Previous multifractal spectrum theories can only reflect that an object is multifractal and few explicit expressions of f(α) can be obtained for the practical application of nonlinearity measure. In this paper, an analytical model for multifractal systems is developed by combining and improving the Jake model, Tyler fractal model and Gompertz curve, which allows one to obtain explicit expressio...

Study of a mature petroleum play in the Western Canada Sedimentary Basin (WCSB) indicates that the spatial distribution of petroleum accumulations exhibits a self-affinity characteristic. This characteristic motivated the examination of a fractal model for a quantitative description of petroleum resource spatial distribution. The proposed approach transforms the spatial information with respect...

The fractal and chaos are bound tightly, their relevant researches well-established. Few of them, however, concentrate on the research possibility combining chaotic systems for generating multi-scroll attractors. This paper presents a novel non-equilibrium point system, exhibiting extremely rich complex hidden behaviors including chaos, hyper-chaos, attractors, extreme multi-stability, initial ...

Fractal groups (also called self-similar groups) is the class of discovered by first author in 1980s with purpose solving some famous problems mathematics, including question raising to von Neumann about non-elementary amenability (in association studies around Banach-Tarski Paradox) and John Milnor’s on existence intermediate growth between polynomial exponential. arise various fields theory r...

We numerically investigate the sensitivity to initial conditions of asymmetric unimodal maps x(t+1)=1-a/x(t)/(z(i)) (i=1,2 correspond to x(t)>0 and x(t)<0, respectively, z(i)>1, 0<a< or =2, t=0,1,2,...) at the edge of chaos. We employ three distinct algorithms to characterize the power-law sensitivity to initial conditions at the edge of chaos, namely: direct measure of the divergence of initia...

A novel fractal antenna-array type is proposed. The design is based on the Sierpinski rectangular carpet concept. However, the generator is a circular ring area, filled with radiating elements, so the higher stages of the fractal development produce large arrays of circular rings which, besides the high directivity, have the advantage of the almost uniform azimuthal radiation pattern, attribute...

Fractal structure of the six-vertex model is introduced with the use of the IFS (Iterated Function Systems). The fractal dimension satisfies an equation written by the free energy of the six-vertex model. It is pointed out that the transfer matrix method and the n-equivalence relation introduced in lattice theories have also been introduced in the area of fractal geometry. All the results can b...

The power spectrum S of linear transects of the earth's topography is often observed to be a power-law function of wave number k with exponent close to ?2: S(k) / k ?2. In addition, river networks are fractal trees that satisfy several power-law relationships between their morphologic components. A model equation for the evolution of the earth's topography by erosional processes which produces ...

Jessica L. Green*, John Harte and Annette Ostling Department of Environmental Science and Policy, University of California, One Shields Avenue, Davis, CA 95616, USA Energy and Resources Group, University of California, Berkeley, CA 94720, USA *Correspondence: E-mail: [email protected] Abstract Although scaling relationships that characterize fractal species distributions offer an exciting pot...

In this work, SiO2 –ZrO2 mixed oxides was prepared by the polymeric sol–gel route. The characterization of pore structure, which determines the permeation process of membrane, is of great importance. So far, most investigations have focused on such pore structure as specific surface area and pore size distribution, but the surface fractal, the important parameter reflecting the roughness of por...