三轴压缩煤岩三维裂隙CT图像重构及体分形维研究

通过对煤岩试件进行常规三轴力学试验,并对破坏后的煤岩试件进行CT扫描,之后将处理过的CT图片导入Mimics10.01进行三维重构,得到了煤岩试件内部裂隙空间的分布情况。另外,利用自编的Matlab程序对煤岩试件的体分形维进行了初步分析。结果表明:煤岩试件在三轴加载条件下主要发生压剪破坏;且围压不同,煤岩试件表现出了特定的力学规律;利用Mimics10.01重构得到的煤岩三维裂隙空间分布情况显示,随着围压的增大,煤岩试件剪切破坏面的连通率和体密度有增大的趋势;体分形维计算的结果显示,煤岩内部破坏越严重,体分形维值越小。

钨镍铜粉体分形维数对烧结密度的影响

钨镍铜复合粉体作为破甲弹药型罩新材料,其烧结密度是影响性能稳定性的关键因素之一。本文通过对还原粉及不同球磨时间的超细粉进行粒度分布测量,分析了体分形维数应用的适用性;通过对还原粉和不同粒度分布的超细粉按质量比75∶25混合后进行烧结及其粒度分布测量,压坯烧结后进行密度测量,探究体分形维数对烧结密度的影响。结果表明:球磨4h以上的超细粉不适合用分形维数表征,钨镍铜粉的粒度分布对其烧结度有一定影响;还原粉与6h球磨粉按75∶25的比例混合时,钨镍铜混粉的烧结密度最高,为17.431g/cm^3,此时混粉的特征粒径为25.689μm,体分形维数为2.339。定量分析粒度分布对烧结密度的影响,得到在现有实验条件下最大烧结密度时的工艺参数,对进一步研究药型罩原料制备,提高破甲弹性能具有一定的参考作用。

冲击作用下粘性土壤破碎体的分形维数与影响因素

给出冲击破碎分析的两倍尺度控制约定,研究粘结态土壤破碎体生成的影响因素,建立了土壤破碎体分形维数与落锤质量、冲击行程、土壤含水率、破碎比能之间的关系。结果表明,土壤破碎体的分形维数与落锤质量及冲击行程没有联系,但分形维数与土壤含水率及破碎比能具有明显的相关性。另外,通过比较得知土壤在冲击作用下的破碎体分形维数远远低于植被土样的分形维数。

采用二维光学图像和三维断层扫描研究单一粒径土壤团聚体的分形特征

分别通过二维光学图像法和三维X射线断层扫描法计算单一粒径土壤团聚体分形维值.土样采自重庆北碚西南大学稻田垄作免耕长期定位试验点,采用湿筛法对土样进行粒径分级,二维分形特征研究的团聚体粒级分别为：〈0.0 5 3,0.0 5 3-0.2 0 0,0.2 0 0-0.4 5 0,0.4 5 0-1.0 0 mm;CT扫描研究所用原状土样粒级分别为：〈0.0 5 3,0.0 5 3-0.0 2 5,0.0 2 5-1,1-2 mm.结果表明：二维光学图像法得到的单一粒径土壤团聚体孔隙分形维值介于1.1 7-1.5 4;三维X射线断层扫描结果显示团聚体中孔隙分形维值在1.3 5-1.6 5之间,团聚体的分形维数介于2.0 6-2.2 0之间,且分形维数随粒径增大而减小.采用二维光学图像和三维断层扫描均可用于定量研究不同粒径土壤团聚体中孔隙的分形特征,而采用三维X-射线断层扫描可以定量描述单一粒径土壤团聚体的分形特征.

子午岭林区植被自然恢复下土壤剖面团聚体特征研究

研究了子午岭林区七种植被类型土壤>0.25 mm水稳性团聚体含量、团聚体破坏率和水稳性团聚体分形维数随植被恢复的变化规律以及这3个指标随土壤有机碳含量增加的变化规律。结果表明:植被恢复对>0.25 mm水稳性团聚体含量、团聚体破坏率和水稳性团聚体分形维数的影响可以达到70 cm土层;除白羊草群落外,0-70 cm土层上>0.25 mm水稳性团聚体含量随植被恢复逐渐提高,团聚体破坏率和水稳性团聚体分形维数随植被恢复逐渐减小,土壤结构随植被恢复逐渐改善。>0.25 mm水稳性团聚体含量、团聚体破坏率和水稳性团聚体分形维数与土壤有机碳之间呈极显著对数相关关系(p=0.01,n=32),当有机碳含量低于18.1 mg/g时,>0.25 mm水稳性团聚体含量随有机碳含量提高而明显提高、团聚体破坏率和水稳性团聚体分形维数则随有机碳含量提高而明显降低,即土壤结构稳定性明显提高;当有土壤机碳含量高于18.1 mg/g,>0.25 mm水稳性团聚体含量、团聚体破坏率和水稳性团聚体分形维数渐趋稳定,即在白羊草、虎榛子、山杨和辽东栎阶段的0-5 cm土层土壤结构达到稳定状态。

