断裂和裂缝的分形特征

在详细剖析断裂和裂缝组成和结构相似性的基础上, 计算了贝尔断陷T₅和T₂两层构造图上断裂信息维和10口井布达特群岩心裂缝信息维, 分析了影响断裂和裂缝信息维的因素, 达到了从断裂信息维去预测裂缝分布的目的.影响断裂和裂缝信息维的因素包括密度、延伸长度、断层性质以及岩性, 但从根本上讲断层性质及岩性对信息维影响体现在断裂的密度上, 因此信息维应该是断裂发育程度的度量, 利用断裂信息维与裂缝信息维关系、裂缝信息维与裂缝密度关系预测裂缝的分布, 有利的裂缝发育带有3个区域, 与现今见油气井分布吻合.      

干旱沙区植被恢复过程中土壤颗粒分形特征

统计分析了干旱沙漠地区植被恢复过程中土壤颗粒分形特征及其与土壤沙粒(>0.05mm)、粉粒(0.05~0.002mm)和粘粒(<0.002mm)含量和土壤养分状况间的关系。结果表明:土壤颗粒分形维数随恢复时间延长有增大的趋势,土壤颗粒分形维数大小与土壤质地的细粒化有一致的变化趋势。0.05mm粒径成为土壤各粒径的分界值--即土壤分形维数的临界粒径,大于这一粒径颗粒含量越高,土壤分形维数越小;而小于这一粒径的颗粒含量越高,分形维数越大。土壤各养分状况均与土壤颗粒分形维数有极显著的线性正相关关系(p<0.0001),表明了土壤颗粒分形维数能客观地反映土壤肥力特征。在干旱沙漠地区,伴随着植被恢复和流沙固定,土壤颗粒分形维数可作为一个评价土壤演变程度的综合定量指标。     

天体运行轨道的背景介质理论导引与自相似分形测度计算的分维微积分基础

通过讨论天体运行背景介质理论的连续轨道及离散轨道这二个研究方向的基础假设,介绍了天体运行轨道的具体方程形式及理论框架概要;进一步地通过讨论天体运行轨道Binet方程的一般形式及其行星近日点进动角的解,给出了连续轨道理论与Newton理论及Einstein广义相对论的联系与区别;通过讨论天体运行轨道的分维扩展方程,给出了包括太阳系行星、天王星卫星、地球卫星、绕月航天器等在内的离散轨道（稳定性轨道）方程及其预言数据.特别地,作为对天体在较为广泛区域作用曲线的初步探讨推论,指出仅由天体引力难以形成质量密度趋于无穷大的理想黑洞.通过讨论一般函数的分维导数的位置假设及幂函数的分维导数的形式假设,进一步明晰了幂函数的分维导数、分维微分及分维积分的具体方程形式,给出分维导数与分数阶导数的区别,随后讨论了基于一般分形测度的分维微积分形式定义导出的自相似分形的测度计算方程具体形式,给出了其与目前Hausdorff测度方法（覆盖方法）的区别,并对包括三分Cantor集合、Koch曲线、Sierpinski垫片及正交十字星形等自相似分形在内的测度进行了计算分析.     

Seafloor Geomorphology and Processes on the Western Continental Margin of India based on Multibeam Acoustic Backscatter Data Analysis

An assessment of the multibeam sonar data of the central Western Continental Margins of India has been carried out to evaluate the seafloor geomorphology and processes by examining the geomorphological attributes e.g., slope, sediments, structures, etc. associated with geomorphic features. The variation in relief and the features located in the region have been mapped and interpreted collectively by utilizing several geospatial mapping tools. The backscatter strength across the area, apparently congruent with the local relief, has helped to examine the sediment movement on the seafloor. The prominent features found in the region include faults, pockmarks, mounds, submarine terraces, and submerged fossil reefs. Several areas with varying topography engender comparable fractal dimension at short scale breaks, and the probability density functions (PDFs) utilizing backscatter data depicting overlapping classes. The present study highlights how fractals and scale break parameters can be utilized to determine the seafloor processes and associated sedimentological dynamics in a complex geographical environment with strong bottom currents, seasonal upwelling, and faulted structure. The role and impact of the various geomorphic processes on the reworking of sediment movement and the overall progression of the seafloor morphology has been revealed for the first time in this part of the ocean bottom.     

基于粒径分维值检验的松散介质渗透系数空间估值——以河北平原为例

为了克服松散含水介质非均质性各向异性对介质渗透系数的求取所带来的困难,以水动力条件为线索,利用互相关法寻找同一时代地层及同一时代地表水的主、次流方向.在主流方向上,建立了石家庄-束鹿-衡水段介质颗粒粒径随距离递变的数学模型,并以此为基础推求无钻孔地段的粒径.同时,运用分形理论,计算了中、上更新统地层主流方向平均粒径空间分布的分维值,并将其作为检验粒径估值正确与否的判据.通过不同岩性的渗透系数-深度模型,实现了用平均粒径预测渗透系数的全过程.     

