相关论文: Fractal Structure of Equipotential Curves on a Con…
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…
We construct a theory of distributions in the setting of analysis on post-critically finite self-similar fractals, and on fractafolds and products based on such fractals. The results include basic properties of test functions and…
While classical percolation is well understood, percolation effects in randomly packed or jammed structures are much less explored. Here we investigate both experimentally and theoretically the electrical percolation in a binary composite…
The Gaussian model of discontinuous percolation, recently introduced by Ara\'ujo and Herrmann [Phys. Rev. Lett., 105, 035701 (2010)], is numerically investigated in three dimensions, disclosing a discontinuous transition. For the…
We suggest treating a conducting network of oriented polymer chains as an anisotropic fractal whose dimensionality D=1+\epsilon is close to one. Percolation on such a fractal is studied within the real space renormalization group of Migdal…
The properties of the similarity transformation in percolation theory in the complex plane of the percolation probability are studied. It is shown that the percolation problem on a two-dimensional square lattice reduces to the Mandelbrot…
The effect of fractal clusters on magnetic and transport properties of percolative superconductors is considered. The superconductor contains percolative superconducting cluster, carrying a transport current, as well as clusters of a normal…
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…
Electrodynamics of composite materials with fractal geometry is studied in the framework of fractional calculus. This consideration establishes a link between fractal geometry of the media and fractional integro-differentiation. The…
We introduce the concept of boundaries of a complex network as the set of nodes at distance larger than the mean distance from a given node in the network. We study the statistical properties of the boundaries nodes of complex networks. We…
The harmonic measure (or diffusion field or electrostatic potential) near a percolation cluster in two dimensions is considered. Its moments, summed over the accessible external hull, exhibit a multifractal spectrum, which I calculate…
In this paper we present the complete derivation of the effective contour model for electrical discharges which appears as the asymptotic limit of the minimal streamer model for the propagation of electric discharges, when the electron…
Computer simulations are used to generate two-dimensional diffusion-limited deposits of dipoles. The structure of these deposits is analyzed by measuring some global quantities: the density of the deposit and the lateral correlation…
We investigate the geometry of a critical system undergoing a second order thermal phase transition. Using a local description for the dynamics characterizing the system at the critical point T=Tc, we reveal the formation of clusters with…
Almost periodic particle chains exhibit peculiar propagation properties that are not observed in perfectly periodic ones. Furthermore, since they inherently support non-negligible long-range interactions and radiation through the…
We apply connectedness percolation theory to fractal liquids of hard particles, and make use of a Percus-Yevick liquid state theory combined with a geometric connectivity criterion. We find that in fractal dimensions the percolation…
By assuming a self-similar structure for Kelvin waves along vortex loops with successive smaller scale features, we model the fractal dimension of a superfluid vortex tangle in the zero temperature limit. Our model assumes that at each step…
We study the multifractal spectrum of the current in the two-dimensional random resistor network at the percolation threshold. We consider two ways of applying the voltage difference: (i) two parallel bars, and (ii) two points. Our…
While the universe becomes more and more homogeneous at large scales, statistical analysis of galaxy catalogs have revealed a fractal structure at small-scales (\lambda < 100 h^{-1} Mpc), with a fractal dimension D=1.5-2 (Sylos Labini et al…
Fragment properties of hot fragmenting sources of similar sizes produced in central and semi-peripheral collisions are compared in the excitation energy range 5-10 AMeV. For semi-peripheral collisions a method for selecting compact…