Improving the efficiency of magnetic coupling energy transfer byetching fractal patterns in the shielding metals

Thin metal sheets are often located in the coupling paths of magnetic coupling energy transfer(MCET) systems. Eddy currents in the metals reduce the energy transfer efficiency and can even present safety risks. This paper describes the use of etched fractal patterns in the metals to suppress the eddy currents and improve the efficiency. Simulation and experimental results show that this approach is very effective. The fractal patterns should satisfy three features, namely, breaking the metal edge, etching in the high-intensity magnetic field region, and etching through the metal in the thickness direction. Different fractal patterns lead to different results. By altering the eddy current distribution, the fractal pattern slots reduce the eddy current losses when the metals show resistance effects and suppress the induced magnetic field in the metals when the metals show inductance effects. Fractal pattern slots in multilayer high conductivity metals(e.g., Cu) reduce the induced magnetic field intensity significantly. Furthermore, transfer power, transfer efficiency, receiving efficiency, and eddy current losses all increase with the increase of the number of etched layers. These results can benefit MCET by efficient energy transfer and safe use in metal shielded equipment.

Formation and growth of fractal patterns in high energy P^+-implanted silicon and N+Zn-implanted SiO_2/GaAsP during thermal annealing

The fractal patterns in implanted samples are observed. Possible correlation of fractal patterns with the annealing temperature and the electrical activation ratio are given. The formation and growth process of fractal patterns are compared for implanted layers both in silicon and in SiO2/GaAsP during thermal annealing. The mechanism of formation and growth process of fractal pattern is discussed.

Fractal Pattern of Gravity Fields and Its Appfication in Bouger Density Determination

1 Introduction In order to calculate the Bouguer gravity anomaly, the average density (Bouguer density) for the topography whose gravitational influence is to be removed must first be computed. A common approach is to estimate this density by minimizing the resulting correlation of the Bouguer gravity anomaly with the topography or other similar but more easily calculated quantities. The underlying assumption of these methods is that the topography is supported by a rigid crust rather than by

Multifractal Simulation of GeochemicalMap Patterns

Using a simple multifractal model based on the model De Wijs, various geochemical map patterns for element concentration values are being simulated. Each pattern is self-similar on the average in that a similar pattern can be derived by application of the multiplicative cascade model used to any small subarea on the pattern. In other experiments, the original, self-similar pattern is distorted by superimposing a 2-dimensional trend pattern and by mixing it with a constant concentration value model. It is investigated how such distortions change the multifractal spectrum estimated by means of the 3-step method of moments. Discrete and continuous frequency distribution models are derived for patterns that satisfy the model of De Wijs. These simulated patterns satisfy a discrete frequency distribution model that as upper bound has a continuous frequency distribution to which it approaches in form when the subdivisions of the multiplicative cascade model are repeated indefinitely. This limiting distribution is lognormal in the center and has Pareto tails. Potentially, this approach has important implications in mineral and oil resource evaluation.

Introduction of Multiscaled Longitudinal Vortices by Fractal-Patterned Surface Roughness

To determine the type of surface roughness pattern that is suitable for adaptive suppression of the drag of an obstacle, we observed flow structures introduced by such obstacles. Several roughness patterns were tested: geometric patterns, fractal patterns, reptile-skin patterns, and patterns of circular cylinders arranged in a lattice and in a zigzag manner. A suitable pattern for adaptive control of flow is one that generates longitudinal vortices with nonconstant distances. The preferred instability mode of a laminar boundary layer is expected to be selected automatically from fluctuations involving many frequencies and caused by fractal patterns. Snake- and reptile-skin patterns may have a similar ability as fractal patterns because they consist of multiscale patterns. The longitudinal vortices generated from peculiar positions and concave corners in patterns were observed. The distance between these vortices is not constant because the onset of vortices is at concave corners in fractal patterns. These vortices have differing strengths and easily cause nonlinear interactions, so they can disturb a laminar boundary layer with several higher-harmonic frequencies. The velocity profiles of the laminar boundary-layer flow over the fractal patterns were measured by using hydrogen bubbles. The results show the down-wash flow between the longitudinal vortices, which means that the vortices may effectively suppress the boundary layer separation in an adverse pressure gradient.

