Fractal features of size distribution of Chinese intercity bus hubs

Size distribution characteristics of intercity bus hubs in China from 1997 to 2（104 were analyzed regarding highway passenger volume as a size index of intercity bus hubs. Yearly fractal dimensions of intercity bus hub sizes were exactly calculated by a novel model. Fractal dimensions of the 200 biggest intercity bus hubs from 2000 to 2004 were 1. 486 2 to 1. 511 8, and that is consistent with fractal dimensions of Chinese urban system sizes. It showed that the size distribution of intercity bus hubs had fractal structure. Fractal dimensions from 1997 to 2004 indicated that intercity bus hub size distribution grew from bi-fractal to single fractal. It is concluded that the intercity bus hub system is in evolutionary progress, and the Central Government should support large intercity bus hubs more to optimize system structure.

Sediment texture and grain-size implications: the Changjiang subaqueous delta

Sediment cores were collected from the subaqueous delta of the Changjiang Estuary. Sediment grain-size profiles and their fractal dimensions were analyzed, to elucidate responses to long-term sedimentary processes. In addition, the environmental sensitive populations of grain size have been extracted. The sediment cores can be divided into two parts, according to the sedimentary structures present. The upper part （0-12 cm） is interpreted as being the active layer, which is influenced frequently by changes in the short-term hydrodynamic environment. The lower part extends from a depth of 12 cm, to the bottom of the core. The pattern of fluctuation is linked to sediment grain size. Moreover, two grain-size sensitive populations can be identified. The fine sensitive population is 6.0-7.2 μm, which is a similar grain size to the suspended sediment from up-river. The coarse sensitive population varies from 40.7 to 57.5 μm, revealing complex changes. Thus, the riverine inputs from the Changjiang River may be an important source, which contributes to seasonal fluctuations of grain-size distribution, over the area. The sediments, with grain-sizes ranging from 0.9 to 20.3 μm, are characterised by self-similar in the fractal non-scale region. The fraetal dimension is eonsistant with the grain-size parameter varatioins, which could be used as a replacement index to reveal and reconstruct the sedimentary environmental evolution.

Fractal characteristics of cracks and fragments generated in unloading rockburst tests

True triaxial rockburst experiments with four different unloading rates were performed on four prism specimens of granite sampled from Beishan, China. The damage evolution in the rockburst test was investigated from two aspects including fracture surface crack and fragment characteristics. The scanning electron microscopy was used to observe the micro crack information on fragment surface. Combing binarization and box counting dimensions, the fractal dimensions of cracks were obtained. Meanwhile,the fragments were collected and a sieving experiment was conducted. We weighed the fragments qualities, counted the amount of fragments and measured the fragments length, width and thickness.Utilizing four methods to calculate damage fractal dimensions of fragments, the trend of fractal value changing with unloading rates can be roughly described. It can be concluded from these experiments that the fractal dimension either for crack or for fragment holds a decreasing trend with the decreasing unloading rate, indicating a reduction of damage level.

Influence of Acid Treatment on Pore Structure and Fractal Characterization of a Tight Sandstone:A Case Study from Wudun Sag,Dunhuang Basin

In this study,X-ray diffraction,N_(2)adsorption(N_(2)A),and mercury intrusion(MI)experiments were used to investigate the influence of acid treatment on pore structure and fractal characterization of tight sandstones.The results showed that acid treatment generated a certain number of ink-bottle pores in fine sandstone,aggravated the ink-bottle effect in the sandy mudstone,and transformed some smaller pores into larger ones.After the acid treatment,both the pore volume in the range of 2–11 nm and 0.271–8μm for the fine sandstone and the entire pore size range for the sandy mudstone significantly increased.The dissolution of sandstone cement causes the fine sandstone particles to fall off and fill the pores;the porosity increased at first but then decreased with acid treatment time.The fractal dimension obtained using the Frenkel-Halsey-Hill model was positively correlated with acid treatment time.However,the total fractal dimensions obtained by MI tests showed different changes with acid treatment time in fine sandstone and sandy mudstone.These results provide good guiding significance for reservoir acidification stimulation.

