Self-similar fractals with a given dimension and the application to quantitative linguistics

Stimulated by the modeling of language structures, we present three adequate constructions of self-similar fractals with a given dimension. A concrete example of an application to quantitative linguistics is then supplied.     

非光滑热曲线的分数阶次可微性研究

自然界存在诸多的非光滑现象, 如海岸线、岩石的裂隙和截面形貌等.经典的微积分理论和欧氏几何中的常用方法无法用来刻画其可微性.局部分数阶导数是局部化的分数阶导算子, 是潜在的研究非光滑曲线微尺度性态的工具之一.本文首先回顾了基于分数阶积分和类Cantor集生成的阶梯曲线, 然后利用一般的二项式展开, 从分数阶可微函数的角度得到了非光滑热曲线的分数阶次可微性.     

Fractional transport equation on random fractals

According to the ways of H.E. Roman and M. Giona with the constitutive equation of diffusive particles in isotropic and homogeneous three dimensions and the Laplace transform we derive the multiscaling fractional transport equation in disordered fractal media, whose solution is consistent with literature results.     

Cluster Assembled Nanostructures: Designing Interface Properties

Overlayer structures can be formed on surfaces by the deposition of preformed clusters from the gas phase containing from only a few up to a few hundred atoms. By this method, nanostructures with novel chemical and physical properties can be stabilized. This article presents the results obtained using the simple molecular cluster Sb₄ as the precursor for deposition and nanoparticle assembly on various surfaces, and under various conditions. A rich variety of phenomena is observed and discussed.     

Fractal Character of Dynamic Light Scattering of Particles

Dynamic light scattering signals from particles, exhibit fractal characteristics. This feature can be used to determine the particle size. The use of the fractal dimension, as a quantitative method to analyze the properties of dynamic light scattering signals from submicron particles, is presented. The analysis is performed directly on the time‐resolved scattered intensity, and the Box Dimensions of light scattering signals of particles with diameters 100, 200, 500 and 1000 nm. The experimental results show that the fractal dimensions of light scattering signals correlate well with particle size. In the submicron size range, the smaller the particles, the larger their fractal dimensions. Compared with the PCS technique, only several hundreds of samples are required in the fractal method. Therefore, the data processing is easily accomplished. However, this method only provides the mean particle size, but not the particle size distribution.     

小波变换的信号分形分析及其在心电信号处理中的应用研究

介绍了一种基于小波变换的分形分析方法,并将它成功地应用于心房纤颤的检测中.该方法提取了一个特征值r,结果表明在心房纤颤开始时,特征值是上升的,心房纤颤结束后,特征值又慢慢恢复到原来的数值,由此可以成功地检测出心房纤颤的开始和结束.此外,由于特征值同时反映了heartratevariability(HRV)信号的复杂程度,所以同时它也表明:心房纤颤开始后,HRV信号的复杂度是下降的 关键词： HRV 小波变换 分形     

Review: Multifractal Analysis of Packed Swiss Cheese Cosmologies

The multifractal spectrum of various three-dimensional representations of Packed Swiss Cheese cosmologies in open, closed, and flat spaces are measured, and it is determined that the curvature of the space does not alter the associated fractal structure. These results are compared to observational data and simulated models of large scale galaxy clustering, to assess the viability of the PSC as a candidate for such structure formation. It is found that the PSC dimension spectra do not match those of observation, and possible solutions to this discrepancy are offered, including accounting for potential luminosity biasing effects. Various random and uniform sets are also analyzed to provide insight into the meaning of the multifractal spectrum as it relates to the observed scaling behaviors.     

Bifractality of the devil’s staircase appearing in the burgers equation with brownian initial velocity

It is shown that the inverse Lagrangian map for the solution of the Burgers equation (in the inviscid limit) with Brownian initial velocity presents a bifractality (phase transition) similar to that of the Devil’s staircase for the standard triadic Cantor set. Both heuristic and rigorous derivations are given. It is explained why artifacts can easily mask this phenomenon in numerical simulations.     

Adsorption of a flexible self-avoiding polymer chain: Exact results on fractal lattices

The large-scale behavior of surface-interacting self-avoiding polymer chains placed on finitely ramified fractal lattices is studied using exact recursion relations. It is shown how to obtain surface susceptibility critical indices and how to modify a scaling relation for these indices in the case of fractal lattices. We present the exact results for critical exponents at the point of adsorption transition for polymer chains situated on a class of Sierpinski gasket-type fractals. We provide numerical evidence for a critical behavior of the type found recently in the case of bulk self-avoiding random walks at the fractal to Euclidean crossover.     

Dynamical scaling for spin waves in dilute ferromagnets

The ambiguity in the application of the principle of dynamic scaling to spin waves in dilute ferromagnets is resolved by taking account of the fractal nature of the infinite percolation cluster.