Fractal scaling of effective diffusion coefficient of solute in porous media

Fractal approach is used to derive a power law relation between effective diffusion coefficient of solute in porous media and the geometry parameter characterizing the media. The results are consistent with the empirical equations analogous to Archie`s law and are expected to be applied to prediction of effective diffusion coefficient. Key words: diffusion; effective diffusion coefficient; fractal; porous media.

New Approach of Geomechanical Properties by Scale Effect and Fractal Analysis in the Kedougou-Kenieba Inlier (Senegal-West Africa)

This paper shows geometric aspects of rock masses in the Senegalese side of Kédougou-Kéniéba inlier. The studies are done in one part on sedimentary rocks (represented by sandstones) with stratification and on the other part in igneous rocks (represented by basalts). Geometric studies are the fractal configuration and the scale effect. Scale effect is stud- ied by comparing the results of mechanical tests done in the laboratory and on outcrops. For all samples, laboratory pa- rameters are higher than values of field. In this paper, scale effect is characterized by the decrease of mechanical pa- rameters from laboratory samples to field. The scale coefficient is defined and characterizes the relation between me- chanical properties. More importantly, the scale effect is more significant. This scale effect depends largely on the rock anisotropy. The anisotropy depends on the fracturation and the filling. The scale effect takes into account the fracturation, the filling minerals and their diversity which define the complexity of the rock. The anisotropy is complex;the impact of scale effect traduced by an increase of scale coefficient is the highest. Configuration of discontinuities also defines fractal geometry. This fractal aspect appears on the asperities, the spacing and the apertures of discontinuities. The fractal dimension is different from a parameter to another. All these two parameters estimate the stage of fracturation of the rock in a geological system and depend one on another if they are studied in the same element.

Effects of fractal gating of potassium channels on neuronal behaviours

The classical model of voltage-gated ion channels assumes that according to a Markov process ion channels switch among a small number of states without memory, but a bunch of experimental papers show that some ion channels exhibit significant memory effects, and this memory effects can take the form of kinetic rate constant that is fractal. Obviously the gating character of ion channels will affect generation and propagation of action potentials, furthermore, affect generation, coding and propagation of neural information. However, there is little previous research on this series of interesting issues. This paper investigates effects of fractal gating of potassium channel subunits switching from closed state to open state on neuronal behaviours. The obtained results show that fractal gating of potassium channel subunits switching from closed state to open state has important effects on neuronal behaviours, increases excitability, rest potential and spiking frequency of the neuronal membrane, and decreases threshold voltage and threshold injected current of the neuronal membrane. So fractal gating of potassium channel subunits switching from closed state to open state can improve the sensitivity of the neuronal membrane, and enlarge the encoded strength of neural information.

Application of fractal theory to size effect of disordered materials

For disordered materials it is impossible to measure constant material properties using the Euclidian geometrical dimension of the test specimens. Based on the theory of fractal geometry, the fractal dimension of the damaged microstructure is applied to measure the strength and fracture toughness of imitation marbles, which turn out to be scale invariant material constants. In this paper, the experimental data are treated and interpreted by the theory of fractal geometry. Reasonable results are obtained and the size effects on strength and fracture energy are observed.

一种基于Fractal-DenseNet的电磁血管断层图像重建算法

针对电磁血管断层图像重建中存在的欠定性、病态性,提出一种基于Fractal-DenseNet的电磁血管断层图像重建算法.基于血流磁电耦合效应的血管断层图像重建原理,将FractalNet的分形思想与DenseNet的密集紧密连接思想相结合,构建了一种适用于反演血液流速分布的Fractal-DenseNet网络模型,用于血管断层图像重建.通过人体前臂尺动脉血流磁电耦合测量模型,建立血管断层剖面流速和血流磁电效应引起的电压信号的对应数据对,分别作为网络模型输入和输出;通过监督学习,实现基于血管断层流速分布的血管断层图像重建.结果表明:Fractal-DenseNet重建结果的均方根误差和相关系数分别为0.0078,99.28%;本文算法具有良好的抗噪性,可在复杂边界条件下实现血管断层图像重建.