Effect of Fiber Properties on Nonwovens' Pore Structures with Fractal Geometry Analysis

Nonwovens＇ pore structures are very important to their mechanical and physical properties. And the pore structures are influenced by the fiber properties and fibers arrangement in web. In this paper, the fractal geometry, in combination with computer image anaysis, is used to express the irregularity of pore size distribution in nonwovens, and the effect of fiber properties on fractal dimension of pore size distribution is discussed by using simulated images which are composed of nonlinear staple fibers. The results show that the fiber properties, such as crimp, diameter, angular distribution, and especially the number of fibers prominently influence the pore structure.

Textural and Geochemical Characteristics of Proglacial Sediments: A Case Study in the Foreland of the Nelson Ice Cap, Antarctica

This paper presents a detailed study on the textural and geochemical characteristics of the proglacial sediments near the edge of modern Nelson Ice Cap, Antarctica. The grain size distributions of the proglacial sediments are characteristic of glacigenic deposits, but very different from those of aeolian and lacustrine sediments. Moreover, the grain size distributions of the proglacial sediments are fractal with a dimension of about 2.9, and the fractal dimensions can be used as another summary statistical parameter for quantifying the relative amounts of coarse and fine materials. Correlations between the absolute element abundances of the proglacial sediments are very weak due to mineral partitioning and other effects of glacial processes, but correlations between the element/Rb ratios are statistically significant. This finding indicates that element/Rb ratios can be used to reduce or eliminate the effects of glacial processes, evaluate geochemical data and determine the sediment provenance in the foreland of Antarctic glacier. Comparisons on the element concentrations among different environments suggest that the proglacial sediments are derived predominantly from local bedrocks and appear to be natural in origin. Thus these natural sediments can be used to study chemical weathering in the proglacial foreland of modern glacier.

Fractal Characteristics of Particle Size Distribution in Dynamic Flocculation Process

This study selected polyaluminum chloride（PAC） coagulant to remove suspended particles in Kaolin suspension solution and used a turbidimeter and particle counter to monitor the flocculation process online and collected the experiment data. The experiments were conducted to study the dynamic distribution characteristics of suspended particles under different hydrodynamic conditions. The results show the self-similarity and scale invariance of particle size distribution. The study further proposed the concept of fractal dimension of particle size distribution and found out that fractal dimension changed in a similar way as residual turbidity did and could excellently indicate the variation of coagulation effect. Therefore, fractal dimension could be adopted to optimize the addition of coagulants and the quality of outflow could be further improved to reduce production costs.

Interactions between wind and water erosion change sediment yield and particle distribution under simulated conditions

Wind and water erosion are among the most important causes of soil loss, and understanding their interactions is important for estimating soil quality and environmental impacts in regions where both types of erosion occur. We used a wind tunnel and simulated rainfall to study sediment yield, particle-size distribution and the fractal dimension of the sediment particles under wind and water erosion. The experiment was conducted with wind ero- sion firstly and water erosion thereafter, under three wind speeds （0, 11 and 14 m/s） and three rainfall intensities （60, 80 and 100 ram/h）. The results showed that the sediment yield was positively correlated with wind speed and rain- fall intensity （P〈0.01）. Wind erosion exacerbated water erosion and increased sediment yield by 7.25%-38.97% relative to the absence of wind erosion. Wind erosion changed the sediment particle distribution by influencing the micro-topography of the sloping land surface. The clay, silt and sand contents of eroded sediment were also posi- tively correlated with wind speed and rainfall intensity （P〈0.01）. Wind erosion increased clay and silt contents by 0.35%-19.60% and 5.80%-21.10%, respectively, and decreased sand content by 2.40%-8.33%, relative to the absence of wind erosion. The effect of wind erosion on sediment particles became weaker with increasing rainfall intensities, which was consistent with the variation in sediment yield. However, particle-size distribution was not closely correlated with sediment yield （P〉0.05）. The fractal dimension of the sediment particles was significantly different under different intensities of water erosion （P〈0.05）, but no significant difference was found under wind and water erosion. The findings reported in this study implicated that both water and wind erosion should be controlled to reduce their intensifying effects, and the controlling of wind erosion could significantly reduce water erosion in this wind-water erosion crisscross region.

STATISTICALLY FRACTAL STRENGTH THEORY FOR BRITTLE MATERIALS

Based on the hypothesis of the fractal distribution of crack sizes in brittle materials and the weakest link principle, the relationship between the fractal dimension of the size-frequency distribution of cracks and the Weibull Modulus is derived, which reveals the geometrical nature of the Weibull Modulus. The influences of the size distribution and the orientation distribution of cracks as well as the irregularity of the crack propagation on the strength are all taken into account. Finally, a general expression for the statistical strength of brittle materials in complex tensile stress state is obtained.