Fractal features of soil profiles under different land use patterns on the Loess Plateau, China

Fractal theory is becoming an increasingly useful tool to describe soil structure dynamics for a better understanding of the performance of soil systems. Changes in land use patterns significantly affect soil physical, chemical and biological properties. However, limited information is available on the fractal characteristics of deep soil layers under different land use patterns. In this study, the fractal dimensions of particle size distribution（PSD） and micro-aggregates in the 0–500 cm soil profile and soil anti-erodibility in the 0–10 cm soil profile for 10 typical land use patterns were investigated in the Zhifanggou Watershed on the Loess Plateau, China. The 10 typical land use patterns were： slope cropland, two terraced croplands, check-dam cropland, woodland, two shrublands, orchard, artificial and natural grasslands. The results showed that the fractal dimensions of PSD and micro-aggregates were all significantly influenced by soil depths, land use patterns and their interaction. The plantations of shrubland, woodland and natural grassland increased the amount of larger micro-aggregates, and decreased the fractal dimensions of micro-aggregates in the 0–40 cm soil profile. And they also improved the aggregate state and aggregate degree and decreased dispersion rate in the 0–10 cm soil profile. The results indicated that fractal theory can be used to characterize soil structure under different land use patterns and fractal dimensions of micro-aggregates were more effective in this regard. The natural grassland may be the best choice for improving soil structure in the study area.

Rhythmic precipitate patterns and fractal structure

Liesegang patterns of parallel precipitate bands are obtained when solutions containing co-precipitate ions interdiffuse in a 1D gel matrix.The sparingly soluble salt formed,displays a beautiful stratification of discs of precipitate perpendicular to the 1D tube axis.The Liesegang structures are analyzed from the viewpoint of their fractal nature.Geometric Liesegang patterns are constructed in conformity with the well-known empirical laws such as the time,band spacing and band width laws.The dependence of the band spacing on the initial concentrations of diffusing（outer）and immobile（inner）electrolytes（A0 and B0,respectively）is taken to follow the Matalon-Packter law.Both mathematical fractal dimensions and box-count dimensions are calculated.The fractal dimension is found to increase with increasing A0 and decreasing B0.We also analyze mosaic patterns with random distribution of crystallites,grown under different conditions than the classical Liesegang gel method,and report on their fractal properties.Finally,complex Liesegang patterns wherein the bands are grouped in multiplets are studied,and it is shown that the fractal nature increases with the multiplicity.

Visitor flow pattern of Expo 2010

Expo 2010 Shanghai China was a successful, splendid, and unforgettable event, leaving us with valuable experi- ences. The visitor flow pattern of the Expo is investigated in this paper. The Hurst exponent, the mean value, and the standard deviation of visitor volume indicate that the visitor flow is fractal with long-term stability and correlation as well as obvious fluctuation in a short period. Then the time series of visitor volume is converted into a complex network by using the visibility algorithm. It can be inferred from the topological properties of the visibility graph that the network is scale-free, small-world, and hierarchically constructed, confirming that the time series are fractal and a close relationship exists among the visitor volumes on different days. Furthermore, it is inevitable that will be some extreme visitor volumes in the original visitor flow, and these extreme points may appear in a group to a great extent. All these properties are closely related to the feature of the complex network. Finally, the revised linear regression is performed to forecast the next-day visitor volume based on the previous 10-day data.

Growth pattern of reed in Caogang Lake,Huanghuaihai Plain,China

The researches about reed growth were mainly concentrated on seasonal dynamics, investigation of reed resource, and comparison of different ecotypes of reed. By means of fractal geometric theory of non linear science, the fractal character of growth pattern of reed, for the purpose of quantitatively exploring the mechanism of reed growth was studied. The way to calculate fractal dimension of reed growth is box dimension (BD) and information dimension (ID). The results showed that the difference between two samplings in May and those among three samplings in June and later were not remarkable for both BD or ID. It was noted that the difference between samplings in and after May is significant. It was demonstrated that the fractal dimension of size distribution of reed ranged from 0 6235 to 0 8761 The distribution pattern could be statistically divided as two significant periods: the size of reed is quite well distributed at the beginning of reed growth (fractal dimension>0 8), but is irregular in the middle and later growth season (fractal dimension<0 7). These results are benefit to reach the goal of rational use of reed resources and to protect the biodiversity in wetland ecosystem.

