Application of Complexity Theory to an Information Processing Model in Science Education

The current work examines the role of working-memory capacity in problem solving in science education. It treats an information-processing model with tools of complexity theory. Nonlinear methods are used to correlate the subjects' achievement scores with working-memory capacity. Data have been taken from the achievement scores in simple organic-synthesis chemical problems. The subjects (N = 319) were in grade twelve (age 17–18). Problems of various Z-demands (that is the number of steps needed to solve the problem) from two to eight were used. Rank-order sequences of the subjects, according to their scores, were generated, and each score was then replaced by the value of subject's working memory capacity measured by the digit backward span test. Then the sequences were mapped onto a one-dimensional random walk model and when treated as dynamic flows were found to possess fractal geometry with characteristics depending on the Z-demand of the problem. The findings were interpreted using concepts from complexity theory, such as correlation exponents, fractal dimensions and entropy. The null hypothesis was tested with surrogate data.     

Using Fractal Function Auto-correlative Method to Confirm Fractal Dimension of Function Graph

The effects of light wave propagating in atmospheric turbulence are investigated experimentally, it is essential to measure the physical variable with time. In order to analyze appropriately these data, it is utilized the fractal function auto-correlative method to describe the fractal dimension of function graph of image-space. The fractal dimension Dg=1.47 of function graph is derived from the power spectral analysis of measuring data. It shows that the Kolmogorov' turbulent model is not completely in accord with actual atmospheric turbulence.     

A fractal approach to low velocity non-Darcy flow in a low permeability porous medium

In this paper, the mechanism for fluid flow at low velocity in a porous medium is analyzed based on plastic flow of oil in a reservoir and the fractal approach. The analytical expressions for flow rate and velocity of non-Newtonian fluid flow in the low permeability porous medium are derived, and the threshold pressure gradient （TPG） is also obtained. It is notable that the TPG （J） and permeability （K） of the porous medium analytically exhibit the scaling behavior J ~ K-D＇r/（l＋Or）, where DT is the fractal dimension for tortuous capillaries. The fractal characteristics of tortuosity for capillaries should be considered in analysis of non-Darcy flow in a low permeability porous medium. The model predictions of TPG show good agreement with those obtained by the available expression and experimental data. The proposed model may be conducible to a better understanding of the mechanism for nonlinear flow in the low permeability porous medium.     

周期受击陀螺系统波函数的分形

研究了周期受击陀螺系统波函数的分形. 发现在打击强度系数较弱时 (即≤ 1时), 相空间是规则的, 分形维接近于1; 随着打击强度系数的增大, 相空间开始变得混沌, 分形维也随之增大; 当打击强度系数达到6时, 相空间完全混沌, 分形维将达到最大值, 此时若继续增大打击强度系数, 分形维保持基本不变. 关键词： 陀螺 波函数 分形维 相空间     

近地层大气光学湍流的分形和间歇性特征分析

利用光纤湍流测量系统获得了合肥西郊科学岛上气象观测场内下垫面平坦的水面上方0.48m、草地上方1.8m和23m高处的大气折射率起伏的观测数据,采用R/S分析法计算了近地层大气光学湍流的赫斯特指数和分形维数,统计分析了分形维数的日变化特征及概率分布特征。结果表明:对于一天的不同时段,分形维数在一定范围内动态变化,且中午时段相对稳定;在三种下垫面条件下,全天分形维数的值大多在1.3~1.4之间,其最可几概率位于1.35处,从均值来看,草地上方1.8m的分形维数最大,水面上方0.48m次之,草地上方23m处最小。最后,初步探讨了近地层大气光学湍流分形维数、间歇性指数和湍流发展程度的相关性。     

磨石磨损分形预测研究

磨合是新机器投入正常运行前所必须经历的一个过程。合理的磨合可防止机器在早期发生咬合,从而极大地延长其使用寿命,基于磨损表面的分形表征,经典接触理论和磨损理论,建立了磨合磨损预测分形模型,以铜合金销和４５＃钢盘试样组成摩擦副,在销－盘摩擦磨损试验机上进行了磨合试验。研究结果表明,基于所建立的模型的磨损率预测结果与试验结果基本吻合。     

粗糙表面分维计算的立方体覆盖法

针对三角形棱柱表面积法和投影覆盖法在计算粗糙表面分形维数中存在的问题,提出了计算粗糙表面分维的立方体覆盖法,对计算结果进行了对比分析,并进一步对表面分维计算中的有关理论问题进行了分析,发现立方体覆盖法作为一种几何意义上的覆盖法,并计算结果比三角形棱柱表面积法和投影覆盖法更接近实际。     

Small Deviations for Some Multi-Parameter Gaussian Processes

We prove some general lower bounds for the probability that a multi-parameter Gaussian process has very small values. These results, when applied to a certain class of fractional Brownian sheets, yield the exact rate for their so-called small ball probability. We show by example how to use such results to compute the Hausdorff dimension of some exceptional sets determined by maximal increments.     

一类分形曲面的精细计盒维数公式

本文研究由一个二变元四阶差分方程边值问题生成的分形曲面的精细计盒维数问题,给出了一个自然的维数公式,若该边值问题的边界上的连续函数的图象的精细计盒维数为γ,则该解曲面的精细计盒维数为（1＋γ）。     

煤燃烧过程中表面结构变化的SEM图像分析

介绍了SEM图像分析的多种方法,并讨论了各自的描述能力,利用这些方法分析煤在燃烧各阶段SEM图像,通过研究得到煤在燃烧过程中表面分形维数的变化规律,同时可获得表面孔的某些参数变化历程。分析表明,淮南低变质煤在850℃燃烧过程中,煤焦颗粒表面的分维数有一个先变低后变高的过程,煤焦表面分维数在2.2至2.5区间内变化;同时孔径分布由近双曲线分布变化为近正态分布,孔油加权平均形状因子增加,在研究过程中发现,不同的计算方法会对图像的分形维数值产生影响,确定合适的计算方法是分形理论在煤燃烧领域中应用的关键。通过比较发现Xie法较为适合计算煤焦表面SEM图像。