图像分形维数计算技术

在分形科学的研究中,分形维数的求取方法一直是人们所关注的,本文基于目前常见的图像分形维数的求取方法,对各种方法的计算量,适用范围进行分析和比较,给出推荐模型。     

Structure of Crack in Thermally Dried Sludge Cake

We examined in this work the drying characteristics of wastewater sludge, considering the weight loss using an electronic balance and the morphology change of drying cake by an X-ray micro-computerized tomography scanner (micro-CT). The drying rates for sludge cake was 50-60% of the pure water test. The corresponding micro-CT images were scanned to explore the change in cake volume and development of internal crack over drying. The Otsu's method was applied to bilevel the scanned images, based on which the three-dimensional model for crack's internal structure was reconstructed. The cake porosity and the geometric factors of cracks, such as the compactness, the boundary fractal dimension, and the Sierpinski carpet fractal dimension, were evaluated. The shrinkage of cake volume and the development of internal crack occurred simultaneously. The skin layer formed by the former mechanism retards further drying. On the other hand, the internal cracks were shown to exhibit zigzagging with a noncircular cross section and fractal-like boundary, which should be able to enhance local drying. A possible role of change in crack structure on the rate of drying was discussed.     

一类非线性分形插值曲面的构造与性质

讨论了二元连续函数振幅与变差的性质,并构造了一类非线性多参数迭代函数系;证明了在一定条件下吸引子的唯一性和分形插值曲面的存在性,利用连续函数变差的性质研究了所构造的分形插值曲面的维数,并给出了此类分形插值曲面计盒维数的计算公式.     

Dimension splitting algorithm for a three-dimensional elliptic equation

This paper presents a finite-element dimension splitting algorithm (DSA) for a three-dimensional (3D) elliptic equation in a cubic domain. The main idea of DSA is that a 3D elliptic equation can be transformed into a series of two-dimensional (2D) elliptic equations in the X–Y plane along the Z-direction. The convergence speed of the DSA for a 3D elliptic equation depends mainly on the mesh scale of the Z-direction. P ₂ finite-element discretization in the Z-direction for DSA is adopted to accelerate the convergence speed of DSA. The error estimates are given for DSA applying P ₁ or P ₂ finite-element discretization in the Z-direction. Finally, some numerical examples are presented. We apply the parallel solving technology to our numerical examples and obtain good parallel efficiency. These numerical experiments test and verify theoretical results.     

Texture analysis of poly-adenylated mRNA staining following global brain ischemia and reperfusion

Texture analysis provides a means to quantify complex changes in microscope images. We previously showed that cytoplasmic poly-adenylated mRNAs form mRNA granules in post-ischemic neurons and that these granules correlated with protein synthesis inhibition and hence cell death. Here we utilized the texture analysis software MaZda to quantify mRNA granules in photomicrographs of the pyramidal cell layer of rat hippocampal region CA3 around 1 h of reperfusion after 10 min of normothermic global cerebral ischemia. At 1 h reperfusion, we observed variations in the texture of mRNA granules amongst samples that were readily quantified by texture analysis. Individual sample variation was consistent with the interpretation that animal-to-animal variations in mRNA granules reflected the time-course of mRNA granule formation. We also used texture analysis to quantify the effect of cycloheximide, given either before or after brain ischemia, on mRNA granules. If administered before ischemia, cycloheximide inhibited mRNA granule formation, but if administered after ischemia did not prevent mRNA granulation, indicating mRNA granule formation is dependent on dissociation of polysomes. We conclude that texture analysis is an effective means for quantifying the complex morphological changes induced in neurons by brain ischemia and reperfusion.     

多层大跨度桁框结构体系及优化设计

多层大跨度桁框结构主要由桁架梁和框架柱组成,在我国尚属新型结构体系,为探讨桁框结构合理的经济尺寸和用钢量,进而对结构初步设计提出优化建议;文章针对不同建筑尺寸、不同荷载情况,设计了21个桁框结构模型试件,并进行了用钢量分析,重点探讨了结构用钢量与楼面活载、开间、跨度、跨数、层数的关系。结果表明：多层桁框结构的单位面积用钢量与多层框架结构基本相同,跨度、楼面荷载对用钢量的影响最显著。分析发现桁框结构的经济跨度为18m左右,经济开间为6—10m,跨数不宜少于2跨。     

R/S分析法在大坝安全监测中的应用

R/S分析法可以描述自然界非线性系统的某种复杂性。以某水电站大坝坝顶水平位移为研究对象,采用R/S分析法得到其测点水平位移序列的Hurst指数,并根据Hurst指数在不同区间表现出的不同特性,分析坝顶未来的变化趋势。结果表明:该测点未来位移有较明显的增加趋势,应加强监测,以确保未来大坝的安全运营。     

液体壁面滑移的分子动力学研究

以平行板间液氩的Poiseuille流为例,用分子动力学模拟的方法,对壁面润湿性、外部驱动力以及通道宽度影响液体壁面滑移现象进行了研究.结果表明:在疏水性微通道中,液体的流动存在边界正滑移;在亲水性微通道中,在外力较小时,液体的流动存在边界负滑移,即有类似宏观的边界粘滞层存在,而当外力逐渐增大时,边界滑移从负滑移变为正的滑移.液体在不同宽度的微通道中流动时,绝对滑移长度均随外力的增大而变小,并趋向于定值.研究还发现在不同空间大小的通道中,壁面滑移速度随外力的增大而增大的变化存在拐点,在拐点两侧,界面作用的影响不同.     

层状土入渗试验中指流发育的分形特征及入渗规律

土质结构差异较大的层状土入渗过程中易出现指流.为了了解层状土下层介质对指流发生发育的影响,以三种不同粒径的石英砂为下层介质和以砂壤土为上层介质进行了室内积水入渗的染色示踪试验.结果表明,下层介质粒径越大越易出现指流,且指流行进速度越快.指流发生后,入渗过程趋向于稳定,且下层土壤粒径越大,稳定入渗率与累积入渗量越小.采用湿润面积和湿润比描述指流发育的宏观特性,发现湿润面积和平均湿润比都随时间而增大,表明湿润锋趋于均匀.为定量研究层状土入渗中指流发育的分形特征,采用像素点覆盖法编制了计算染色示踪试验中分形维数发育的Matlab程序,对程序进行了验证并计算了四组试验指流发育的计盒维数.结果表明指流分布具有明显的分形特征,下层介质粒径越大计盒维数越小,且计盒维数随时间而增大.     

基于分形理论的水体富营养状况评价及其验证

在简要介绍分形维数算法的基础上,以乌梁素海2006年5月实测资料为例,初步分析分形理论在水体营养状况评价中的适用性;将基于分形理论的评价结果与国家环境保护部推荐使用的综合营养状态指数法评价结果进行比较分析。结果表明:在对22个采样点的评价中,二者评价的一致性达到91%。两种方法的评价结果仅有两个采样点不同。从全湖的评价结果看,乌梁素海已经达到富营养重富营养水平,与已有的研究成果相一致。评价结果充分说明分形维数法可以应用于乌梁素海的富营养化评价研究,但其在其他水体的普适性尚待进一步验证。另外,分析了分形理论在水体营养状况评价研究中存在的问题和不足,并对未来的发展趋势进行展望。