锡基巴氏合金磨损表面的分形与磨损率

利用结构函数分析法研究了滑动摩擦学系统中金属磨损表面轮廓线的分形特性。结果表明：磨损表面轮廓线在小于Ｓｍ的尺度上具有分形结构。采用结构函数法可以方便地确定粗糙表面轮廓线的分形参数，即垂直于滑动方向上磨损表面轮廓线的分维Ｄ可作为磨损表面分维的特征值，它与金属磨损率的变化有着密切的关系，最佳分维Ｄｏｐｔ值对应于材料的最低磨损率。     

Fractal Prediction Model of Spontaneous Imbibition Rate

By utilizing fractal dimension as one of the parameters to characterize rocks, a mathematical model was derived to predict the production rate by spontaneous imbibition. This fractal production model predicts a power law relationship between spontaneous imbibition rate and time. Fractal dimension can be estimated from the fractal production model using the experimental data of spontaneous imbibition in porous media. The experimental data of recovery in gas-water-rock and oil–water–rock systems were used to test the fractal production model. The rocks (Berea sandstone, chalk, and The Geysers graywacke) in which the spontaneous water imbibition experiments were conducted had different permeabilities ranging from 0.5 to over 1000 md. The results demonstrate that the fractal production model can match the experimental data satisfactorily in the cases studied. The fractal dimension data inferred from the model match were approximately equal to the values of fractal dimension measured using a different technique (mercury-intrusion capillary pressure) in Berea sandstone.     

粗糙表面的分形特征与分形表达研究

得用触针轮廓仪和数据采集系统对磨削和车削表面的粗糙轮廓曲线进行了测量，并就粗糙表面的分形特征作了分析与讨论，同时还提出了粗糙表面的特征粗糙度概念及其定义，并将其用表面粗糙度水平的表述。     

PEN薄带在沙尘环境中磨粒磨损分形特征研究

选取聚萘二甲酸乙二酯(PEN)薄带在ATM自动取款机摩擦学系统中进行了沙尘磨粒磨损试验,利用表面形貌仪以一定时间间隔测量薄带磨损形貌,采用结构函数法考察磨损形貌的分形特征,并利用扫描电子显微镜分析其磨损机理.结果表明:经过沙尘磨粒磨损的PEN薄带表面形貌表现出二重分形特征,沙尘粒子的犁沟和切削磨损及PEN材料的微观断裂是引起大尺度和小尺度区间分形特征的主要机理.     

Fractal dimensions of terrain profiles

Analysing terrain profiles of fields, roads, and other terrains, it was determined that terrain profiles are random and non-periodical. Mandelbrot has defined non-scaling, self-similar figures as fractals, and many investigators have tried to characterize natural forms and structures using fractal geometry. The work here investigates whether terrain profiles can be defined as fractals. Fractal dimensions of profiles were calculated. These were compared with a locus of Brownian motion further to investigate characteristics of terrain profiles. Fractals are defined to be self-similar and irregular. Measuring and analysing terrain profiles, it was established that the statistical characteristics of any part of a terrain profile are similar and that the statistical characteristics of profiles of any kind of terrain are similar irrespective of roughness. This means that terrain profiles are self-similar, and irregular. From these results, it was determined that terrain profiles are fractals. The fractal dimensions were calculated with a coarse-graining method and by Power Spectral Densities (PSD), and fractal dimensions by Scaling were between 1.1 and 1.8 and by PSD between 1.3 and 1.5. Using the locus of Brownian motion, fractal dimensions were 1.5 or slightly larger than those of the terrain profiles. Fractal dimensions for the locus of smoothed Brownian motion were nearly equal to terrain profiles. Therefore terrain profiles could be artificially generated from the locus of smoothed Brownian motion. It appears that terrain roughness is formed by random and non-periodical force.     

Correlation dimension of paddy soil strength in China

Embedding phase space R^m is reconstructed from the spatial series g(x) of cone indices measured in two paddy fields near Nanjing, China. The correlation dimension D₂^m for each field is derived from the correlation integral C^m(r) and the neighbours distance r in log–log scale. Results show D₂^m increases as m, and tends to 5.0, which expresses the estimate of correlation dimension for each soil strength profile measured.     

On star product fractal surfaces and their dimensions

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Calculating fractal parameters from low-resolution terrain profiles

Driver comfort on rough terrain is an important factor in the off-road performance of wheeled and tracked ground vehicles. The roughness of a terrain has typically been quantified by the U.S. Army as the root-mean-square elevation deviation (RMS) of the terrain profile. Although RMS is an important input into many mobility calculations, it is not scale invariant, making it difficult to estimate RMS from low resolution terrain profiles. Fractal parameters are another measure of roughness that are scale invariant, making them a convenient proxy for RMS. While previous work found an empirical relationship between fractal dimension and RMS, this work will show that, by including the cutoff length, an analytic relationship between fractal properties and RMS can be employed. The relationship has no free parameters and agrees very well with experimental data - thus providing a powerful predictive tool for future analyses and a reliable way to calculate surface roughness from low-resolution terrain data in a way that is scale invariant. In addition, we show that this method applies to both man-made ride courses and natural terrain profiles.     

Analytical solutions for anomalous transport of volatile pollutants in nonaqueous-phase liquid contaminated soil

In this paper, we study a fractal model for the transport of a volatile component from a nonaqueous-phase liquids (NAPL) trapped in homogeneous soil. By introducing a kind of new integral transform in fractal space, analytical solutions of fractal model are given. Numerical results are presented graphically for various values of fractal dimension.     

Self-affine cracks in a brittle porous material

Fractal mechanics and probabilistic methods are applied to an ideal porous material (gypsum rock). The behavior of the material fracture is brittle in essence, concluding that the lines of fracture propagation have self-affine invariance, due to the high rugosity of the crack developed within a wide but limited length interval of scale in the cracks. The validity of the mechanic equations of self-affine cracks are verified by a comparison between the predictions of self-affine fracture mechanics and the results of standardized mechanical tests, obtaining the fractal fracture toughness of gypsum rock.