量化三维网格模型复杂度的Fractal Dimension^(+)方法

对三维网格模型复杂度的评估及应用进行研究,提出基于Fractal Dimension^(+)方法量化三维网格模型复杂度。该方法利用分形几何学的分形维度来确定三维网格模型的不规则性;为了全面量化复杂度并且提高量化的准确性和可信度,在分形维度算法中添加孔隙比和亏格数的概念,全面考虑介质内部空间分布和几何结构的连接性以及孔洞分布的信息。对大量三维网格模型进行实验,结果表明Fractal Dimension^(+)方法可以有效计算出准确的复杂度。

Performance-based fractal fracture model for complex fracture network simulation

The paper presents a novel hydraulic fracturing model for the characterization and simulation of the complex fracture network in shale gas reservoirs. We go beyond the existing method that uses planar or orthogonal conjugate fractures for representing the ＇＇complexity＇＇ of the network. Bifurcation of fractures is performed utilizing the Lindenmayer system based on fractal geometry to describe the fracture propagation pattern, density and network connectivity. Four controlling parameters are proposed to describe the details of complex fractures and stimulated reservoir volume（SRV）. The results show that due to the multilevel feature of fractal fractures, the model could provide a simple method for contributing reservoir volume calibration. The primary-and second-stage fracture networks across the overall SRV are the main contributions to the production, while the induced fracture network just contributes another 20% in the late producing period. We also conduct simulation with respect to different refracturing cases and find that increasing the complexity of the fracture network provides better performance than only enhancing the fracture conductivity.

基于曲率和分形理论的构造复杂程度评价及构造煤预测

为了提高矿井地质构造复杂程度评价精度,以龙滩煤矿为研究对象,在矿井地质构造发育特征与规律分析的基础上,定量计算了矿井褶皱构造和断裂构造的构造主曲率值和分维值,将结果归一化处理获得了井田构造综合复杂程度指标值,并对其复杂程度进行定量评价,预测了矿井构造煤的分布,评价结果与矿井实际构造特征相吻合,达到了预期效果,证实了该综合评价方法的有效性,为煤矿未来瓦斯防治及采掘部署工作提供了地质依据。

基于概率穿越可视图的时间序列网络多重分形研究与应用

对有限穿越可视图进行改进,提出了概率穿越可视图.首先,将间接可视的节点之间的关联处理为穿越距离的函数,而且节点之间的关联随穿越距离的增加而减小,从而将无权图形式的时间序列网络推广到带权图;其次,采用复杂网络中的网络维数计算方法处理所得到的时间序列网络的分形维数,从而对其自相似特性进行分析;最后,通过划分不同的时间粒度得到多个不同的时间序列网络,对应有多个不同的分形维数,进而分析了所得到的时间序列网络的多重分形特性.在与经典的可视图法、水平可视图法及有限穿越可视图法的对比中论证了所提出的概率穿越可视图的优势.

On the Fractal Design in Human Brain and Nervous Tissue

Digital imaging techniques have enabled to gain insight into complex structure-functional processes involved in the neo-cortex maturation and in brain development, already recognized in anatomical and histological preparations. Despite such a refined technical progress most diagnostic records sound still elusive and unreliable because of use of conventional morphometric approaches based on a unique scale of measure, inadequate for investigating irregular cellular components and structures which shape nervous and brain tissues. Instead, these could be efficiently analyzed by adopting principles and methodologies derived from the Fractal Geometry. Through his masterpiece, The Fractal Geometry of Nature [1], Benoît Mandelbrot has provided a novel epistemological framework for interpreting the real life and the natural world as they are, preventing whatever approximation or subjective sight. Founded upon a body of well-defined laws and coherent principles, the Fractal Geometry is a powerful tool for recognizing and quantitatively describing a good many kinds of complex shapes, living forms, organized patterns, and morphologic features long range correlated with a broad network of functional interactions and metabolic processes that contribute to building up adaptive responses making life sustainable. Scale free dynamics characterized biological systems which develop through the iteration of single generators on different scales thus preserving proper self-similar traits. In the last decades several studies have contributed to showing how relevant may be the recognition of fractal properties for a better understanding of brain and nervous tissues either in healthy conditions or in altered and pathological states.

