Related papers: Triangular Constellations in Fractal Measures
The fact that galaxy distribution exhibits fractal properties is well established since twenty years. Nowadays, the controversy concerns the range of the fractal regime, the value of the fractal dimension and the eventual presence of a…
We consider dense random packing of disks with a power-law distribution of radii and investigate their correlation properties. We study the corresponding structure factor, mass-radius relation and pair distribution function of the disk…
The present paper describes a stochastic model of fracture, whose fragment size distribution can be calculated analytically as a power-law-like distribution. The model is basically cascade fracture, but incorporates the effect that each…
Observations of galaxies over large distances reveal the possibility of a fractal distribution of their positions. The source of fractal behavior is the lack of a length scale in the two body gravitational interaction. However, even with…
We describe the fractal solid by a special continuous medium model. We propose to describe the fractal solid by a fractional continuous model, where all characteristics and fields are defined everywhere in the volume but they follow some…
Following \cite{Visintin}, we exploit the fractional perimeter of a set to give a definition of fractal dimension for its measure theoretic boundary. We calculate the fractal dimension of sets which can be defined in a recursive way and we…
Growth in crystals can be { usually } described by field equations such as the Kardar-Parisi-Zhang (KPZ) equation. While the crystalline structure can be characterized by Euclidean geometry with its peculiar symmetries, the growth dynamics…
Urban form has been empirically demonstrated to be of scaling invariance and can be described with fractal geometry. However, the rational range of fractal dimension value and the relationships between various fractal indicators of cities…
This paper presents a review of the fractal approach for describing the large scale distribution of galaxies. We start by presenting a brief, but general, introduction to fractals, which emphasizes their empirical side and applications…
This is the first of a series of three articles that treats fracture localization as a critical phenomenon. This first article establishes a statistical mechanics based on ensemble averages when fluctuations through time play no role in…
Fractal plays an important role in nonlinear science. The most important parameter to model fractal is fractal dimension. Existing information dimension can calculate the dimension of probability distribution. However, given a mass function…
We present structural properties of two-dimensional polymers as far as they can be described by percolation theory. The percolation threshold, critical exponents and fractal dimensions of clusters are determined by computer simulation and…
We analyze the fragmentation behavior of random clusters on the lattice under a process where bonds between neighboring sites are successively broken. Modeling such structures by configurations of a generalized Potts or random-cluster model…
We consider scattering exponents arising in small-angle scattering from power-law polydisperse surface and mass fractals. It is shown that a set of fractals, whose sizes are distributed according to a power-law, can change its fractal…
Active fluids, composed of individual self-propelled agents, can generate complex large-scale coherent flows. A particularly important laboratory realization of such an active fluid is a system composed of microtubules, aligned in a…
A class of simplified measures is constructed to capture the key features of generic spatio-temporally chaotic systems. A combined analytical and numerical investigation allows us to extablish the scaling beahviour of the fractal dimension…
There is a general agreement that galaxy structures exhibit fractal properties, at least up to some small scale. However the presence of an eventual crossover towards homogenization, as well as the exact value of the fractal dimension, are…
Fractal behavior and long-range dependence have been observed in an astonishing number of physical systems. Either phenomenon has been modeled by self-similar random functions, thereby implying a linear relationship between fractal…
In the last years there has been a growing interest in the understanding a vast variety of scale invariant and critical phenomena occurring in nature. Experiments and observations indeed suggest that many physical systems develop…
The Q-parameter is used extensively to quantify the spatial distributions of stars and gas in star-forming regions as well as older clusters and associations. It quantifies the amount of structure using the ratio of the average length of a…