程的细观图片进行了系统的分析，表明裂纹扩展路径具有明显分形性质。此外，从理论上分析得出断裂路径的分维数D与传统方法计算的断裂能GF之间存在着InGF∝D的关系，这一结论与试验结果吻合较好。     

煤粉碎粒度分布的分形模型

从自相似分形几何原理出发,建立了煤粉碎粒度分布的分形模型,得到了煤粉碎的分形粒度分布公式。结果表明:煤粉碎的粒度分布维数取决于煤粒的粉碎概率和粉碎相似比,影响煤粉碎粒度分布的因素有煤粉碎的粒度分布维数和煤粉碎后煤粒的最大粒径,煤粉碎的粒度分布维数反映了煤粉碎后煤粉颗粒群粒级的粗细程度。通过分形粒度分布与实际粒度分布的比较,验证了本模型的正确性,可用于指导工程实际。     

富钴结壳截割粒度分布分形规律的研究

应用分形理论研究螺旋切削采集法截割富钴结壳粒度分布规律，结果表明，其粒度分布具有很好的分形结构，可以用分形维数定量描述。通过大量试验，初步测定截割破碎富钴结壳及其模拟料粒度分布的分形维数在2．4236～2．6112之间，提出了切削深度与粒度分布关系的回归模型，用于预测截割破碎富钴结壳的情况，对于深海采矿系统的设计具有重要意义。     

破碎岩石物理力学性质的分形度量

本文论述了破碎岩石块度分布分形维数与其物理力学性质的关系，为破碎岩石物理力学性质研究开辟了一条新的途径。     

Coagulation dynamics of fractal flocs induced by enmeshment and electrostatic patch mechanisms

The size and structure of flocs during floc formation were monitored for various coagulation mechanisms. Two distinctive mechanisms, namely, enmeshment and electrostatic patch, govern the dynamics of kaolin particles coagulation by polyaluminum chloride (PACl). They were investigated by small angle static light scattering (SASLS) and solid-state ²⁷Al NMR. In addition, a novel wet SEM (WSEM) was used in-situ to image the morphology of the aggregate in aqueous solution. Synthetic suspended particles were coagulated by two PACl products, a commercial product (PACl) and one laboratory product (PACl-E). The PACl-E contained more than 60% Al₁₃ while the PACl contained only 7% Al₁₃, with large percentage of colloidal Al. For coagulation by PACl at neutral pH and high dosage where the strong repulsion between particles occurs, the enmeshment ruled by reaction-limited aggregation (RLA) results in larger sweep flocs as well as higher fractal dimensional structure. For coagulation by PACl-E at alkaline pH and low dosage, the flocs were coagulated predominately by electrostatic patch with Al₁₃ aggregates. At such condition, it is likely that diffusion-limited aggregation (DLA) predominately rule PACl-E coagulation. The fractal dimension (D_s) values of PACl and PACl-E flocs formed at enmeshment and electrostatic patch increased with dosage, respectively. When breakage of flocs occurs, the breakage rate of PACl-E flocs is slower than that of sweep flocs. By WSEM imaging, the adsorption of spherical Al precipitates onto the particles was observed to form sweep flocs with a rough and ragged contour, while the PACl-E flocs were formed with a smooth and glossy structure.     

城市分形与城市建筑策划

从分形角度研究城市，得出传统城市的精髓，并将之应用到未来的城市建筑策划。