基于Fractal模型的复电阻率法2.5D有限元数值模拟

复电阻率法在油气资源、矿产勘查中发挥了重要的作用,为了深刻认识复电阻率法异常特征变化规律,本文对复电阻率2.5D正演问题展开研究。首先直接给出复电阻率法2.5D有限元正演所满足的变分问题,并详细地推导相应的刚度矩阵的计算过程。引入Fractal模型作为等效模型研究频谱激电异常特征。对单元内的复电导率及复电位均进行线性插值,而后,采用不完全LU分解的稳定双共轭梯度算法求解有限元线性方程组,获得异常复电位值。设计3个典型的地电模型验证了本文算法的正确性及精确性,并分析了不同装置下,不同频率的2.5D复电阻率异常响应特征。数值模拟结果表明,采用Fractal模型研究激发极化异常特征是可行、有效的;不同装置、不同频率下的复电阻率法异常特征有着显著的差异。

ADVANCES IN FRACTAL IMAGE AND VIDEO CODING

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Complexity analysis of precipitation in changing environment in Chien River Basin,China

The hydrological processes influenced by the multiple factors of climate, geography, vegetation, and human activities are becoming more and more complex, which is an important characteristic of hydrological systems. The different complexity distributions of precipitation processes of the Chien River Basin （a sub-basin of the Minjiang Basin） in two periods （from 1952 to 1980, and from 1981 to 2009） are illustrated using the fractal based on the continuous wavelet transform （CWT）. The results show that （1） at the basin scale the precipitation process in the latter period is more complex than in the former period; （2） the maximum value of the complexity distribution moved from the east to the middle; and （3） through analysis of the time-information and space-information concealed in this complexity change, the precipitation characteristics in the changing environment in the basin can be illuminated. This study could provide a reference for research on disaster pre-warning in changing environments and for integrated water resources management in the local basin.

Coordination and evolution mechanism of fractal crack network in mining rock mass destruction

Based on the natural characters of stratum, complicated geological mining conditions and the essence of mining rock mass destruction, the complexity of rock mass destruction caused by miningw as analyzed. The inner link between rock mass destruction phenomena caused by mining and nonlinear science was revealed. There are numerous cracks in natural rock mass. The cracks’ distribution is irregular and is of statistical fractal structure. Self-organizational nonlinear evolution of the inner structure flaws leads to the rock mass destruction with external force. The evolution includes single fault’s fractal development, formation and evolution of fractal crack network and coordination of fractal crack network, etc. The law of fractal crack network’s evolution was introduced, at the same time, the coordination of fractal crack network was analyzed. Finally, based on coordination the principal equation of mining-caused subsidence of structural rock mass was established and its steady-state solution and unsteady-state solution were found.

The Influence of the Model Fractal Parameters on the Electromagnetic Response in Environment with Cylindrical Layers

The induced polarization response of an environment presenting cylindrical layers was obtained. The fractal model for complex resistivity was employed as an intrinsic property of the polarizable layers. The influence of the model fractal parameters on the electromagnetic response was investigated. The results demonstrated that the fractal parameters dominate the apparent resistivity phase response;measurements of the induced polarization data allow for the determination of the fractal properties of the environment without noticeable electromagnetic coupling effects at frequencies below 104 Hz.

基于复杂网络的空中交通流分形特征分析

为准确把握空中交通流量变化规律,掌握空中交通系统内在特性,需要对空中交通流时间序列进行基于复杂网络的分形特征分析。收集空中交通流量数据,利用可视图方法构建复杂网络模型,分析网络拓扑结构,验证了该网络度分布服从幂律分布,拟合直线斜率为-2.086,证明了网络是无标度网络,具有单分形特征。验证了覆盖整个网络所有节点所需要的最少盒子数目与盒子直径成幂律关系,拟合直线斜率为-0.2121,相关系数为-0.8722,再次证明了网络具有单分形特征。通过验证网络广义分形维数关于参数的图像为非线性,拟合直线斜率分别为-1.942、-1.936、-1.78,相关系数均在0.8以上,拟合效果较好,证明了网络具有多重分形特性。通过计算重整化前后网络的幂指数相似,证明了网络具有自相似性。结果表明,应用复杂网络的理论分析空中交通流时间序列是可行有效的,为进一步深入应用研究奠定了基础。