Collision Statistics of Driven Polydisperse Granular Gases

We present a dynamical model of two-dimensional polydisperse granular gases with fractal size distribution, in which the disks are subject to inelastic mutual collisions and driven by standard white noise. The inhomogeneity of the disk size distribution can be measured by a fractal dimension df. By Monte Carlo simulations, we have mainly investigated the effect of the inhomogeneity on the statistical properties of the system in the same inelasticity case. Some novel results are found that the average energy of the system decays exponentially with a tendency to achieve a stable asymptotic value, and the system finally reaches a nonequilibrium steady state after a long evolution time. Furthermore, the inhomogeneity has great influence on the steady-state statistical properties. With the increase of the fractal dimension df, the distributions of path lengths and free times between collisions deviate more obviously from expected theoretical forms for elastic spheres and have an overpopulation of short distances and time bins. The collision rate increases with df, but it is independent of time. Meanwhile, the velocity distribution deviates more strongly from the Gaussian one, but does not demonstrate any apparent universal behavior.

云南永胜古滑坡堰塞湖沉积物粒度多重分形特征及其指标适用研究

本文以云南永胜县下院滑坡堰塞湖沉积物为研究对象,依据粒度测试结果采用传统粒度指标与分形理论相结合的方式对其沉积环境进行系统化研究,探讨各传统指标在堰塞湖沉积解析中的适用性,探索多重分形理论在沉积学中的应用价值。研究结果表明:①堰塞湖沉积物粒度统计参数明显不同于其他环境下的沉积物,具有河湖相沉积独特的分布曲线形式、分选状态和分形特征。优势粒级在分形计算中起主导地位,全局分形维数与分选系数有着良好的对应关系。不同的分形维数对应着不同的堰塞湖沉积条件,分形维数在堰塞湖粒度解析中有着很好的运用前景;②多重分形结果显示2种不同时期的堰塞湖沉积物均以高聚集度组分为主体,表明粒径分布集中,反映出堰塞湖沉积过程中水动力的稳定性,沉积来源的唯一性,进一步证明了该堰塞湖曾长期存在。细粒组沉积粒径分布范围较窄,分布相对集中,优势粒组多但单个含量低,尾端含量低,内部分异较大;粗粒组分布呈局部集中整体分散的趋势,高聚集度粒组数量少但含量高,低聚集度粒组数量多但单个含量低,呈现中间高,四周低的特点。③多重分形分析表明Δα、Δf在沉积物粒度分析中能够解析粒组内部分布特征,具有传统指标不可替代的作用,D_(0)和D_(1)两者结合可作为沉积环境解析的替代指标,与其他q阶多重分形联合可进一步作为堰塞湖解析指标,而D_(1)/D_(0)和D2则存在一定局限。

正态分布矸石侧限压缩特征与声发射特征研究

为研究矸石集料的承载力学特征及声发射特征规律,通过采用岩石力学伺服加载系统和声发射系统对矸石集料进行侧限压缩试验和声发射信息采集,考虑采空区破碎矸石粒径分布特征和受力状态,以平均级配矸石集料为对比,研究正态分布矸石集料在不同轴向应力加载过程中的应力应变关系、声发射能量、粒径级配和分形维数的变化。结果表明:矸石集料应力应变曲线呈指数函数关系,正态分布矸石集料在承载过程中产生的应变更大;较平均级配,正态分布矸石集料先发生大范围破碎现象,且频率更高,分布更均匀,但其最高声发射能量小于平均级配;分形维数与加载应力呈对数函数关系,正态分布矸石集料分形维数增长率高于平均级配,具有更大的跨度区间。

基于颗粒分布分形模型毛细水上升高度计算分析

由表面张力引起的弯液面两侧压力差推动毛细水上升,造成低路堤路基产生毛细水病害,毛细水上升高度是防治路基毛细水病害的关键所在。克服了毛细水上升高度测量试验的缺陷,基于土粒分布的分形模型,提出毛细水上升高度的计算方法。采用筛分试验计算粉土颗粒分布分维,建立粉土颗粒级配的分形模型,系统地分析分维、进气值、孔隙率、毛细水最大上升高度和饱和渗透系数对毛细水上升高度和速度的影响。计算结果表明:毛细水上升高度与时间呈幂函数正相关关系,毛细水上升高度随颗粒分布分维、进气值、毛细水最大上升高度和饱和渗透系数增大而增大,随孔隙率增大而减小;毛细水上升速度只与颗粒分布的分维有关,随颗粒分布分维增大而增大,不受进气值、孔隙率、毛细水最大上升高度和饱和渗透系数的影响。