Experimental studies on the evolution process of microcrack patterns in concrete samples con-taining hard inclusions

Under biaxial pressure, the microcrack patterns of concrete samples with hard inclusion are as followings: Microcracks generate around the sample at the early pressured period, and gap is formed in the middle part with the increase of σ 1; microcrack gap is becoming smaller gradually with σ 1 increase again; microcracks become active within the original gap, but they in an original active area become small. Approaching the main fracture, microcracks form as a belt and jump back and forth in the belt. The spatial fractal D s of microcracks changes from small to big, but turns decrease when approaching the main fracture. All of the features were seldom mentioned in the past experiment, however, which have some similarities with the long seismicity patterns before strong earthquakes. In this paper, Lancang Gengma earthquake was taken as an example to analyse.〖KH*2D]

Dense Fractal Networks, Trends, Noises and Switches in Homeostasis Regulation of Shannon Entropy for Chromosomes’ Activity in Living Cells for Medical Diagnostics

We analyze correlations and patterns of oxidative activity of 3D DNA at DNA fluorescence in complete sets of chromosomes in neutrophils of peripheral blood. Fluorescence of DNA is registered by method of flow cytometry with nanometer spatial resolution. Experimental data present fluorescence of many ten thousands of cells, from different parts of body in each population, in various blood samples. Data is presented in histograms as frequency distributions of flashes in the dependence on their intensity. Normalized frequency distribution of information in these histograms is used as probabilistic measure for definition of Shannon entropy. Data analysis shows that for this measure of Shannon entropy common sum of entropy, i.e. total entropy E, for any histogram is invariant and has identical trends of changes all values of E (r) = lnr at reduction of rank r of histogram. This invariance reflects informational homeostasis of chromosomes activity inside cells in multi-scale networks of entropy, for varied ranks r. Shannon entropy in multi-scale DNA networks has much more dense packing of correlations than in “small world” networks. As the rule, networks of entropy differ by the mix of normal D 2 and abnormal D > 2 fractal dimensions for varied ranks r, the new types of fractal patterns and hinges for various topology (fractal dimension) at different states of health. We show that all distributions of information entropy are divided on three classes, which associated in diagnostics with a good health or dominants of autoimmune or inflammatory diseases. This classification based on switching of stability at transcritical bifurcation in homeostasis regulation. We defined many ways for homeostasis regulation, coincidences and switching patterns in branching sequences, the averages of H&ouml;lder for deviations of entropy from homeostasis at different states of health, with various saturation levels the noises of entropy at activity of all chromosomes in support regulation of homeostasis.

Stimulation Therapies and the Relevance of Fractal Dynamics to the Treatment of Diseases

This paper provides an overview of the conventional therapeutic stimulation methodologies and proposes a more effective stimulation approach based on a consideration of the inherently fractal nature of normal biological dynamics. There are varying forms of physiological stimulations including the use of electrical currents, electromagnetic fields, temperature change, ultrasound, light and so forth. These stimulation therapies can be categorized into three main modalities: electrical stimulation modalities, thermal modalities, and non-thermal modalities. Electrical stimulation modalities include therapeutic techniques where electrical current is directly applied to the body of treated subject. Direct application of electrical current to the brain also falls under this category. Thermal modalities consist of stimulations that induce temperature change on the body for therapeutic effects without the direct transfer of electrical current. Non-thermal modalities functions through energy transfer without directly applying electrical current and without the effects of temperature change. A fourth miscellaneous category for stimulation techniques consists of the stimulation effects of music along with physical stimulation as in massage therapy. Common to most of these therapeutic strategies is that the stimulation is delivered at certain fixed periods or frequencies. We introduce some rudiments of fractal dynamics, and the notions of self-similarity, scale-invariance, and long-range correlation or memory in the dynamics of a system. We present evidence that fractal dynamics is commonly observed in healthy physiological systems while unhealthy systems are shown to veer away from fractal dynamics towards periodic or random motion. This difference in dynamics can be observed in many biological signals such as in neural activity, heart rate variations, and breathing patterns. We propose that an optimal stimulation technique should thus be one that encourages an unhealthy, non-fractal pathological system towards a healthy, fractal dynamic. Given the ubiquity of fractality in healthy biological dynamics, we argue that a fractal pattern of stimulation is a more optimal approach to functional restoration than the widely used conventional periodic stimulation, which may further consolidate the existing pathological dynamics.