基于混隐色特征背景引导融合的伪装效能评估

现有迷彩伪装效能评估方法重点关注目标与背景在颜色、纹理等特征上的相似度,未能从伪装策略角度分析目标边缘和表面的融合程度,无法准确评估复杂环境下目标的伪装效果。本文提出一种基于混隐色特征背景引导融合的伪装效能评估模型,利用多重分形理论和Gabor滤波器估计目标轮廓和表面破坏程度;引入特征拥塞指数计算背景复杂度,通过逻辑斯蒂方程自适应调整评估特征权重,提高模型对环境变化的适应性。实验表明,该模型在Search_2数据集上的搜索时间相关性系数(皮尔逊相关系数、斯皮尔曼相关系数、均方根误差)分别达到0.888、0.773、0.054,在自建CamData数据集上分别达到0.835、0.805、0.126,评估结果与人眼搜索实验结果符合性较高,能够有效表征目标在不同复杂场景下的伪装效能。

Chaos, Fractal and Recurrence Quantification Analysis of Surface Electromyography in Muscular Dystrophy

We analyze muscular dystrophy recorded by sEMG and use standard methodologies and nonlinear chaotic methods here including the RQA. We reach sufficient evidence that the sEMG signal contains a large chaotic component. We have estimated the correlation dimension (fractal measure), the largest Lyapunov exponent, the LZ complexity and the %Rec and %Det of the RQA demonstrating that such indexes are able to detect the presence of repetitive hidden patterns in sEMG which, in turn, senses the level of MU synchronization within the muscle. The results give also an interesting methodological indication in the sense that it evidences the manner in which nonlinear methods and RQA must be arranged and applied in clinical routine in order to obtain results of clinical interest. We have studied the muscular dystrophy and evidence that the continuous regime of chaotic transitions that we have in muscular mechanisms may benefit in this pathology by the use of the NPT treatment that we have considered in detail in our previous publications.

Fractal Networks of Real Worlds of Fluorescing DNA in Complete Set of Chromosomes inside Blood Cells for Medical Diagnostics

We analyze fluorescence due to oxidizing activity of DNA in neutrophils of peripheral blood in the large populations ~104 - 105 of cells. Fluorescence is registered by flow cytometry method. Spatial resolution is about a few nanometers for varied complex three-dimensional (3D) DNA nanostructures of all non-coding and coding parts of DNA. It’s shown that oxidative activity of all 3D DNA in the full set of chromosomes inside cells is defined by new standards for complex networks of “exponentially small worlds”, with more dense packing than in the well known networks of “small worlds”. Analysis of various blood samples in vivo and during medical treatment shown that only two classes of Good and Bad Networks of DNA for a good and a bad health existed. This division is defined by any network to one from two classes of “n” or “s” shaped curves for typical deviations and from straight line in perfect networks of “exponentially small worlds”, as for two types of hysteresis curves at phase transitions or at switching of bistability. These deviations coincide with two types of positive and negative trends of changing fractal dimension by changing the scales of multi-scale networks of fluorescing DNA. These trends give the overall assessments of human immunity, including hidden and unidentified diseases, and as a sum of all kinds of health and illness of given person, from the point of view the inner life of neutrophils, living in different parts of human body in given time. Characteristics of deviations associated with type, level and complexity of illness in the dependence on

The Multi-Fractal Singularity Value Decomposition and Its Application in Extraction of Gravity Anomaly Associated with Gold Mineralization in Tongshi Gold Field

Because of the complication of geological procedures,the recorded data have the feature of nonlinear.The multi-fractal singularity value decomposition (MSVD) was used to decomposed the gravity data.In this paper,the MSVD was utilized to extract the gravity anomaly associated with the gold mineralization in Tongshi gold field in the southwest of Shandong province.The results showed that the Tongshi complex with negative circular gravity anomaly is an important ore-controlling factor.And the positive ring gravity anomaly distributed

