Percolation, Fractal Behavior, and High-Tc Superconductivity

Hole suppliers like Sr in doped La₂CuO₄ are mainly randomly distributed. Assuming that the holes are dislocated over a few lattice constants away from the Sr atom, the conducting areas form randomly distributed circles in the CuO₂ layer planes. Conductivity and also superconductivity can occur only when these circles touch each other and form percolation clusters. Mobile holes are accompanied by diffusing d-electrons. Their spin direction is no longer localized on distinct places, and antiferromagnetism breaks down. The phase diagram of high-T _c superconductors is discussed on the basis of a modified continuum percolation model for which the centers of each circle are located on lattice points. The inhomogeneities due to the random hole distributions lead to broad peaks instead of sharp singularities in the static and dynamic response functions.     

利用分形编码进行基于形状的图像检索

分形编码在图像压缩方面取得了很好的效果,同时也能够用于基于内容的图像检索。该文结合分形技术,提出了一种有效的抽取特征检索图像的新方法。针对目前基于形状的图像检索领域中存在的问题,首先提出了一种通过构造不规则区域的相似膨胀分形编码算法,该算法能获得较高的压缩比。在图像检索中,该算法用一新的方式提取形状特征,实现了基于该算法的图像检索操作。实验结果表明该文算法能较好地描述图像的形状及空间分布信息,明显地提高了检索效率及准确度。     

基于分形和数学形态学的图像边缘检测方法

图像处理是视觉测量方法必需的技术,图像处理结果的好坏直接影响到了测量的质量。其中,边缘检测是重要的一步。视觉测量不仅需要较好地检测到边缘,还需要边缘尽可能是连续的。该文提出了一种基于分形理论和数学形态学的边缘检测方法。该方法利用分形理论中离散分数布朗随机场来抑制噪声得到按分形维分布的灰度图像,采用数学形态学检测连续的特征边缘。试验表明,采用该方法比经典的边缘检测算子能够更好地达到视觉测量的要求。     

分形理论在摩擦学研究中的应用

对近年国内外分形理论在摩擦学研究中应用的新进展作了综述,介绍了分形的概念以及分形维数的计算方法,讨论了包括磨损表面形貌分析,材料表界面分形研究和磨合磨损分形模型的建立等分形理论在摩擦学研究中的应用状况,并提出了当前相关研究中所遇到的问题,及今后分形理论在摩擦学研究中的发展方向。     

基于分形理论的RIFLE线表面磨损动态模型

根据实测数据得出分形维数D随着枪支发射子弹量变化的动态方程，并分析了尺度系数G的变化规律．应用分形几何理论和分形接触模型公式，建立了枪管RIFLE线表面磨损率与枪支发射子弹量之间的动态预测分形模型．其动态预测趋势与实验数据吻合．从而为枪管RIFLE线磨损的检测提供了新的思路。     

金属垫片泄漏模型理论研究

依据分形几何理论,结合不可压缩粘性流体层流流动理论,建立基于分形参数的金属垫片泄漏模型,该模型揭示了泄漏率与密封表面形貌之间的关系。研究表明,密封表面分形维数D越大,螺栓-法兰-金属垫片密封系统越不易发生泄漏,这对于法兰和金属垫片密封表面的加工具有重要指导意义。     

Dried jujube classification using support vector machine based on fractal parameters and red,green and blue intensity

A new method that combines fractal theory and red, green and blue (RGB) colour intensity was developed to sort dried jujube fruits by using support vector machine (SVM). Our result shows that the new method is fast and accurate in dried jujube fruits classification. The SVM models based on fractal parameters only achieved 85.18–92.73% total accuracy rate. The total classification accuracy of SVM based on RGB intensity values was 94.44%. However, the SVM models based on combining fractal parameters with RGB intensity values achieved 94.44–98.15% total accuracy rate. The best classification accuracy (98.15%) was found when using SVM model based on combining fractal measures (FM) with RGB intensity values (C = 512, γ = 0.0078125). Therefore, the SVM model based on combining FMs with RGB intensity is recommended in dried jujube fruits classification.     

Fractal characterization of ceramic crack patterns after thermal shocks

This work utilized a combination of experimental evidence and fractal geometric method to assess the effect of crack extension concerning the thermal shock on residual strength of ceramics. Sintered alumina (Al₂O₃) ceramic slabs were bundled and quenched in water under different thermal shock temperatures. The fractal dimension of thermal shock crack patterns on the interior surface and the cooled surface was calculated by the Box-counting method. Fracture energy of a fractal pattern of microcracks in quasi-brittle solids was employed to explain the relationship between crack length and fractal dimensions. The results show that if the crack propagation has the same crack length but a larger fractal dimension, it will absorb more fracture energy. The thermal shock crack patterns of Al₂O₃ ceramics with different grain sizes were analyzed, and the smaller grain size ceramic had a higher fractal dimension of crack patterns than the larger one.     

Optimization of multi-product economic production quantity model with partial backordering and physical constraints: SQP,SFS, SA,and WCA

A multi-product economic production quantity model with several real-world technical and physical constraints is developed in this paper. The cost function includes ordering, holding, backordering, lost sale, and the cost caused by unused space in the warehouse. The goal is to minimize the total inventory cost, where shortages are allowed and partially backordered with fixed and linear costs. The aim is to determine the length of the inventory cycle, the length of positive inventory period, and the backordering rates of the products during the shortage period in order to minimize the total inventory costs while satisfying all constraints. Due to complexity and non-linearity of the proposed model, sequential quadratic programming (SQP), stochastic fractal search (SFS), simulated annealing (SA), and water cycle algorithm (WCA) are utilized for solution. Ninety numerical examples in small, medium, and large sizes are solved to evaluate the efficiency of the solution methods. The performances of the solution methods are compared statistically. Besides, sensitivity analysis is performed to determine the effect of change in the main parameters of the problem on the objective function value and decision variables.     

Comparative evaluation of microwave‐assisted extraction and preheated solvent extraction of bioactive compounds from a plant material: a case study with cabbages

Preheated solvent extraction (PSE) was evaluated via the analysis of the extraction kinetics, microstructure of extracted samples and energy consumption as alternative to microwave‐assisted extraction (MAE). Cabbage outer leaves and ethanol were used as test material and extraction solvent, respectively. MAE was first optimised in terms of glucosinolates and phenolics yields; total antioxidant activity of the extracts was also assessed. MAE at a specific absorbed power of 0.37 W g^?1 for 9 min was selected as optimum condition to extract glucosinolates and phenolics, while PSE was optimised at 6 min of the extraction. The highest normalised total glucosinolates and phenolic contents as well as antioxidant activities of the extracts obtained via MAE were not significantly different from those obtained via PSE. Confocal laser scanning microscopy revealed no significant differences in cabbage cell damages rendered by MAE and PSE. PSE nevertheless exhibited slightly higher specific energy consumption than MAE.