Fractal analysis of polyferric chloride-humic acid(PFC-HA) flocs in different topological spaces

The fractal dimensions in different topological spaces of polyferric chloride-humic acid （PFC-HA） flocs, formed in flocculating different kinds of humic acids （HA） water at different initial pH （9.0, 7.0, 5.0） and PFC dosages, were calculated by effective densitymaximum diameter, image analysis, and N2 absorption-desorption methods, respectively. The mass fractal dimensions （De） of PFC-HA floes were calculated by bi-logarithm relation of effective density with maximum diameter and Logan empirical equation. The Df value was more than 2.0 at initial pH of 7,0, which was 11% and 13% higher than those at pH 9.0 and 5.0, respecively, indicating the most compact flocs formed in flocculated HA water at initial pH of 7.0. The image analysis for those flocs indicates that after flocculating the HA water at initial pH greater than 7.0 with PFC flocculant, the fractal dimensions of D2 （logA vs. logdL） and D3 （logVsphere vs. logdL） of PFC-HA floes decreased with the increase of PFC dosages, and PFC-HA floes showed a gradually looser structure. At the optimum dosage of PFC, the D2 （logA vs. logdL） values of the flocs show 14%-43% difference with their corresponding Dr, and they even had different tendency with the change of initial pH values. However, the D2 values of the floes formed at three different initial pH in HA solution had a same tendency with the corresponding Df. Based on fractal Frenkel-Halsey-HiU （FHH） adsorption and desorption equations, the pore surface fractal dimensions （Ds） for dried powders of PFC-HA flocs formed in HA water with initial pH 9.0 and 7.0 were all close to 2.9421, and the Ds values of flocs formed at initial pH 5.0 were less than 2.3746. It indicated that the pore surface fractal dimensions of PFC-HA floes dried powder mainly show the irregularity from the mesopore-size distribution and marcopore-size distribution.

Edge Effect Correction in the S-A Method for Geochemical Anomaly Separation

Anomaly separation using geochemical data often involves operations in the frequency domain, such as filtering and reducing noise/signal ratios. Unfortunately, the abrupt edge truncation of an image along edges and holes (with missing data) often causes frequency distribution distortion in the frequency domain. For example, bright strips are commonly seen in frequency distribution when using a Fourier transform. Such edge effect distortion may affect information extraction results; sometimes severely, depending on the edge abruptness of the image. Traditionally, edge effects are reduced by smoothing the image boundary prior to applying a Fourier transform. Zero-padding is one of the most commonly used smoothing methods. This simple method can reduce the edge effect to some degree but still distorts the image in some cases. Moreover, due to the complexity of geoscience images, which can include irregular shapes and holes with missing data, zero-padding does not always give satisfactory results. This paper proposes the use of decay functions to handle edge effects when extracting information from geoscience images. As an application, this method has been used in a newly developed multifractal method (S-A) for separating geochemical anomalies from background patterns. A geochemical dataset chosen from a mineral district in Nova Scotia, Canada was used to validate the method.

FRACTAL INVESTIGATION OF THE MICROSTRUCTURE IN Alnico8 THERMOMAGNETICALLY TREATED

Fe-Co rich particles in the Alnico8 samples thermomagnetically treated for various times at 800 °C have been found to be of self-similarity and of fractal characteristics both in two-dimensional space and three-dimensional space. Fe-Co rich particles for 1.5, 3 and 5 min treatment have also shown a different fractal nature both in two-dimensional space and three-dimensional space as compared with the case for 10 min, which implies that Fe-Co rich particles evolve through different kinetic mechanisms. The fractal dimensions for 1.5, 3 and 5 min as well as 10 min treatment derived from the SAXS data in three-dimensional space are in agreement with the theoretical dimensions for two models introduced respectively. The fractal dimensions in two-dimensional space greater than the theoretical ones for two models can be attributed to the strong anisotropy of Fe-Co rich particle evolution in three-dimensional space.

