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fractal
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     Fractal in Crystals
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  fractal
Fractal differential equations on the Sierpinski gasket
      
Dimension and differentiability of a class of fractal interpolation functions
      
We investigate the fractal interpolation functions generated by such a system and get its differentiability, its box dimension, its packing dimension, and a lower bound of its Hausdorff dimension.
      
The smoothness and dimension of fractal interpolation functions
      
In this paper, we investigate the smoothness of non-equidistant fractal interpolation functions.
      
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Numerical investigations of a differential equation describing a rf-biased Josephson junction, in which the interference term (?)urrent is included, are carried out in some parameter region. The existanee of the intermittant transition to chaos is obtained and the critical exponent of the scaling law is determined in agreement with theoretical predictions. Furthermore, the Lyapunov exponent is calculated for several parameters, then the fractal dimension of strange attraetor dL is obtained, its dependence...

Numerical investigations of a differential equation describing a rf-biased Josephson junction, in which the interference term (?)urrent is included, are carried out in some parameter region. The existanee of the intermittant transition to chaos is obtained and the critical exponent of the scaling law is determined in agreement with theoretical predictions. Furthermore, the Lyapunov exponent is calculated for several parameters, then the fractal dimension of strange attraetor dL is obtained, its dependence on the Lyapunov exponent is defined by Kaplan and Yorke. In addition, the Kolmogorov capacity of strange attractor dc is also calculated by box-counting algorithm. Such calculated values of dL and dc are close to each other as expected.

本文对射频电流驱动下的包含干涉项电流的Josephson结系统的阵发混沌行为进行了研究,得到的标度关系与理论预言的相符。此外,我们计算了一些参数下的里亚普诺夫指数以及由此引入定义的吸引子的维数d_L,并且还用盒子计数法计算了几组参数下奇异吸引子的柯尔莫哥洛夫容量d_c,其值与d_L相近。

This paper reports the concepts of the fractal and exciton percolation (random walk) and the most new results of the luminescence in fractal structures of organic compounds and proteins.We show that the energy transfer on fractal structures of organic compounds where the direct trapping depends on the fractal dimension d, while the multistep trapping is given in terms of the spectral dimension d.Triplet-triplet exciton (neutral Frenkel triplet exciton) annihilation on percolation clusters...

This paper reports the concepts of the fractal and exciton percolation (random walk) and the most new results of the luminescence in fractal structures of organic compounds and proteins.We show that the energy transfer on fractal structures of organic compounds where the direct trapping depends on the fractal dimension d, while the multistep trapping is given in terms of the spectral dimension d.Triplet-triplet exciton (neutral Frenkel triplet exciton) annihilation on percolation clusters produces a singlet exciton. On fractal spaces, the kinetic equation of the annihilation depends on the spectral dimension d. It is observed from experiment that dimensionality changes asymptoticly from 3 (fractal space) to dimension d (Euclidean space) with the change of local heterogeneity of the system.

本文介绍了分数维结构和激子渗透概念,概述了分数维结构有机物体系中能量传递和发光动力学研究的基本现状。

Kinetic Growth Walk on two kinds of fractals is studied via a renormalisationgroup transformation in position space. The correlation-length critical exponents are calculated and two generalised Flory formulas which might be applied are examined. It has been found that these two generalised Flory formulas are not satisfactoy for these fractals.

本文运用实空间重正化群研究了两种Fractals(Koch曲线和Sierpinski gasket)上的动态生长行走行为,得到了这两种Fractals上动态生长行走的临界指数,并考察了推广的Flory公式,发现这种推广的Flory公式对这一类Fractals结构并不成立.

 
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