The apparent fractal properties of TCP data tra c have recently attracted con siderable interest Most prominently fractional Brownian motion FBM has been used to model the long range dependence of tra c traces through self similarity Tra c being by nature a process of positive increments though a multifractal ap proach appears more natural In this study various traces of TCP tra c have been ana...

Soil complexity and environmental heterogeneity may be viewed as a consequence of deterministic chaotic dynamics and therefore highly irregular patterns with so-called multifractal behavior should be common. This approach introduces a distinct viewpoint as compared with fractal models for soil surface roughness based on fractional Brownian motion. It suggests that it would be useful to move awa...

Pore spaces heterogeneity in carbonates rocks has long been identified as an important factor impacting reservoir productivity. In this paper, we study the heterogeneity of carbonate rocks pore spaces based on the image analysis of scanning electron microscopy (SEM) data acquired at various magnifications. Sixty images of twelve carbonate samples from a reservoir in the Middle East were analyze...

We find that multifractal scaling is a robust property of a large class of continuous stochastic processes, constructed as exponentials of long-memory processes. The long memory is characterized by a power law kernel with tail exponent phi+1/2, where phi>0. This generalizes previous studies performed only with phi=0(with a truncation at an integral scale) by showing that multifractality holds o...

We first motivate the study of multifractals. We then present a rigorous mathematical foundation for the multifractal analysis of Gibbs measures invariant under dynamical systems. Finally we effect a complete multifractal analysis for several classes of hyperbolic dynamical systems. (c) 1997 American Institute of Physics.

The multifractal dimension of chaotic attractors has been studied in a weakly coupled superlattice driven by an incommensurate sinusoidal voltage as a function of the driving voltage amplitude. The derived multifractal dimension for the observed bifurcation sequence shows different characteristics for chaotic, quasiperiodic, and frequency-locked attractors. In the chaotic regime, strange attrac...

During 2002, the Voyager 1 spacecraft was in the heliosphere between 83.4 and 85.9 AU (1 AU is the mean distance from the Sun to Earth) at 34 N heliographic latitude. The magnetic field strength profile observed in this region had a multifractal structure in the range of scales from 2 to 16 days. The multifractal spectrum observed near 85 AU is similar to that observed near 40 AU, indicating re...

One-dimensional detrended fluctuation analysis (DFA) and multifractal detrended fluctuation analysis (MFDFA) are widely used in the scaling analysis of fractal and multifractal time series because they are accurate and easy to implement. In this paper we generalize the one-dimensional DFA and MFDFA to higher-dimensional versions. The generalization works well when tested with synthetic surfaces...

We demonstrate analytically and numerically the possibility that the fractal property of a scale-free network cannot be characterized by a unique fractal dimension and the network takes a multifractal structure. It is found that the mass exponents τ(q) for several deterministic, stochastic, and real-world fractal scale-free networks are nonlinear functions of q, which implies that structural me...

This paper describes three visually interactive tools for the analysis, modeling, and generation of long-range dependent (LRD) network traffic. The synTraff toolkit uses a three-step modeling approach based on F-ARIMA processes to generate monofractal traffic; the WsynTraff toolkit implements the Wavelet-domain Independent Gaussian (WIG) model from the literature for representing multifractal t...