基于分形图案的透孔织物的设计和开发

为了丰富花式透孔织物的花纹种类,利用平纹和透孔组织的特点,采用分形图案设计,将平纹和简单透孔组织结合,形成有规律的花式透孔组织图案,以谢尔宾斯基地毯图案作为花式透孔组织的分形图案纹样,进行花式透孔织物的组织设计、上机设计及工艺参数设计等,并进行试织。结果得出:采用谢尔宾斯基地毯图案作为分形图案进行纹样设计,使平纹和透孔组织形成的花式透孔组织图案更有规律性,同时纹样新颖,具有装饰性,分形图案的使用也为多组织组合形成多种类的透孔花纹图案提供了新思路。

Fractal geometry and topology abstracted from hair fibers

Based on the concepts of fractal super fibers, the （3, 9＋2）-circle and （9＋2, 3）-circle binary fractal sets are abstracted form such prototypes as wool fibers and human hairs, with the （3）-circle and the （9＋2）-circle fractal sets as subsets. As far as the （9＋2） topological patterns are concerned, the following propositions are proved： The （9＋2） topological patterns accurately exist, but are not unique. Their total number is 9. Among them, only two are allotropes. In other words, among the nine topological patterns, only two are independent （or fundamental）. Besides, we demonstrate that the （3, 9＋2）-circle and （9＋2, 3）-circle fractal sets are golden ones with symmetry breaking.

水力耦合下煤样声发射分形−渗透率模型及试验研究

煤样轴向应力加载-水压渗流作用下裂隙(孔隙)发展直接影响煤样试件的力学指标与渗流特性,文中通过理论解析与力学试验方法,分析了煤样试件裂隙(孔隙)主导下渗透率与声发射分形维数、振铃计数响应关系,建立了水力耦合作用下煤样声发射分形-渗透率模型,开展了不同围压(2~5 MPa,Δpw(渗透压)/p'c(围压)=0.75)下水力耦合煤样渗流试验,分析了不同围压(水压)下煤样试件的力学行为、声发射规律与渗流特征,探讨了不同围压下煤样试件的强度提升特点与破坏形态-声发射定位关系,验证了水力耦合下煤样试件的声发射分形-渗透率模型合理性。结果表明:煤样试件渗流试验中裂隙(孔隙)变化与声发射振铃具有一致性,裂隙(孔隙)扩展与声发射分形维数、渗透率密切相关,声发射分形、渗透率可用体积应变表征,基于声发射分形的水力耦合下煤样试件的声发射分形-渗透率模型可采用2段式数学模型解析;煤样渗流全应力-应变过程中渗透率表现为短时减少—长时缓慢增加—急速增加—小幅回落过程,振铃计数呈快速增加—减少—增加—减少波浪型发展,渗透率最小值滞后体积应变压缩与膨胀临界点,最小渗透率变化在0.124×10^(-17)~1.250×10^(-17)m^(2);随着围压(2~5 MPa)增加,煤样峰值偏应力、峰值轴向应变与峰值体积应变均呈增大趋势,线性特征显著,煤样峰值渗透率滞后峰值强度呈减小趋势,减幅达到93.34%,最大声发射振铃计数(对应峰值强度位置)表现为增加趋势;水力耦合下煤样试件有效黏聚力和有效内摩擦角分别提高到6.5116 MPa与36.56º,随着围压(2~5 MPa)增加,煤样试件的声发射信息由单斜面向不规整斜面过渡,主控破裂面角度由小角度向高角度转变,失稳由单块体剪切变为多块体压缩形态,试件破裂可采用声发射定位振铃计数表达;煤样试件声发射分形-体积应变、渗透率与体积应变、分形与渗透率3个试验曲线与理论曲线较为吻合,围压2~5 MPa试件压缩阶段相关性分别在0.882~0.999、0.950~0.998与0.849~0.997,围压2~5 MPa试件膨胀阶段相关性0.937~0.996、0.891~0.998与0.873~0.966。

基于参数化技术的图案设计综述

参数化、变量化技术是学术界、产业界的一个交叉学科研究热点。分析了包括形状语法、分形理论、数学模型等参数化图案设计的理论和方法,讨论与比较了建筑、产品以及图案设计3个领域的参数化设计语言。在此基础上,总结了在理论算法、设计流程以及参数化软件方面的共性,为图案设计的发展与多样性提供新的驱动力。针对服装图案特性,研究了参数化技术的应用现状与难题,提出了参数化技术在图案设计领域未来的发展方向。