Long time behavior of solutions to coupled Burgers-complex Ginzbury-Landau(Burgers-CGL) equations for flames governed by sequential reaction

This paper studies the existence and long time behavior of the solutions to the coupled Burgers-complex Ginzburg-Landau （Burgers-CGL） equations, which are derived from the nonlinear evolution of the coupled long-scale oscillatory and monotonic instabilities of a uniformly propagating combustion wave governed by a sequential chem- ical reaction, having two flame fronts corresponding to two reaction zones with a finite separation distance between them. This paper firstly shows the existence of the global solutions to these coupled equations via subtle transforms, delicate a priori estimates and a so-called continuity method, then prove the existence of the global attractor and establish the estimates of the upper bounds of Hausdorff and fractal dimensions for the attractor.

Complexity and Self-Organized Criticality of Solid Earth System(Ⅰ)

The author puts forward the proposition of Complexity and Self Organized Criticality of Solid Earth System in the light of: (1) the science of complexity studies the mechanisms of emergence of complexity and is the science of the 21st century, (2) the study of complexity of the earth system would be one of the growing points occupying a strategic position in the development of geosciences in the 21st century. By the proposition we try to cogitate from a new viewpoint the ancient yet ever new solid earth system. The author abstracts the fundamental problem of the solid earth system from the essence of the generalized geological systems and processes which reads: the complexity and self organized criticality of the global nature, structure and dynamical behavior of the whole solid earth system emerging from the multiple coupling and superposition of non linear interactions among the multicomponents of the earths material and the multiple generalized geological (geological, geophysical, and geochemical) processes . Starting from this cognizance the author proposes eight major themes and the methodology of researches on the complexity and self organized criticality of the solid earth system.

核磁共振成像和多层螺旋CT在复杂踝关节损伤诊断及分型诊断中的应用价值

目的 探讨对复杂踝关节损伤采用核磁共振成像(magnetic resonance imaging,MRI)、多层螺旋CT(multislice spiral computed tomography,MSCT)进行诊断及分型诊断的价值。方法 选择2019年1月—2021年12月泰州市中西医结合医院收治的疑似复杂踝关节损伤患者80例,均予以MRI、MSCT检查,比较两种方法对复杂踝关节损伤的诊断效能,并分析其对复杂踝关节损伤的分型诊断价值。结果 MRI诊断准确率91.25%较MSCT的98.75%低,差异有统计学意义(P<0.05)。MSCT对SA型、PA型、PE型、SE型、PD型的诊断准确率分别为92.86%、100.00%、91.67%、95.45%、100.00%,MRI分别为85.71%、83.33%、90.90%、94.74%、100.00%;MSCT、MRI整体分型诊断准确率96.20%、91.78%,均与金标准一致性较好(Kappa=0.95、0.90)。结论 MSCT对复杂踝关节损伤的诊断准确性较MRI更高,MSCT与MRI在复杂踝关节损伤分型诊断中均有较高应用价值。

典型黄土地貌类型区的地形复杂度分形研究

黄土高原地貌形态与地形复杂度自南向北有序变化,构成了举世瞩目的独特的地理景观。选择陕西省南北剖面六个典型黄土地貌样区为基本实验区,以其1∶1万栅格DEM为数据源,探讨典型黄土地貌类型区的地形复杂度分形与空间分异特征。首先提出的元分维模型方法,以计算得到的DEM元分维值作为特征指标,研究样区的地形复杂度问题。这种通过滑动窗口的扩展分维分析方法,既可以用于分析该区域不同尺度下的地形复杂度变化情况,也可以探讨区域的局部单元复杂程度及其空间分布,从而不再局限于对全区域的单一分维评价。以此为基础,进一步应用元分维谱方法,研究地貌网格单元的元分维分级分布情况。实验结果表明:以绥德和延川为代表的黄土峁状丘陵沟壑区最为复杂,以宜君和甘泉为代表的梁状丘陵沟壑区居中,而以淳化为代表的黄土塬区和以神木为代表的风沙黄土过渡区最为平缓。实验进一步证明了扩展分形方法在黄土地貌研究中的可行性。