基于开采高度对工作面覆岩裂隙演化影响的钻孔瓦斯抽采研究

采动覆岩裂隙演化规律对层间瓦斯运移起主导作用,研究覆岩裂隙发育分布规律对于提高瓦斯抽采效率至关重要。以甘肃省魏家地矿西2107综采工作面为工程背景,采用UDEC模拟软件建立不同采高的数值模型,利用分形几何理论分析了工作面覆岩近场裂隙演化与不同开采高度的关系,确定了钻孔瓦斯抽采最优工作面高度,并通过理论经验公式、覆岩裂隙窥视情况与现场瓦斯抽采结果对其验证。结果表明:采动裂隙总数随着采高增大而增大,但不同阶段增大的幅度皆不相同,覆岩裂隙不断向覆岩四周呈“伞状”发育;不同开采高度的工作面覆岩近场裂隙均经历产生、扩张贯通、压实稳定的3个阶段,且采高越大,压实区范围越小,适当增加采高,有助于提高覆岩瓦斯抽采效果;当采高选择4 m时,顶板裂隙在位于10 m与40 m位置处的裂隙发育密度与范围均明显大于其他区域,该区域与布置高、低巷双位一体的协同抽采巷最佳位置相一致。

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

By the fractal dimension method, the polaron properties in cylindrical GaAs/AlxGa1-xAs core-shell nanowire are explored. In this study, the polaron effects in GaAs/AlxGa1-xAs 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/AlxGa1-xAs core-shell nanowire are solved simply by using the fractal dimension method to avoid complex and lengthy calculations.

Modeling porous structure of oil-pressboard interface and its effect on electric field distribution

The oil-pressboard insulation is a typical composite insulation system widely used in the design and manufactory of large power apparatus. The implement of oil-pressboard insulation may lead to surface electrification and discharge at the interface under certain condition. It is of significant importance to take an insight into the phenomenon occurring at the interface. Through experiment, the pressboard is found as a porous material. The interface changes abruptly from bulk pressboard to the bulk oil as a result of the porous structure. A new model is proposed which divides the interface into bulk oil region, transition region, and bulk pressboard region. The width of the transition region is decided according to the microtome figure. The effective permittivity of the transition region is calculated using a new model based on fractal theory. The model is validated and compared with previous calculation model. The effect of the existence of transition region on the electric field distribution is discussed.

Influence of permeation effect on themicrofabric of the slip zone soils: A case study from the Huangtupolandslide

This study aims to investigate the correlation between the permeation effect and microfabric of the slip zone soils with Huangtupo landslide in the Three Gorges Reservoir as the study case. Based on the permeability test and scanning electron microscope(SEM) images analysis, the fractal theory and probability entropy are used to quantify the characteristics of the remodeling specimens. First, the relationships between initial moisture content(IMC) and microstructure of the soil(percentage of particle area(PPA), pore roundness(Rp)) before and after permeability test are summarized. Then, the fractal dimension of the soil(pore distribution(Dpd), pore size(Dps)) are analyzed under the permeation effect. Based on the probability entropy, the entropy of pore(Ep) is used to characterize the porosity orientation, and the rose diagrams are used to show the particle orientation under the permeation effect. Finally, the relationship between the microstructure of the soil and its mechanical property is discussed. Results show that under the permeation effect, the microstructure of the soil has undergone tremendous changes. A flat long pore channel is formed. The order of the pore arrangement is enhanced, and soil particles switch the long axis to parallel infiltration direction to reach a new steady state. It can be inferred that the strength of soil would be weakened if the fractal dimension of soil pore decreases under any external environment.