不同变质程度煤体微孔多重分形特征研究

为研究不同变质程度煤体微孔孔径多重分形的特征,根据低温液氮吸附实验数据,运用多重分形理论对4种不同变质煤体样品微孔的多重分形特征、以及孔隙特征与变质程度之间的关联展开研究。结果表明:4种煤样微孔均具备了多重分形的典型特征,变质程度越高煤样的微孔分布非均质性越强,其微小孔拥有更大的比表面积,将会为瓦斯气体提供更多的吸附位,拥有更大的解吸量;4种煤样的微孔孔径多分布在孔隙空间较为狭小的区域中,约为7~9 nm;微孔结构在弱变形作用下的非均质性明显,在此区域内,较大的孔径分布均一;但从整体看,其连通性与变质程度关系不明显且孔隙以聚集和分布不均匀为主导。

喀斯特石漠化区不同植被恢复下土壤颗粒分形特征

【目的】研究喀斯特石漠化地区的土壤颗粒分布和分形特征,为石漠化地区水土保持和土壤评价提供科学依据。【方法】在贵州师范大学喀斯特野外观测研究站,选取石漠化治理区中火龙果(Hylocereus undulatus)、玉米(Zea mays)、核桃(Juglans regia)、柚木(Tectona grandis)和种植于坡上和坡谷的花椒(Zanthoxylum bungeanum)等6种植被作为研究对象,分析了雨、旱两季的土壤粒径分布,并基于单重和多重分形理论计算了土壤颗粒分形参数。【结果】(1)研究区土壤粒径集中在1.5~300μm,质地较细以粉粒为主,黏粒含量最少,粒径分布呈非均匀性;(2)植被和季节对单重体积分形维数D_(v)均存在显著影响(P<0.05),决定系数R^(2)表明D_(v)与黏粒关系最为密切。旱季D_(v)的均值(2.56)较雨季(2.64)相比有所下降,细粒物质流失程度在不同植被之间存在显著差异(P<0.05);(3)各样地土壤粒径分布以体积分数占比较大的颗粒为主,广义维数谱D_(q)的递减程度在指数q<0时要大于q>0时,稀疏区土壤颗粒对环境因子的影响更敏感;(4)D_(v)与黏粒和粉粒呈极显著正相关,与砂粒呈极显著负相关。容量维数D_(0)、信息熵维数D_(1)、D_(1)/D_(0)、关联维数D_(2)和土壤颗粒的相关性与D_(v)相反。土壤有机碳/全氮(SOC/TN)与粉粒呈显著正相关,而与砂粒呈显著负相关,这说明粉粒组分在发挥固碳功能方面发挥主导作用。【结论】土壤分形维数能够作为喀斯特石漠化区土壤物理结构改善效果的指标,为石漠化水土保持和土壤评价提供科学理论支持。

基于低场核磁共振技术和多重分形理论的高阶煤样孔裂隙分维特征

结合沁水盆地中高阶煤样品NMR饱和及离心T_(2)谱分布曲线,将中高阶煤样划分为三种类型。分析了单重分形和多重分形模型对中高阶煤样孔径分布定量表征的适用性,并综合孔隙结构和储层物性参数揭示了孔隙分形特征。表明A类样品T_(2)值在1~1000 ms之间,饱和T_(2)谱分布呈“单峰态”,以大孔隙发育为主,物性条件较好。B类样品T_(2)值主要为0.1~300 ms,T_(2)谱呈对称状“三峰态”,束缚水饱和度相对较高,平均孔隙度和渗透率均小于A类。C和D类样品T_(2)值分别为0.01~200和0.01~10 ms之间,饱和T_(2)谱分布均呈“单峰态”,孔渗结构最差。单重分维值与孔隙度、T_(2cutoff)等物性参数具有良好的线性关系,主要适用于微孔相对发育的B、C和D型样品。同时,多重分形参数与单重分形参数间具有良好的负相关关系。受计算原理的差异性影响,小孔和大孔是影响单重分形参数变化的关键孔径,而介孔孔隙分布是影响多重分形参数变化的关键孔径。

