Multifractal phenomena in physics and chemistry

  title={Multifractal phenomena in physics and chemistry},
  author={H. Stanley and P. Meakin},
The neologism 'multifractal phenomena' describes the concept that different regions of an object have different fractal properties. Multifractal scaling provides a quantitative description of a broad range of heterogeneous phenomena. 
Phase-transition from fractality to homogeneity in a large-scale universe
Abstract Multifractal analysis of generalized luminosity fields gives evidence that the spatio-luminous distribution of galaxies in the observable universe has characteristic features of a phaseExpand
Fractals and Multifractals
To provide a brief introduction to fractals. To introduce the notion of fractal dimension. To provide a brief introduction to multifractals and define a multifractal formalism. ToExpand
Multifractal Statistics of Mesoscopic Systems
A generalization of the Havlin–Bunde multifractal hypothesis is used to obtain a probability distribution corresponding to mesoscopic systems close to the critical regime. Good agreement betweenExpand
Fractals in the Biological Sciences
The importance of spatial and temporal scaling to the study of biological systems and processes has long been recognized. We demonstrate that concepts derived from fractal and chaos theory areExpand
Multifractals in diffusion and aggregation
The origin of the multifractal features which appear in several random systems is discussed. It is shown that for random fractals the multifractal features in the probability density of the diffusionExpand
Generalized Dimensions and Multifractals
In the preceding two chapters, we studied the information dimension dI of a probability distribution and of a network. However, in general a single fractal dimension does not suffice to quantify theExpand
Multifractal scaling analysis of reactions over fractal surfaces
Abstract Simulations of the Eley-Rideal diffusion-limited reaction mechanism and its modified versions over surfaces of different fractal objects having different fractal dimensions were performedExpand
Fractal Aspects of Galaxy Clustering
In the past decade, the mathematical concept of fractal has exerted a great influence in a large variety of scientific disciplines. It is very common to find recent papers on the application ofExpand
Calculation of multi-fractal dimensions in spin chains
  • Y. Atas, E. Bogomolny
  • Physics, Medicine
  • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2014
Analytical derivations and numerical confirmations of the statement that the ground-state wave functions for a large variety of one-dimensional spin- models are multi-fractals in the natural spin-z basis are presented. Expand
A program for fractal and multifractal analysis of two-dimensional binary images: Computer algorithms versus mathematical theory
In this paper we present a tool to carry out the multifractal analysis of binary, two-dimensional images through the calculation of the Renyi D(q) dimensions and associated statistical regressions.Expand


Multifractal structure of clusters and growing aggregates
Various phenomena on a given fractal object have different critical behavior. This is related to the underlying multifractal structure of the aggregate. Here we discuss the problem with particularExpand
Fractal growth processes
  • L. Sander
  • Physics, Materials Science
  • Nature
  • 1986
The methods of fractal geometry allow the classification of non-equilibrium growth processes according to their scaling properties. This classification and computer simulations give insight into aExpand
Phase transitions in the thermodynamic formalism of multifractals.
Les non-analyticites dans les dimensions generalisees d'ensembles multifractals d'interet physique sont interpretees comme des transitions de phase
We give a brief overview of the impact of fractal geometry on physical sciences. In particular we will describe the prototype of fractal growth models and the recent developments in the direction ofExpand
On the multifractal nature of fully developed turbulence and chaotic systems
It is generally argued that the energy dissipation of three-dimensional turbulent flow is concentrated on a set with non-integer Hausdorff dimension. Recently, in order to explain experimental data,Expand
Fractal Dimension of Dielectric Breakdown
It is shown that the simplest nontrivial stochastic model for dielectric breakdown naturally leads to fractal structures for the discharge pattern. Planar discharges are studied in detail and theExpand
Radial viscous fingers and diffusion-limited aggregation: Fractal dimension and growth sites.
Etude de la formation de doigts fractaux visqueux dans une cellule de Hele-Shaw a symetrie radiale
Stochastic model for dielectric breakdown
We discuss a model for the development of discharge patterns in dielectric breakdown based on the Laplace equation associated with a probability field. The model gives rise to random fractals withExpand
Fractal Geometry of Nature
This book is a blend of erudition, popularization, and exposition, and the illustrations include many superb examples of computer graphics that are works of art in their own right. Expand
Diffusion-limited aggregation, a kinetic critical phenomenon
A model for random aggregates is studied by computer simulation. The model is applicable to a metal-particle aggregation process whose correlations have been measured previously. Density correlationsExpand