海洋中示踪物等值线的分形长度及其与混合效率的关系

涡致混合扩散是物理海洋研究中的热点和难点问题。本文基于“有效扩散”理论,研究示踪物等值线在海表地转湍流的多尺度搅拌作用下,发生拉伸、扭曲、变形、折叠等改变其几何拓扑结构的现象,并探讨了等值线分形长度的变化与混合效率的关系。研究结果表明,在地转流场的搅拌下,示踪物的等值线会被迅速拉长,并产生丰富的精细结构。这种分形式的增长可达原长度的10~20倍,是混合效率提高的主要原因;而涡丝和锋面伴随的梯度增强虽然也有贡献,但为次要因素。另一方面,在示踪物模拟过程中,小尺度扩散会通过不可逆混合对示踪物进行均匀化,从而抹平等值线的精细结构,抑制等值线的增长,限制混合效率的提高。基于“数盒子”算法计算了等值线的分形维度,其数值在1.4到1.6之间,介于一维和二维之间。但由于地转湍流数据分辨率的限制,无法考虑更小尺度(次中尺度过程)的搅拌作用,可能低估了等值线的分形长度和混合效率。本研究将海洋混合与等值线几何特征联系了起来,初步得到了分形长度和混合效率两者的经验关系式,未来可以利用图像识别等成熟遥感技术将海洋示踪物等值线的几何特征直接转换为混合效率,为诊断分析海洋混合及其参数化提供了一种新的思路。

SUBCOOLED BOILING REGIME RECOGNITION BASED ON FRACTAL CHARACTERISTIC QUANTITIES OF SOUND PRES-SURE

Based on acquisition of sound pressure in subcooled boiling twophase system and through dynamic data processing methods, the dynamical behavior of the system is discussed. With the introduction of fractal concept, an analysis to the fractal feature of sound pressure signal is carried out. Moreover, the pseudo phase diagrams of typical time series of sound pressure are given. Finally, through dynamic clustering and on the basis of calculating correlation dimension and Hurst exponent of sound time series on different subcooling conditions, the recognition of developing regime of the twophase system is delivered, which provides a new practical approach of recognition and diagnosis for vaporliquid boiling system.

Application of fractal characteristic quantities of pressure fluctuation in subcooled boiling regime recognition

The dynamical behavior of the subcooled boiling two-phase system was introduced and discussed. With the introduction of fractal concept, an analysis of the fractal feature of pressure wave signals from nonlinear dynamics point of view, was carried out. Meanwhile, the pseudo phase diagrams of typical time series of sound pressure were given. Finally, through dynamic clustering and on the basis of calculating correlation dimension and Hurst exponent of pressure wave time series on different subcooling conditions, the recognition of developing regime of the two-phase system was delivered, which might provide a promising approach of recognition and diagnosis of a boiling system.

岩石节理接触特征尺寸效应的数值试验研究

为探究岩石节理接触特征尺寸效应,采用自仿射分形方法构建系列尺寸数值模型,利用离散弹塑性计算方法求解闭合变形,定量分析节理接触特征尺寸效应规律,并探究不同岩性和粗糙度对其尺寸效应的影响差异。自仿射分形方法构建的岩石节理其粗糙程度随尺寸增加逐渐变小,接触面积比和组合形貌微凸体参数之间具有关联,接触面积比的尺寸效应可归因于组合形貌微凸体参数ηR的尺寸变化。岩石节理尺寸越大,闭合变形引起的塑性部分占比越多。塑性变形对接触面积比尺寸效应具有弱化作用,对闭合变形尺寸效应具有强化作用,硬岩节理的接触特征尺寸效应强于软岩节理,其接触特征代表性长度也更大。岩石节理的粗糙度对其闭合变形和接触面积比的尺寸效应具有相反的效果。

基于CT扫描技术的煤样三维重构及气体表观渗透率研究

基于CT扫描技术对煤样扫描成像,并进行滤波和二值化处理,获取孔裂隙尺寸、孔隙率等特征参数。通过盒维法计算煤样的分形维数,推导煤样孔裂隙的平均迂曲度及迂曲度维数。结合分形理论和克努森数,推导煤体中经滑移修正的气体表观渗透率模型并进行验证。通过ANASY有限元软件研究煤体中的瓦斯渗流规律。结果表明,瓦斯在孔裂隙弯折处压力变化剧烈,渗流速度在孔裂隙弯折处达到最大,瓦斯在个别孔隙发生凝滞、不流通。采用经过滑移修正的气体表观渗透率模型计算瓦斯表观渗透率,并与通过Forchheimer公式拟合得到的瓦斯表观渗透率及通过FT模型计算得到的瓦斯表观渗透率相比较,发现经过滑移修正后的气体表观渗透率模型适用于微尺度介质中气体表观渗透率研究。