强降雨作用下引入分形理论的浅层边坡入渗及稳定性分析

为探究降雨过程中土体实际入渗能力动态变化对边坡降雨入渗规律及其稳定性的影响,从土体级配特征的角度出发,首先基于分形理论推导了不同级配特征土体的饱和渗透系数分析模型;进一步考虑入渗区椭圆形过渡带的影响,根据不同降雨历时下过渡带与入渗区的厚度比例关系对入渗区等效渗透系数进行实时修正,提出了不同级配特征土体的改进GA入渗模型;最后,基于改进GA入渗模型建立了考虑土体抗剪强度随级配特征及降雨时间变化的浅层边坡稳定性分析修正模型。与已有结果对比表明建立的模型能够准确地表征降雨过程中土体入渗状态及剪切强度变化特征。参数分析表明:土体孔隙分布特征与饱和渗透系数具有明显的正相关关系,其直接影响坡体水分剖面分布及坡面径流出现时间;湿润峰推移速率随坡体初始含水率的增大而加快,致使相同降雨历时下入渗区过渡带占比减小,进而实时影响入渗区等效渗透系数;坡体过渡带稳定性受土体级配特征及初始含水率的影响较为显著,坡体容易在过渡带发生失稳破坏。故在强降雨作用下边坡的失稳分析中,需额外注意入渗区过渡带的稳定性。

上游法筑坝尾矿沉积规律及固结情况预测

以马家田尾矿库为工程背景,通过现场钻探取样进行室内颗分实验,结合尾砂结构特征、“分形-分维”理论进行综合分析,研究尾矿颗粒在整体沉积过程中的沉积规律,并以研究的沉积规律为理论依据,将尾矿库划分为6个固结区,对尾矿库固结程度进行计算与预测。研究结果表明:尾矿库坝前多沉积尾粉砂,坝尾多沉积尾粉质黏土,呈“坝前粗、坝中粗细交替、坝尾细”的沉积特征。尾矿颗粒在垂向上呈“下细上粗”、水平上呈“由粗到细”的沉积规律。尾矿粗细颗粒含量整体分布均匀,其中,粗粒尾矿的中值粒径d_(50)变化有规律,细粒尾矿的中值粒径d_(50)变化规律不明显,尾粉土分选差异性较大。尾矿库的主固结已完成,次固结相对变形较小,且最小固结度为0.27。

基于Julia集的潮汕抽纱装饰纹样分形设计

分形普遍存在于自然环境的微观之中,在农业上常用于土壤特征与农作物结构等的分析。分形图案因其生于自然的特点,在解释自然结构的同时具有艺术性,与传统植物纹样搭配相适应。农作物作为潮汕抽纱纹样的主要题材,文章提出基于Julia集的潮汕抽纱植物装饰纹样分形设计模型,试图更好地实现潮汕抽纱数字化,提供符合当下审美的分形纹样设计,缓解自20世纪90年代工业化冲击后,抽纱从业人员凋零,缺乏从事其纹样设计人员的现状。通过对葡萄、麦穗、花卉等纹样进行归类与分形维度的计算,总结潮汕抽纱植物纹样的分形特征,应用分形艺术软件UF6完成分形纹样设计,与传统潮汕抽纱植物纹样遵循类别、形制进行组合。最后,针对青年群体进行模型输出结果的问卷调研,从民族性、创新性、艺术性、喜爱度验证分形引入潮汕抽纱的可行性,并邀请非遗工作者从生产角度做出评价。结果表明:潮汕抽纱可通过分形设计扩充新的纹样素材,青年群体希望潮汕抽纱能以局部装饰的形式融入日常应用的产品中。在生产上,根据应用于织品、印刷等不同需求,对分形纹样的复杂程度作出考量或简化,为刺绣织品图案的创新设计提供参考,展现分形通过农业所表现的艺术性。

分形理论在木材美学图案设计中的应用

木材花纹的自然属性决定了分形几何是用来描述木材花纹形态的最有力的武器之一,分形理论对于美学艺术研究具有深远意义。通过对分形几何的理论和特点进行研究,分析分形设计美学特征,导入红木木材宏观、微观构造图案进行设计,得到具有美学价值的纹理设计图案。以分形维数较高的檀香紫檀微观木材纹理构造图像为素材,应用Ultra Fractal 6分形软件对檀香紫檀构造图像进行分形设计,从而生成3种木材美学图案,再进行艺术设计得到具有规律与秩序感花纹图案,使之更具有装饰性,充分利用木材的非物质属性,丰富人们的精神文化生活,充分展现红木木材美学的应用价值。