致密砂岩储层孔隙结构分形特征表征方法研究

分形理论为定量表征储层孔隙结构提供了有效手段,但致密砂岩储层孔隙结构复杂,常规孔隙结构分形特征表征方法是否适用需要进一步研究。系统梳理了孔隙结构分形特征表征方法,然后基于致密砂岩压汞曲线对各方法适用性进行了评价,并对致密砂岩储层的分形特征进行了研究。结果表明,分形定义法能够有效表征致密砂岩孔隙结构分形特征,贺成祖法适用于渗透率大于0.1×10-3 μm2的致密砂岩储层,Li Kewen法适用于渗透率小于0.1×10-3 μm2的致密储层,而Brooks⁃Corey法完全不适用于致密砂岩储层。致密砂岩储层在整个孔隙半径区间上具有分形特征,不存在分段分形特征。分形维数是储层评价的重要参数,分形维数越大,储层物性越差,平均孔隙半径越小,排驱压力越大,束缚水饱和度越大。     

仿生叶脉分形微结构表面的平板热管传热性能研究

基于植物叶片的蒸腾作用,以叶脉结构作为蓝本,设计了分形角度为50°、60°、70°、80°、90°的仿叶脉槽道结构,并将其应用于平板热管冷凝端。其中上一级槽道与下一级槽道的长度比、宽度比均为0.7,第一级槽道长度为16.0 mm、宽度为2.0 mm、深度为0.3 mm,并且设置一组未经表面处理的平板热管作为对照。实验结果表明:分形角为80°时性能最优,其冷凝热阻最小可达39.420℃/kW,相比未经表面处理平板热管的热阻降低了40.29%;相对于传统的直槽道结构,置于冷凝端的仿叶脉槽道结构能极大地降低工质流阻,有利于工质回流。     

Relationship of energy to geometry in brittle fracture

Numerous investigators have noticed that there is a relationship between the energy of branching and the energy of initiation during a fracture event in materials that fail in a brittle manner. Usually, this is measured in terms of the stress intensities, i.e., K_B/K_c. The ratio has been reported between 3 and 4, implying a constant value. However, data suggests that it is a constant for a material, but not a universal constant. The fractal dimension of the fracture surface is related to the critical stress intensity factor. It is a measure of the tortuosity of the fracture surface. We show that the K_B/K_C ratio is directly related to the square root of the fractal dimensional increment, indicating a relationship between the energy of crack propagation and the tortuosity of the fracture surface.     

Modified OFS-RDS bat algorithm for IFS encoding of bitmap fractal binary images

This work is an extension of a previous paper (presented at the Cyberworlds 2019 conference) introducing a new method for fractal compression of bitmap binary images. That work is now extended and enhanced through three new valuable features: (1) the bat algorithm is replaced by an improved version based on optimal forage strategy (OFS) and random disturbance strategy (RDS); (2) the inclusion of new similarity metrics; and (3) the consideration of a variable number of contractive maps, whose value can change dynamically over the population and over the iterations. The first feature improves the search capability of the method, the second one improves the reconstruction accuracy, and the third one computes the optimal number of contractive maps automatically. This new scheme is applied to a benchmark of two binary fractal images exhibiting a complex and irregular fractal shape. The graphical and numerical results show that the method performs very well, being able to reconstruct the input images with high accuracy. It also computes the optimal number of contractive maps in a fully automatic way. A comparative work with other alternative methods described in the literature is also carried out. It shows that the presented method outperforms the previous approaches significantly.     

腐蚀管道评定方法研究--对B31G公式的分形修正

对于腐蚀缺陷,应用最为广泛的评定方法是美国ASME B31G规范,在B31G中,将缺陷简化成矩形或抛物线,但实际的腐蚀剖面曲线十分不规则,并且具有近似的自相似嵌套结构,具有分形的特征.文中运用分形理论表征腐蚀缺陷的的剖面曲线,进而求得分形曲线所形成的面积,并用此面积修正B31G公式.实际算例表明,所提的方法是可行的.     

脆性材料中的分形损伤

材料损伤演化过程中的微裂纹分布是分形分布，本文由此探讨了脆性材料损伤演化过程中的分形机理，从纯几何和实验测定分析了损伤演化过程中的分形特征。进而讨论了损伤材料强度中的分形。     

An empirical formulation relating boundary lengths to resolution in specimens showing ‘non-ideally fractal’ dimensions

The concept of fractal dimension offers an elegant basis for the understanding of changes in boundary lengths due to different resolutions. However, in many cases, the usual log-log ‘fractal plot’ does not quite fit the observed data, with most biological structures for instance. An automated boundary following algorithm has been used with an IBAS image analyser on various objects, to evaluate boundary lengths at different magnifications and with a wide range of discrete divider stride lengths on each digitized image. A formula which relates the boundary length to the divider stride length and fits very closely the experimental data has been empirically obtained. Examples are shown with various object boundaries observed by TV-camera, macroscopically or with a light microscope. At different magnifications, the same constants are obtained for a given object, notably a theoretical maximum boundary length (B_m) when the divider stride tends towards zero. The formula allows to calculate a variation of the log-log plot slope which fits very closely the upper convex plots observed when the boundaries do not display an ideally fractal behaviour. Plots derived from the Lineweaver-Burk and Hill ones (used in enzymology) allow a relatively easy graphic determination of the parameters of the proposed formula, which may offer useful criteria for object shape classification, as demonstrated by a biological example. Instead of a true (constant) fractal dimension, it seems that, in many situations, exists a ‘continuous fractal dimensional transition’, inside which an apparently linear segment in a given range of resolution of the usual log-log plot could be explained by asymptotic limits at higher and lower resolutions. The ideal situation with a constant fractal dimension over all resolution ranges could be considered as a limit, achieved when the maximum boundary length (B_m) tends towards infinity.     

Fractal coding of subbands with an oriented partition

We propose a new image compression scheme based on fractal coding of the coefficients of a wavelet transform, in order to take into account the self-similarity observed in each subband. The original image is first decomposed into subbands containing information in different spatial directions and at different scales, using an orthogonal wavelet-generated filter bank. Subbands are encoded using local iterated function systems (LIFS), with range and domain blocks presenting horizontal or vertical directionalities. Their sizes are defined according to the correlation lengths and resolution of each subband. The edge degradation and the blocking effects encountered at low bit-rates using conventional LIFS algorithm are reduced with this approach. The computation complexity is also greatly decreased by a 12:1 factor in comparison to fractal coding of the full resolution image. The proposed method is applied to standard test images. The comparison with other fractal coding approaches and with JPEG shows an important increase in terms of PPSNR/bit-rate. Especially for images presenting a privileged directionality, the use of adaptive partitions results in about 3 dB improvement in PPSNR. We also discuss the distorsion versus rate improvement obtained on high-frequency subbands when fractal coding instead of pyramidal vector quantization is used. Our approach achieves a real gain in PPSNR for low bit-rates between 0.3 and 1.2 bpp.     

网络维数:一种度量复杂网络的新方法

如何对复杂网络进行刻画与度量,一直是人们关注的热点。在研究自相似复杂网络分形维数的基础上,提出了一种度量复杂网络的新方法——网络维数,即复杂网络边权重和的对数值与节点权重和的对数值的比值,可以将边权重及点权重推广到实数域和复数域;同时给出了不同类型权重对应的网络维数的计算方法;最后以几个代表性的经典复杂网络模型为例,讨论了所提出的网络维数的若干性质。