垃圾渗滤液的延时搅拌造粒混凝处理特性研究

混凝沉淀在垃圾渗滤液的深度处理工艺中是非常必要的预处理环节。传统的混凝工艺处理垃圾渗滤液普遍存在水资源回收率低、污染物去除率低、絮凝体松散等缺点。基于收缩脱水絮体致密化理论,提出了垃圾渗滤液的延时搅拌造粒工艺,通过长时间高强度的机械搅拌实现悬浮物的均一化。研究结果表明,在pH=12、搅拌强度为1500 r/min、PAC和PAM投加量分别为3000 mg/L和60 mg/L的最佳条件下,SS、浊度、COD的去除率分别可达92.33%、99.92%、35.84%。通过图像粒子测算系统测得最佳条件下絮凝体d_(50)为3.76 mm,沉速为20.08 mm/s,与常规混凝相比,沉速提升约60%。基于絮体沉速、投影面积、有效粒径等数据,计算得到三维分形维数为2.8909,有效密度为0.0876 g/cm^(3)。延时搅拌造粒生成的絮体沉速快、密度大,混凝后的上清液回收率可由常规混凝的45%提升至85%。

大倾角工作面飞矸冲击破碎特征研究

飞矸灾害长期威胁大倾角、急倾斜煤层长壁工作面人员和设备安全,单一飞矸迁移过程碰撞破碎衍生出大量“子矸”,其动力损害具有突发性,揭示冲击载荷作用下煤岩体破碎特征是准确掌握飞矸动力损害的重要前提。综合运用分离式霍普金森压杆试验、数值SHPB试验和物理模拟开展冲击载荷作用下煤岩体破碎特征与碎裂机制研究,得到以下主要结论:高速冲击作用下煤岩破坏模式分为相对完整、单一劈裂和完全粉碎,破碎程度随着加载应变率增加而增加,分形维数D与应变率呈对数函数关系。相同应变率水平,煤岩抗压强度越小分形破碎程度越高;煤岩分形维数D与其几何尺度负相关;圆盘和立方体煤岩分形维数D与应变率均呈对数函数关系。立方体煤岩累积碰撞作用下内部节理裂隙发育,应力波传播呈现弥散性,在边缘应力集中并诱发破坏,即不规则形状煤岩外缘易率先与主体破坏分离从而导致其球形度增加。相反,飞矸运动过程棱角处更易受到碰撞而承受直接应力冲击而产生局部崩解。研究成果可为大倾角、急倾斜煤层飞矸灾害防控实践中挡矸网形状以及网格大小的选择提供一定的科学指导。飞矸涉及材料、几何等多源不确定因素,内部层理、裂隙分布及发育程度受开采扰动影响较大,其破碎分形特征更加趋于复杂,下一步将考虑以上因素对飞矸破碎特征的影响。

应力作用下岩石介质两相流束缚流体饱和度分形预测模型研究

束缚流体饱和度是预测两相流中相对渗透率的重要参数,在油气藏开发等工程领域有着重要作用。为此,基于分形理论和毛细管模型,首先将岩石等效为固体团簇的集合体,引入不同分形维数分别表征固体团簇的尺度分布特征和流动路径的迂曲性,然后提出了一种预测束缚流体在应力作用下的饱和度模型,并使用试验数据进行了验证,最后分析了束缚流体饱和度的应力敏感性和模型中各参数的影响机制。结果表明:束缚流体饱和度与流体黏度、孔隙结构参数、压降梯度以及弹性模量密切相关,有效应力会增大束缚流体饱和度,分形维数可以反映束缚流体形成的流体膜厚度和实际流动长度,量化了孔隙结构特征对束缚流体饱和度的影响。