广元市不同土地利用类型土壤的分形特征

以8个植被类型、2个农地和2个退耕地的土壤颗粒组成数据为基础，运用分形模型计算这12个土地利用类型土壤颗粒的分形维数，研究了土壤颗粒分形维数与土壤性状的关系。结果表明：（1）12个土地利用类型表层土壤颗粒的分形维数介于2．8185～2．9249之间。与退耕地和玉米地相比，各林地土壤颗粒分形维数小；与1990年的2．8633相比，2006年土壤颗粒分形维数（2．8592）减小；各团聚体分形维数规律不明显。（2）决定土壤颗粒分形维数大小的首先是〈o．002mm的含量，其次是0．05～0．25mm和0．0020．02mm的含量；决定团聚体分形维数大小的粒级含量由大到小的顺序是：2～5mm，0．5～1mm和1～2mm，其余粒级含量对分形维数影响较小。（3）土壤颗粒分形维数与团聚体分形维数可作为侵蚀指标，前者与土壤可蚀性因子相关关系显著，后者也可作为渗透蓄水指标。（4）在坡耕地基础上的退耕地比生态退化后的营林地具有更有利于水土保持的土壤分形特征。

基于分形理论的菱镁矿粉磨程度表征研究

为了研究菱镁矿粉磨程度的定量表征,以辽宁丹东地区菱镁矿为原料,进行了磨矿试验、粒度检测试验、磨矿细度试验,应用分形理论,建立了用于表征粉磨菱镁矿颗粒粒度分布的体分形维数数学关系。结果表明:体分形维数与磨矿细度呈非线性关系,当体分形维数均值达到极大值,即D3=2.4662时,对应的磨矿细度为-0.074 mm含量81.6%,通过浮选试验发现此时浮选指标最好。该研究实现了菱镁矿粉磨程度的定量表征,建立了体分形维数与选矿浮选的联系。

管束列管式静态混合器的结构参数与应用性能研究

管束列管式静态混合器利用管道边壁的边界层作用,强化形成准均匀各向同性涡旋,实现快速混合。通过研究不同结构的管束列管式静态混合器对水处理效果的影响,发现列管总长与管长之比为1∶3、列管段数为3时,管束列管式静态混合器的混合效果最佳。与普通孔板式混合器相比,在相同的操作条件下,管束列管式静态混合器可以节省23%左右的絮凝剂用量,且其絮体分形维数Df和絮体粒径df分别较前者提高了17%和18%,降低沉后水浊度达2.0 NTU以上。

RELATIONSHIP BETWEEN GROWTH AND MORPHOLOGY OF METARRHIZIUM ANISOPLIAE IN BIOTRANSFORMATION OF STEROID

The fermentation with mold metarrhizium anisopliae has been carried out to determine the relationship between mycelial morphology and growth.Like the biomass concentration,the mycelial morphology seems to be coupled to growth phases:the fractal dimension,a feature calculated from the morphological images,increases during the late lag phase and the early exponential phase,and culminates at a value near 2.4 at half of the exponential phase.This can be attributed to the marked change of rough and smooth pellet proportions during growth and the change can be well expressed by the fractal analysis of mycelial morphology.The mycelial morphology is also strongly related to the biotransformation activity:a mycelial sample was withdrawn from the culture to use for fractal analysis before the steroid substrate (16α,17α epoxy 4 pregnene 3,20 dione) was added;the higher fractal dimension corresponds to the higher conversion rate of steroid biotransformation.And the maximum of fractal dimension appeared prior to the maximum of biomass concentration.It is therefore possible to utilize the fractal dimension curve to supervise the fermentation process more timely and availably than to use the conventional biomass curve to do.

Part-level 3-D object classification with improved interpretation tree

For classifying unknown 3-D objects into a set of predetermined object classes, a part-level object classification method based on the improved interpretation tree is presented. The part-level representation is implemented, which enables a more compact shape description of 3-D objects. The proposed classification method consists of two key processing stages： the improved constrained search on an interpretation tree and the following shape similarity measure computation. By the classification method, both whole match and partial match with shape similarity ranks are achieved; especially, focus match can be accomplished, where different key parts may be labeled and all the matched models containing corresponding key parts may be obtained. A series of experiments show the effectiveness of the presented 3-D object classification method.