CO_(2)高速卸荷粉碎磁铁矿石产品的粒度分布与分形维数研究

针对矿石的高压气体高速卸荷粉化产品的整体粒径分布缺乏系统科学的表征,以某超贫磁铁矿石为原料、液态二氧化碳为工作物质,引入Rosin-Rammler分布函数和分形维数,系统地分析了不同液态二氧化碳渗透压力下所得产品的粒度分布特性。结果表明:粉化产品颗粒粒径分布不均匀,提高二氧化碳压力可以提高细颗粒产率。Rosin-Rammler分布函数可较好地拟合粉化产品的粒径分布,拟合结果表明,粒径分布的均匀性指数随着二氧化碳压力的提高而减小,粉体粒径更不均匀。针对粗颗粒产率较大情况下Rosin-Rammler分布函数表现出的不足,引入分形维数进行了分析。结果表明,随二氧化碳压力的增大,粉化产物的分形维数增大,粉体整体趋于细化。本研究结果可为后续科学系统评价二氧化碳高速卸荷粉化各类矿石的整体效果提供参考。

CO_(2)-水作用下页岩微观孔隙结构变化特征

为明确注CO_(2)提高页岩气开采过程中CO_(2)与水作用后对页岩微观孔隙结构的影响,采用X射线衍射、低温N_(2)吸附和低场核磁共振等实验方法,研究了原始页岩及纯盐水、注入压力为6和12 MPa的CO_(2)水溶液浸泡后页岩的矿物组成、孔径分布和微观孔隙结构变化特征,并结合分形理论,获取了孔表面和孔体积的分形特征,明确了页岩中吸附孔隙和渗流孔隙的变化特征。结果表明:CO_(2)水溶液浸泡后,页岩中石英含量增大,黏土矿物和碳酸盐含量降低;随着CO_(2)注入压力的增加,微孔比表面积和总比表面积减小,平均孔径、核磁孔隙度和大孔孔体积比例增大,表明在CO_(2)水溶液的溶解作用下微孔和介孔逐渐向大孔转化;低温N2吸附和核磁共振(NMR)获得的分形维数均随CO_(2)注入压力的增加逐渐降低,表明页岩在CO_(2)水溶液浸泡后孔隙结构的非均质性和复杂性降低;孔表面分形维数DL1、DN1和孔体积分形维数DL2、DN2与总比表面积和总孔质量体积呈正相关性,这2个指标可分别用于表征页岩中的吸附孔隙和渗流孔隙特征,能够有效评价页岩气体吸附与渗流能力。研究成果为注CO_(2)高效开发页岩气提供了参考和依据。

粒状土孔隙率与其颗粒级配的分形关系

粒状土是填(构)筑地基、路基和土石坝等构筑物最常用的工程材料之一。对粒状土孔隙空间的研究有助于揭示其粒状结构承受和传递外力的机理。以仿真颗粒的相互作用为基础的颗粒离散元法是研究粒状土力学行为的有力有效工具。然而,仿真计算所耗时间与颗粒数量成正比,在计算颗粒数量较多的大模型时会受计算机计算性能的制约,阻碍了颗粒离散元法在工程中的普及。为了减小颗粒数量,常常忽略粒状土中细小的颗粒,带来的问题是,颗粒体的孔隙率被低估,同时影响粒状土中力的传递。借助颗粒流离散元法开展一系列仿真试验。结果表明,模型孔隙率随着最小颗粒粒径的变小而变小且两者呈分形关系。基于分形理论建立粒状堆积体孔隙率与最小粒径的数学关系。研究结果可用于提高颗粒流(或计算流体动力学-离散元法耦合)模型计算的准确性和效率。

分形金相的初步探讨——关于晶粒度的分形特征

对金相的分形特征进行了探讨分析。实验验证晶粒具有分形特征 ,并测量了标准图谱中铁素体晶粒度图形的分形维数。考察了晶粒度与分形维数之间的关系。结果表明 ,金属晶粒可用分形维数定量描述。在 1～ 8级晶粒度范围内 ,随着晶粒度级别的提高 ,分形维数数值逐渐增大 ,其中以 1～ 5级内增大得最为显著。