分形几何对称模型数值分析非稳态热传导——以第一类边界条件为基础

分形几何对称模型已成功地用于单颗粒化学反应工程领域的计算机辅助数值模拟计算,本文讨论了分形几何对称模型在非稳态热传导中的应用,用配点残差法求解非稳态热传导中的分形几何对称模型。     

闭孔泡沫陶瓷气孔微结构的分形表征及其模拟

通过观察发现,闭孔泡沫陶瓷气孔几何结构不是一个整形结构,而是具有分形特征的分形结构。采用分形几何对其气孔结构进行描述,首次获得了闭孔泡沫陶瓷分维表达式D=lnN/lnK。讨论了分维D的大小与闭孔泡沫陶瓷气孔微结构之间关系,并用计算机模拟出闭孔泡沫陶瓷的分形结构。     

硫化物催化剂结构性质与合成甲醇反应性能的关联(Ⅱ)──表面形貌的分形几何特征

应用分形几何理论研究了硫化物催化剂的表面性质及其与合成甲醇反应性能的关系．由分形维数定量地表征了催化剂表面形貌的几何特征．提出了催化剂表面分形维数具有特定的分布,并用正态分布函数进行了拟合．考察了助催化剂和载体对催化剂表面分形维数的影响,由此探讨了分形维数与催化剂结构和反应性能的关系．对甲醇的时空收率和分形维数进行了关联．     

硫化物催化剂结构性质与合成甲醇反应性能的关联(Ⅱ)──表面形貌的分形几何特征

应用分形几何理论研究了硫化物催化剂的表面性质及其与合成甲醇反应性能的关系．由分形维数定量地表征了催化剂表面形貌的几何特征．提出了催化剂表面分形维数具有特定的分布,并用正态分布函数进行了拟合．考察了助催化剂和载体对催化剂表面分形维数的影响,由此探讨了分形维数与催化剂结构和反应性能的关系．对甲醇的时空收率和分形维数进行了关联．     

氧化铝上吸附平衡与动力学的分形特性

在实验测定氧化铝吸附氮气的平衡和动力学过程的基础上 ,由平衡数据得到分形维数 ,对动力学结果分别用欧氏几何和分形几何的动力学模型进行处理 ,比较两种方法得到的扩散系数之间的差别。结果表明 :粉状氧化铝的分形维数为 2 .12 ;采用分形动力学模型得到的扩散系数同欧氏几何扩散模型的结果不一样 ,扩散系数不随浓度的变化而改变 ;而欧氏几何扩散模型中的扩散系数随浓度变化发生改变 ,且变化符合Darken关系     

非均相化学反应的类分形动力学

大多数非均相反应的动力学不遵从经典的动力学规律。随着分形几何理论在表面科学中的应用和发展 ,非均相反应的类分形动力学研究取得了可喜的成果。综述了分形表面上反应的动力学特征及非均相反应的类分形动力学的研究进展。     

分形几何在研究层状岩体断裂滑落中的应用

应用分形几何研究了层状岩体断裂滑落的分形几何特征，并建立了层状岩体断裂滑落的分形模型。研究结果表明，分形维数值的大小与岩体层理面、节理面的分布及其力学特性密切相关，且最低的分形维数通常出现在层状岩体即将发生滑落之处，故可用分形维数的变化预报层状岩体的滑落。此外，还结合块体理论解析法实例，分析了巷道周围层状岩体的断裂滑落，其结果与分维理论分析结果一致，为进一步研究地下开采引起的采场围岩移动，乃至地表沉陷等问题开辟了一条新的途径。     

分形艺术在陶瓷工艺品上的应用

对分形艺术进行了讨论，展示了几种经典的分形图案，并通过将这些图案应用到碗、花瓶、花壶三种传统的陶瓷工艺品上的实例，揭示了分形几何和分形艺术在陶瓷界应用的巨大潜力。     

分形几何在储层微观非均质性研究中的运用

储层岩石的孔隙结构是一种明显的分形结构,具有典型的微观非均性物质特点,以储层岩石的孔隙结构作为研究对象,介绍了分形几何在储层微观非均性中的运用原理与运用方法,并通过实例进行具体分析,希望能为分形几何在储层微观非均质性研究中的运用的未来发展提供一定的帮助。     

分形吸附理论及其对粘土性质的表征方法

粘土被广泛地应用于环境污染物的吸附处理。概述了分形几何的基础及其对粘土吸附和性质表征的方法。归纳了常见的分形吸附模型以及分维数测定方法。     

离心毛管压力曲线分形特征研究

根据分形理论,对某油田区块的离心毛管压力曲线进行分形研究及分形维数的计算结果表明,离心毛管压力曲线具有很好的整体分形特征,比较驱替毛管压力曲线和吸入毛管压力曲线的分维值,发现两者相差很小,具有很好的一致性,说明它们都能较好的描述该区块的孔隙特征;另外,对驱替毛管压力曲线进行分段线性回归后发现,分段分形线性回归相关性好于整体分形,但整体分形更能反映储层岩心的孔隙结构特征。计算的驱替毛管压力分维值和岩样的渗透率有较好的对数关系,和孔隙度具有一定的线性相关性。     

Modeling of three-dimensional groundwater flow using the method to calculate fractal dimension

A three-dimensional finite-difference groundwater flow model was developed by the use of fractal theory. The model developed in this study can simulate the groundwater flow in fractured aquifers as well as in porous aquifers. The model was designed to be able to use other parameters, such as permeability, hydraulic conductivity, porosity and fractal dimension besides hydraulic parameters which are used in MODELOW. Methods which can calculate box fractal dimension used in the Baecher model and mass dimension used in Levy-Lee Fractal model were developed. The results of the model and MODFLOW agreed exactly in the case of the fractal dimension of 2.0 without regard to the use of a fractal equation. The fact that the drawdown along the distance from the well increases by increasing the fractal dimension shows the effect of fracture on groundwater flow.     