Fractal character of lenticles and its influence on sediment state in tailings dam

The distribution of tailings lenticles reflects the sediment state of tailing dam, and has a great influence on the stability of the dam. In order to disclose the distribution law of tailings lenticles in theory, 12 geological cross-sections, including 7 cross-sections of tailings dam constructed by the upstream method and 5 cross-sections by the middle line method, were analyzed with box dimension method. The results show that the distribution of tailings lenticles has better fractal character with box dimension from 1.290 7 to 1.513 6. The box dimension of the tailings dam constructed by upstream method is nearly 1.50 and that by middle line method is 1.30. Thereby the values of lenticles dimension have obvious relation to the method of constructing dam, and reflect the sediment state of tailings dam with the rule that smaller value means better state.

Yarn Architecture Analysis of Two-step 3D Braided Composites

A comprehensive study of yarn architecture of two-step rectangle 3D braided composites is presented. Firstly, the braided surface, the shapes of yarns and the intertwining between braider yams and axial yams are analyzed from experimentation. With the microstructure being defined, three levels of unit cell structure are identified, i.e. large unit cell, second unit cell and minimal unit cell. Secondly, based on the minimal unit cell in the interior and on the boundary of the entire cross-section, the deformations of axial yams squashed by braider yams contribute to the increase of the fiber packing factors of axial yams. Finally, the predicted fiber volume fraction of the composites decreases with the increase of linear density of the braider yam and the pitch length. Favorable correlations between the predicted and the experimental results arc found for six groups of the composites.

Cross-scale characteristics of backfill material using NMR and fractal theory

This paper analyzed the pore structure, quantified the pore fractal dimension, calculated the grading index(GI) of mixed aggregate, and studied the relationship among GI, pore structure, and strength to describe the cross-scale characteristics of backfill, which is made from stone powder and cemented tailing. A series of experiments were conducted on stone powder cement tailings backfill(SPCTB). The GI formulas for mixed aggregates, containing stone powder and tailings, were derived based on the Füller theory. The nuclear magnetic resonance(NMR) fractal dimensions of backfills were derived using fractal geometry principles. Compared to the mesopore and macropore fractal dimensions, the correlation between micropore fractal dimension and macro-properties in terms of NMR porosity, pore structure complexity, uniaxial compression strength(UCS), and GI is the most significant. Macropore fractal dimension is generally correlated with UCS and GI and the other properties such as the shape of mixed aggregates also have an impact on fractal dimension. However, mesopore fractal dimension has no obvious relationship with macro-properties. Finally, the relationship between GI and UCS was studied, which contributed to improving backfill’s strength and optimizing gradation.

Fractal dimensions of flocs between clay particles and HAB organisms

The impact of harmful algal blooms （HABs） on public health and related economics have been increasing in many coastal regions of the world. Sedimentation of algal cells through flocculation with clay particles is a promising strategy for controlling HABs. Previous studies found that removal efficiency （RE） was influenced by many factors, including clay type and concentration, algal growth stage, and physiological aspects of HAB cells. To estimate the effect of morphological characteristics of the aggregates on HAB cell removal, fractal dimensions were measured and the RE of three species of HAB organism, Heterosigma akashiwo, Alexandrium tamarense, and Skeletonema eostatum, by original clay and modified clay, was determined. For all HAB species, the modified clay had a higher RE than original clay. For the original clay, the two-dimensional fractal dimension （D2） was 1.92 and three-dimensional ffactal dimension （D3） 2.81, while for the modified clay, D2 was 1.84 and D3 was 2.50. The addition of polyaluminum chloride （PAC1） lead to a decrease of the repulsive barrier between clay particles, and resulted in lower D2 and D3. Due to the decrease of D3, and the increase of the effective sticking coefficient, the flocculation rate between modified clay particles and HAB organisms increased, and thus resulted in a high RE. The fractal dimensions of flocs differed in HAB species with different cell morphologies. For example, Alexandrium tamarense cells are ellipsoidal, and the D3 and D2 of flocs were the highest, while for Skeletonema costatum, which has filamentous cells, the D3 and D2 of flocs were the lowest.

