Dynamics of the Magnetic Flux Trapped in Fractal Clusters of a Normal Phase in Percolative Superconductors

The effect of the fractal clusters of a normal phase, which act as pinning centers, on the dynamics of magnetic flux in percolative type-II superconductor is considered. The main features of these clusters are studied in detail: the cluster statistics is analyzed; the fractal dimension of their boundary is estimated; the distribution of critical currents is obtained, and its peculiarities are explored. It is found that there is the range of fractal dimension where this distribution has anomalous statistical properties, specifically, its dispersion becomes infinite. It is examined how the finite resolution capacity of the cluster geometric size measurement affects the estimated value of fractal dimension. The effect of fractal properties of the normal phase clusters on the electric field arisen from magnetic flux motion is investigated for the cluster area distribution of different kinds. The voltage-current characteristics of fractal superconducting structures in the resistive state are obtained for an arbitrary fractal dimension. It is revealed that the fractality of the boundaries of the normal phase clusters intensifies the magnetic flux trapping and thereby raises the critical current of a superconductor.     

SiCw/Al-Al3Ni复合材料断口的分维特征

本文所研究的复合材料,其基体Al-Al₃Ni合金具有很好的组织热稳定性,因而可以通过改变拉伸温度并在组织结构基本不发生变化的情况下,使材料的分维和断裂功发生变化.分维的测量采用断口轮廓法(FPM).研究结果指出,SiCw/Al-Al₃Ni复合材料的分维可分为三部分,每部分分维存在的尺寸范围与组织结构有一定的对应关系.文中还讨论了断裂功与分维之间的关系.     

在共混物界面研究中分数维的物理意义

讨论了在共混物界面研究中分数维的物理意义,指出它是反映共混物界面特征的态函数。     

晶粒度的分形特征研究

测量了标准图谱中铁素体晶粒度图形有分形维数。考察了晶粒度与分维之间的关系。结果表明,金属晶粒可用分形维数定量描述。在１～８级晶粒度内,随着晶粒度级别的提高,分维数值逐渐增大,其中以１～５级内增大得最为显著。     

金属断裂表面分形维数与组织、性能之间的关系

借助分形研究了拉伸条件下,分形维数 D_F 与拉伸性能之间的关系,讨论了显微组织对分形维数的影响,并把冲击韧性与分形维数之间的关系和拉伸性能与分形维数之间的关系进行了比较。实验结果表明,拉伸性能与分形维数只存在定性关系。延伸率与分形维数成正比,强度σ_b、σ_s与分形维数成反比,显微组织对分形维数有重要影响。断裂方式对分形维数、断裂性质以及两者的对应关系也有重要影响。     

基于分形理论的CFRP布增强混凝土梁抗弯性能研究

在实验室模拟酸雨腐蚀环境,完成了普通混凝土梁与CFRP布增强混凝土梁的抗弯试验,得到了各级荷载作用下构件表面裂缝的分布与演化过程,验证了受腐蚀CFRP布增强混凝土梁表面裂缝分布的分形特征。基于分形理论分析了受腐蚀混凝土梁在弯曲荷载作用下的开裂及破坏过程,详细讨论了梁表面裂缝的分形维数与其抗弯性能参数(损伤深度、混凝土强度、一阶频率、极限承载力、跨中挠度、位移延性系数)之间的关系。研究表明裂缝分形维数随着损伤深度的增加而减小,CFRP布增强混凝土梁的分形维数大于普通混凝土梁,其分形维数变化率与构件承载力变化率之间存在线性关系;因此梁表面裂缝分布的分形特征可作为CFRP布增强混凝土受弯构件损伤程度的衡量指标的观点,可为今后对“在役混凝土结构承载力和寿命预测的研究”提供参考。     

断口定量分析的分形几何方法

近几年来,分形(fractal)几何已广泛地应用于材料的断裂分析。本文简要介绍了分形几何的发展概况及其几个主要定义,分析了一些简单不规则图形的分形维数的计算。把断口形貌统计地看作分形表面,进行了材料的断口的分析分析。根据断口的分形维数,人们可能去定量地追溯材料断袭时的力学行为。     

Matrix Crack Detection in Composite Plate with Spatially Random Material Properties using Fractal Dimension

Fractal dimension based damage detection method is investigated for a composite plate with random material properties. Composite material shows spatially varying random material properties because of complex manufacturing processes. Matrix cracks are considered as damage in the composite plate. Such cracks are often seen as the initial damage mechanism in composites under fatigue loading and also occur due to low velocity impact. Static deflection of the cantilevered composite plate with uniform loading is calculated using the finite element method. Damage detection is carried out based on sliding window fractal dimension operator using the static deflection. Two dimensional homogeneous Gaussian random field is generated using Karhunen-Loeve (KL) expansion to represent the spatial variation of composite material property. The robustness of fractal dimension based damage detection method is demonstrated considering the composite material properties as a two dimensional random field.     

Depinning at the initial stage of the resistive transition in superconductors with a fractal cluster structure

The effects of the initial dissipation of the energy in a superconductor containing fractal clusters of a normal phase are considered. In the interval of currents preceding the resistive transition, an increase in the fractal dimension of clusters leads to an increase of the sample resistance and widening of the region of initial dissipation in the current-voltage characteristic. This is caused by an increase in the density of free vortices broken away from the pinning centers when the current flows. Dependences of the density of vortices on the fractal dimension of cluster boundaries are found for various values of the transport current.     