用分形理论研究低渗储层孔隙结构

储集层岩石的孔隙结构非均质性对于油气的渗流规律以及水驱油效率都具有重要的影响。利用分形理论对孔隙结构的非均质性进行研究。结果表明,分形维数不同孔隙结构不同,所研究的储集层具有单一分形（分形维数2.690 7～2.814 0）和分段分形特征（分形维数2.414 8～2.995 2）;以分形维数为基础,可以根据孔喉渗透率贡献判断孔隙结构的非均质性和复杂程度。     

Comparison of fractal properties of porous structures during coal devolatilization

This paper investigates fractal property changes of pore structures during coal devolatilization. Similar to char pores, coal pores can also be classified as micro pores and macro pores based on their fractal dimensions. The specific surface area and fractal dimension of micro pores in coal particles are basically unchanged after devolatilization. However, the specific surface area and fractal dimension of macro pores, which are key factors in char combustion, are increased after devolatilization. In fact, the fractal dimensions are basically doubled. These parameters will affect another fractal geometrical factor β in char pores that is correlated to char combustion rate. Since the rate of char combustion can be predicted from their fractal pore properties, it may be possible to predict char combustion directly from the properties of their parent coal pores in the future. This work was presented at the 6 ^th Korea-China Workshop on Clean Energy Technology held at Busan, Korea, July 4–7, 2006.     

Modeling changes of fractal pore structures in coal pyrolysis

Coal pyrolysis processes are numerically investigated in mathematically produced coal pore models which simulate real coal pores in the parameters of the porosity and fractal dimension. The simulations include FG-DVC chemical reaction model, gas molecular diffusion in pores, energy conservation model and coal swelling model. Numerical results are verified by experimental results qualitatively, and they revealed that both the porosity and volatile contents of the parent coal can affect the fractal dimension of the final char pores after pyrolysis linearly. A formula to predict the fractal dimension of char pores from its parent coal properties is obtained by curve fitting in numerous results.     

香气的分维

本文用分形数学理论解释调香行为,计算了香精主题香气奇怪吸引子的分维,总结出“分维越接近1,香精的主题香气就越突出”的结论。通过一系列的计算确认配制香精时用较多种相关香料的有利之处。文中也讨论了香料中“杂气”对主题香气的影响。     

The use of fractal analysis in the textural characterization of coals

The materials studied were four bituminous coals as well as the corresponding coal samples oxidized in air at 543 K for different periods of time. The method proposed by Friesen and Mikula, the procedure of Neimark and the methodology of Zhang and Li were successfully employed to analyze mercury porosimetry data from a fractal perspective. Fractal dimensions as well as fractal profiles are sensitive to oxidation treatment, being useful to follow the changes undergone by the coal samples. The evolution of the fractal dimension of coals with oxidation is determined by a balance between two main mechanisms of pore development: the oxidation of the pore surface itself that tends to lower the fractal dimension and the access of mercury to previously non-accessible regions that tends to increase this dimension.     

分形理论在耐火材料生产中的应用

介绍了分形理论在耐火材料生产过程中的应用 ,提出 :(1)在耐火材料破粉碎工序之前加一个冷却处理工序 ,应用分形理论研究矿石碎裂机制 ,可提高耐火原材料尤其是硬质耐火原料的破粉碎效率 ;(2 )研究粉体颗粒的分形结构 ,既可以预测超微粉体的流动性 ,也可以预测粉体在压制过程中的充填状况 ,从而改良粉体的制备、存储、输送和运输等过程 ;(3)建立受压状态下矿石的分形裂纹结构、矿石构造特征以及施加给矿石的应力应变方式这三者之间的联系 ,对完善磨矿工序中的前馈质量控制有帮助 ;(4 )确定分形级配的颗粒配比 ,将有利于提高材料的性能 ;(5 )在耐火材料中添加分形结构的弥散粒子或纤维 ,能有效提高耐火材料的强度和韧性 ;(6 )加强吸入粉尘分形结构研究 ,防治耐火材料行业的职业病。     

Direct image-based fractal characterization of micromorphology of calcium carbonate fouling crystals

Researches on macroscopic fouling behavior and micromorphology are usually conducted separately. In this paper, the relationship between the macroscopic fouling behavior and micromorphology on different materials is established. A direct fractal-characterization approach based on the micrographs of calcium carbonate fouling crystals is presented. The box-counting method is used to characterize the fouling crystals. For fractal measurements, t-distribution tests of linear regression hypothesis are performed at the significance level of 0.01. If all listed absolute t-statistics with the minimum of 164 are higher than the corresponding t value, the fouling crystals are determined as fractal, with a confidence level of 99%. The fractal dimensions obtained from the micrographs of different visual fields of a specimen are demonstrated to be almost identical, with maximum and minimum relative values of 4.42% and 0.75%, respectively, and standard deviations ranging from 0.0062 to 0.0266. The irregularity of the crystal morphology indicates larger fractal dimensions. Comparison and analysis of the relationship between macroscopic fouling behavior and micromorphology show that the larger fractal dimension of crystal morphology suggests a small amount of surface fouling. Thus, the reasons for the differences in the macroscopic fouling behaviors of different materials are revealed geometrically.