Steady State Properties of One-Dimensional Non-uniform Granular Gases Subjected to Gaussian White Noise Driving

We present a model of non-uniform granular gases in one-dimensional case, whose granularity distribution has the fractal characteristic. We have studied the nonequilibrium properties of the system by means of Monte Carlo method. When the typical relaxation time T of the Brownian process is greater than the mean collision time To, the energy evolution of the system exponentially decays, with a tendency to achieve a stable asymptotic value, and the system finally reaches a nonequilibrium steady state in which the velocity distribution strongly deviates from the Gaussian one. Three other aspects have also been studied for the steady state： the visualized change of the particle density, the entropy of the system and the correlations in the velocity of particles. And the results of simulations indicate that the system has strong spatial clustering; Furthermore, the influence of the inelasticity and inhomogeneity on dynamic behaviors have also been extensively investigated, especially the dependence of the entropy and the correlations in the velocity of particles on the restitute coefficient e and the fractal dimension D.

3-D fracture network dynamic simulation based on error analysis in rock mass of dam foundation

Accurate 3-D fracture network model for rock mass in dam foundation is of vital importance for stability,grouting and seepage analysis of dam foundation.With the aim of reducing deviation between fracture network model and measured data,a 3-D fracture network dynamic modeling method based on error analysis was proposed.Firstly,errors of four fracture volume density estimation methods(proposed by ODA,KULATILAKE,MAULDON,and SONG)and that of four fracture size estimation methods(proposed by EINSTEIN,SONG and TONON)were respectively compared,and the optimal methods were determined.Additionally,error index representing the deviation between fracture network model and measured data was established with integrated use of fractal dimension and relative absolute error(RAE).On this basis,the downhill simplex method was used to build the dynamic modeling method,which takes the minimum of error index as objective function and dynamically adjusts the fracture density and size parameters to correct the error index.Finally,the 3-D fracture network model could be obtained which meets the requirements.The proposed method was applied for 3-D fractures simulation in Miao Wei hydropower project in China for feasibility verification and the error index reduced from 2.618 to 0.337.

北川震裂带柳杉林地土壤功能特性试验分析

汶川地震形成了大面积的震裂带,震裂带内水土流失严重。本文重点从土壤结构体分形维数、有机质含量、土壤抗冲性三个方面探讨了北川震裂带柳杉林地土壤结构功能特性,分析了地震裂隙程度对土壤结构体分形维数、有机质含量、土壤抗冲性的影响及其与土壤深度的相关性。结果表明地震裂隙程度对土壤结构体分形维数影响不显著,而地震3 a后强度裂隙样地土壤有机质含量、抗冲性大于中度裂隙或弱度裂隙样地;各样地土壤有机质含量、抗冲性与土壤深度显著负相关,有机质含量与土壤抗冲性存在显著的正相关关系。

Observation of topological phase with critical localization in a quasi-periodic lattice

Disorder and localization have dramatic influence on the topological properties of a quantum system.While strong disorder can close the band gap thus depriving topological materials of topological features,disorder may also induce topology from trivial band structures,wherein topological invariants are shared by completely localized states.Here we experimentally investigate a fundamentally distinct scenario where topology is identified in a critically localized regime,with eigenstates neither fully extended nor completely localized.Adopting the technique of momentum-lattice engineering for ultracold atoms,we implement a one-dimensional,generalized Aubry-Andrémodel with both diagonal and off-diagonal quasi-periodic disorder in momentum space,and characterize its localization and topological properties through dynamic observables.We then demonstrate the impact of interactions on the critically localized topological state,as a first experimental endeavor toward the clarification of many-body critical phase,the critical analogue of the many-body localized state.

Dimension of Slices Through Fractals with Initial Cubic Pattern

In this paper, the Hausdorff dimension of the intersection of self-similar fractals in Euclidean space R^n generated from an initial cube pattern with an(n-m)-dimensional hyperplane V in a fixed direction is discussed. The authors give a sufficient condition which ensures that the Hausdorff dimensions of the slices of the fractal sets generated by "multirules" take the value in Marstrand's theorem, i.e., the dimension of the self-similar sets minus one. For the self-similar fractals generated with initial cube pattern, this sufficient condition also ensures that the projection measure μVis absolutely continuous with respect to the Lebesgue measure L^m. When μV《 L^m, the connection of the local dimension ofμVand the box dimension of slices is given.

The sloshing of stratified liquid in a two-dimensional rectangular tank

The sloshing of inviscid liquid of stratified density in a rectangular tank is analyzed.As the flow is no longer irrotional,the governing equation is found to be quite different from the Laplace equation used for the liquid of constant density.In particular it contains terms of mixed temporal and spatial derivatives.The problem is solved based on the variable separation method and Laplace transform for the constant Vaisala-Brunt frequency.It is found that the stratification of density may have small effects on those natural frequencies associated with the constant density,but many new natural frequencies have appeared as a result of its effect.