Related papers: Fractal Structures Driven by Self-Gravity: Molecul…
Dynamical systems in nature such as fluid flows, heart beat patterns, rainfall variability, stock market price fluctuations, etc. exhibit selfsimilar fractal fluctuations on all scales in space and time. Power spectral analyses of fractal…
We develop a new definition of fractals which can be considered as an abstraction of the fractals determined through self-similarity. The definition is formulated through imposing conditions which are governed the relation between the…
If a point particle moves chaotically through a periodic array of scatterers the associated transport coefficients are typically irregular functions under variation of control parameters. For a piecewise linear two-parameter map we analyze…
Atmospheric flows exhibit selfsimilar fractal spacetime fluctuations manifested as the fractal geometry to global cloud cover pattern and inverse power law form for power spectra of meteorological parameters such as windspeed, temperature,…
Despite the observational evidence that the Universe appears hierarchically structured up to a distance of at least 30 Mpc/h (and possibly up to 100 Mpc/h), the fractal paradigm has not yet been recognized by the majority of cosmologists…
The observed rapid onset of star formation in molecular clouds requires rapid formation of dense fragments which can collapse individually before being overtaken by global gravitationally-driven flows. Many previous investigations have…
The structures formation of the Universe appears as if it were a classically self-similar random process at all astrophysical scales. An agreement is demonstrated for the present hypotheses of segregation with a size of astrophysical…
The dynamics of a nonequilibrium system can become complex because the system has many components (e.g., a human brain), because the system is strongly driven from equilibrium (e.g., large Reynolds-number flows), or because the system…
The large scale distribution of galaxies in the universe displays a complex pattern of clusters, super-clusters, filaments and voids with sizes limited only by the boundaries of the available samples. A quantitative statistical…
Two fundamental empirical laws have been established in the analysis of galaxy space distribution. First, recent analyses have revealed that the three dimensional distribution of galaxies and clusters is characterized by large scale…
The interstellar medium (ISM) reveals strongly inhomogeneous structures at every scale. These structures do not seem completely random since they obey certain power laws. Larson's law (\citeyear{Larson81}) $\sigma \propto R^{\delta}$ and…
Selfsimilar space-time fractal fluctuations are generic to dynamical systems in nature such as atmospheric flows, heartbeat patterns, population dynamics, etc. The physics of the long-range correlations intrinsic to fractal fluctuations is…
It is shown that conductance fluctuations due to phase coherent ballistic transport through a chaotic cavity generically are fractals. The graph of conductance vs. externally changed parameter, e.g. magnetic field, is a fractal with…
This short communication advances the hypothesis that the observed fractal structure of large-scale distribution of galaxies is due to a geometrical effect, which arises when observational quantities relevant for the characterization of a…
The self-gravitating systems are formed by particles interacting through gravity. They describe structure formation in the universe. As a consequence of the long range interaction of gravity, they are inhomogeneous even at thermal…
Fractal structures are observed in the universe in two very different ways. Firstly, in the gas forming the cold interstellar medium in scales from 10^{-4} pc till 100 pc. Secondly, the galaxy distribution has been observed to be fractal in…
Atmospheric flows, an example of turbulent fluid flows, exhibit fractal fluctuations of all space-time scales ranging from turbulence scale of mm -sec to climate scales of thousands of kilometers - years and may be visualized as a nested…
Three-dimensional fractal models on grids of 200**3 pixels are generated from the inverse Fourier transform of noise with a power law cutoff, exponentiated to give a log normal distribution of density. The fractals are clipped at various…
We discuss correlation properties of a general mass density field introducing a classification of structures based on their complexity. Standard cosmological models for primordial mass fluctuations are characterized by a sort of large-scale…
The fractal structure with a power index of 2 is considered within the framework of the universe with the linear law of evolution. The fractal structure arises due to the linear evolution of the scale of mass. Potential fluctuations connect…