Patterns of animate and inanimate systems show remarkable similarities in their aggregation. One similarity is the double-Pareto distribution of the aggregate-size of system components. Different models have been developed to predict aggregates of system components. However, not many models have been developed to describe probabilistically the aggregate-size distribution of any system regardles...

There are several methods for estimating the fractal dimension of a time series of data such as the box counting method and the correlation method [DeGrauwe, Dewachter and EmbrechtS, 1993] [peitgen and Saupe, 1988]. The application of these methods are often demanding in computing time and require expert interaction for interpreting the calculated fractal dimension. Artificial neural nets (ANN)...

An asymptotic analysis is carried out for an approximate method of estimating the parameters of the power spectrum of a zero-mean stationary Gaussian random process from an observed realization of limited duration. Maximum likelihood estimates are obtained with the approximation that the coefficients of the Fourier series expansion of the realization are uncorrelated. This is equivalent to othe...

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...

This paper presents a method for the classification of nonlinear systems through the study of the free oscillations in the time-frequency plane, when the measured data are affected by fractal noise of the Wiener type. Nonconservative SDOF (Single Degree Of Freedom) oscillators described by a nonlinear second order differential equation are considered. The nonlinearity is due to a nonlinear func...

A direct determination of the fractal dimensions of a fracture surface is essential for a better understanding of its complete topographic characteristics. In this paper, a laser profilometer is employed to measure the topography of a rock’s fracture surface. With the use of the triangular prism surface area and projective covering methods, the resultant data set enables us to directly determin...

[1] The abundance and size distribution of lakes is critical to assessing the role of lakes in regional and global biogeochemical processes. Lakes are fractal but do not always conform to the power law size-distribution typically associated with fractal geographical features. Here, we evaluate the fractal geometry of lakes with the goal of explaining apparently inconsistent observations of powe...