钛酸钾晶须增韧尼龙66及其断面分形研究

钛酸钾晶须用弹性体表面改性后实现了对尼龙66的有效增韧,改性剂 氧树脂用量为晶须的1．5％（质量）时,复合体系的冲击强度比纯尼66提高132％,同时弯曲,拉伸强度分别提高55％和48％,采用显微图像灰度法,对晶须增韧尼龙进行了基于断面小岛周长－面积关系的分形研究,考察了小岛选取对断面分维数测量结果的影响,研究表明,测得的分维数随选取小岛的面积阈值增加而增大,面积阈值达500η^2(η为侧量码尺）后,分维数趋于稳定,晶须增韧尼龙的力学强度与材料断面分维数之间的变化规律一致,对于从材断断裂机制与断面形貌进行了解释。     

DETERMINATION OF THE FRACTAL DIMENSIONS OF COAL FILTER CAKES AND THEIR RELATIONSHIP TO CAKE PERMEABILITY

The permeabilities of various fine coal filter cakes were related to cake microstructure through micrographically measured fractal dimensions. Two other porous systems, consolidated glass beads and CaCO₃ crystal filter cake, were also analyzed for comparison. A variety of coal mesh sizes were examined spanning a reasonable range of permeability The fractal dimension was determined using the dilation function of the image analyzer. This fractal dimension was then related to the Kozeny parameter, K', using experimentally measured porosity and permeability, and micrographically measured specific surface. Finally, with K' as a unique function of fractal dimension, permeabilities were estimated using the Carman-Kozeny equation. Calculated values were in good agreement with experimentally determined values considering the simplicity and direct nature of the approach.     

分形理论在聚合物共混物界面研究中的应用

聚合物界面奶难加以定量描述,采用一种图形变换的方法可以将界面复杂状态转换成几何特征加以描述,文中基于分形理论及ｎ维分形布朗运动,提出用分形数来描述聚合物界面的状态。     

双相钢疲劳断口的分形分析

本文研究了双相钢疲劳门槛值与门槛值附近断口形貌和分形维数的关系。初步实验结果表明:分形维数基本上能反映断口粗糙度。发现门槛值随分形维数呈线性变化,门槛值、分形维数和粗糙度都随马氏体含量呈抛物线型变化。     

Fractal dimension of the surface of porous ceramic materials

The fractal dimension D of the surface of porous ceramic materials has been determined. The dependence of D on the total porous space volume exhibits two bending points, which reflects a change in the character of porosity on the passage from isolated pores to connected pore clusters and to very large pores with smooth boundaries. This behavior reveals a correlation between the fractal dimension and some well-known features in the properties of porous solids.     

The pinning enhancement upon the magnetic flux trapping in the clusters of a normal phase with fractal boundaries

The phenomenon of magnetic flux trapping in a hard superconductor with the normal phase clusters acting as the pinning centers is considered. The critical current distribution for the clusters of an arbitrary fractal dimension is determined. The fractal character favors the magnetic flux trapping, thus increasing the critical current.     

Vortex dynamics at the initial stage of resistive transition in superconductors with fractal cluster structure

The effect of fractal normal-phase clusters on vortex dynamics in a percolative superconductor is considered. The superconductor contains percolative superconducting cluster carrying a transport current and clusters of a normal phase, acting as pinning centers. A prototype of such a structure is YBCO film, containing clusters of columnar defects, as well as the BSCCO/Ag sheathed tape, which is of practical interest for wire fabrication. Transition of the superconductor into a resistive state corresponds to the percolation transition from a pinned vortex state to a resistive state when the vortices are free to move. The dependencies of the free vortex density on the fractal dimension of the cluster boundary as well as the resistance on the transport current are obtained. It is revealed that a mixed state of the vortex glass type is realized in the superconducting system involved. The current-voltage characteristics of superconductors containing fractal clusters are obtained and their features are studied.     

The giant dispersion of critical currents in a superconductor with fractal clusters of a normal phase

The influence of fractal clusters of a normal phase on the dynamics of a magnetic flux trapped in a percolation superconductor is considered. The critical depinning current distribution and the current-voltage characteristics of fractal superconducting structures in the resistive state are determined for an arbitrary fractal dimension of the cluster boundaries. The interval of fractal dimensions is found in which the dispersion of critical currents exhibits unlimited growth. It is established that the fractality of clusters favors a decrease of the electric field arising during the magnetic flux motion, thus increasing the critical current value. The region featuring the giant dispersion of critical currents can be expected to provide for the maximum current-carrying capacity of a superconductor.     

二维广义Ginzburg-Landau方程在Banach空间的指数吸引子

在本文中,我们在Banach空间考虑二维广义Ginzburg-Landau方程的指数吸引子,且得到其分形维度估计。     

Peculiarities of the resistive transition in fractal superconducting structures

The influence of fractal clusters of a normal phase on the current-voltage characteristics of a percolation superconductor in the region of a resistive transition has been studied. The clusters appear as aggregates of columnar defects, the presence of which leads to a correlated microscopic disorder in the system. Dependences of the static and dynamic resistance on the transport current are determined for an arbitrary fractal dimension of the cluster boundaries. In the case under consideration, the superconducting system features a mixed state of the vortex glass type.     

壳聚糖的分维模拟及自组装复合膜的制备与表征

用原子力显微术及计算机模拟计算研究了壳聚糖的分形维数,壳聚糖与肝素形成的自组装复合膜。对壳聚糖的分形维数的模拟计算表明,壳聚糖胶粒堆积程度越高,其分形维数越小．利用两种方法即层层自组装法和混合成膜法制备了壳聚糖／肝素的复合膜,与后一方法所制备的膜相反,前一方法制备的膜的表面颗粒虽然较小但平均粗糙度较大。原子力显微术是生物大分子分形表征、生物膜表征的有力工具。