二维黄金分割法在抗滑桩截面优化设计中的应用

在对抗滑桩截面宽度和截面高度与抗滑桩费用之间的关系进行综合讨论分析的基础上,引入二维黄金分割法与计算机编程方法,编制了专门的计算软件对抗滑桩截面进行优化设计,以实现满足抗滑要求的前提下使单抗滑桩工程总费用达到最低的优化目的.在三峡库区某工程的实例应用表明,该方法具有良好的社会经济效益,对滑坡的治理设计具有较重要的实际应用价值.     

Preconditioned IDR(s) iterative solver for non‐symmetric linear system associated with FEM analysis of shallow foundation

Non‐associated flow rule is essential when the popular Mohr–Coulomb model is used to model nonlinear behavior of soil. The global tangent stiffness matrix in nonlinear finite element analysis becomes non‐symmetric when this non‐associated flow rule is applied. Efficient solution of this large‐scale non‐symmetric linear system is of practical importance. The standard Krylov solver for a non‐symmetric solver is Bi‐CGSTAB. The Induced Dimension Reduction [IDR(s)] solver was proposed in the scientific computing literature relatively recently. Numerical studies of a drained strip footing problem on homogenous soil layer show that IDR(s = 6) is more efficient than Bi‐CGSTAB when the preconditioner is the incomplete factorization with zero fill‐in of global stiffness matrix K_ep (ILU(0)‐K_ep). Iteration time is reduced by 40% by using IDR(s = 6) with ILU(0)‐K_ep. To further reduce computational cost, the global stiffness matrix K_ep is divided into two parts. The first part is the linear elastic stiffness matrix K_e, which is formed only once at the beginning of solution step. The second part is a low‐rank matrix Δ, which is re‐formed at each Newton–Raphson iteration. Numerical studies show that IDR(s = 6) with this ILU(0)‐K_e preconditioner is more time effective than IDR(s = 6) with ILU(0)‐K_ep when the percentage of yielded Gauss points in the mesh is less than 15%. The total computation time is reduced by 60% when all the recommended optimizing methods are used. Copyright © 2013 John Wiley & Sons, Ltd.     

Fractal analysis of long-range paleoclimatic data: Oxygen isotope record of pacific core V28-239

R/S analysis of the oxygen isotope curve of Pacific core V28-239 yields a fractal dimension of 1.22. This value is considered to characterize global climatic change over the last 2 million years as expressed by changing O¹⁸ ratios and confirms that climatic variations are characterized by long-term persistence. The fractal dimension of 1.22 compares favorably with the approximate fractal dimension of 1.26 for annual precipitation records for nine major cities in the United States. Although the precipitation and oxygen isotope data are measured in different physical units and recorded at different time scales, fractal analysis allows for a mathematical comparison of the two phenomena. Additionally, since the fractal dimensions of the oxygen isotope and precipitation records are similar, it is implied that such fractal dimensions are characteristic of climate change over the spectral range of 10 to 10⁶ years. Given this temperature curves based on fractal parameters of long-term O¹⁸ data could be constructed which would allow examination of characteristics of temperature variation over tens and hundreds of years. Such studies may allow the establishment of limits on natural temperature variation and document the persistence of temperature trends through time. If these trends and limits can be resolved, long-range climatic prediction is feasible.     

Dimension and entropy in the soil-covered landscape

Both the Hausdorff dimension and the K-entropy supply a measure of the irregularity of the landspace surface. The relationship between the two measures is investigated over a variety of terrains in Britain and a method of calculating the entropy is checked against an independent estimate of the dimension with reasonable agreement. The calculation of the K-entropy requires that the landscape surface be represented by an homogenous ergodic random field. This condition is satisfied by the tendency of soil-covered terrains to progressively approximate to a form well represented by a Gaussian field. Gaussian random fields can either be very smooth, possessing derivatives of all orders at every point or they are highly irregular and non-differentiable everywhere. Within the regular conceptualization the Rice-Kac theory is used to predict the numbers of crossing points and the extent of excursion sets. These predictions are tested against an example terrain from the High Weald of East Sussex with very good agreement, apart from predictions of local maxima. A worked example of the calculation of the K-entropy is given as an appendix. The potential role of information theory in geomorphology extends beyond the use made of entropy in this investigation. In particular ergodic theory has important practical and theoretical implications.