Multifractal phenomena in physics and chemistry

  title={Multifractal phenomena in physics and chemistry},
  author={Harry Eugene Stanley and Paul 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. 
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. To
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 between
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 are
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 the
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 of
Calculation of multi-fractal dimensions in spin chains
  • Y. Y. Atas, E. Bogomolny
  • Physics
    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.
I Fractals and multifractals: the interplay of Physics and Geometry
In recent years, a wide range of complex structures of interest to scientists, engineers, and physicans have been quantitatively characterized using the idea of a fractal dimension: a dimension that


Fractal growth processes
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 a
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 of
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,
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 the
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 with
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.
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 correlations