Related papers: The scattering from generalized Cantor fractals
It is shown that preferential concentrations of inertial (finite-size) particle suspensions in turbulent flows follow from the dissipative nature of their dynamics. In phase space, particle trajectories converge toward a dynamical fractal…
The electrostatics properties of composite materials with fractal geometry are studied in the framework of fractional calculus. An electric field in a composite dielectric with a fractal charge distribution is obtained in the spherical…
A simple method of calculating the Hausdorff-Besicovitch dimension of the Kronecker Product based fractals is presented together with a compact R script realizing it. The proposed new formula is based on traditionally used values of the…
We establish pointwise and distributional fractal tube formulas for a large class of relative fractal drums in Euclidean spaces of arbitrary dimensions. A relative fractal drum (or RFD, in short) is an ordered pair $(A,\Omega)$ of subsets…
The structure of the large scale distribution of the galaxies have been widely studied since the publication of the first catalogs. Since large redshift samples are available, their analyses seem to show fractal correlations up to the…
We analyze a simple model of deterministic diffusion. The model consists of a one-dimensional periodic array of scatterers in which point particles move from cell to cell as defined by a piecewise linear map. The microscopic chaotic…
Fractals such as the Cantor set can be equipped with intrinsic arithmetic operations (addition, subtraction, multiplication, division) that map the fractal into itself. The arithmetics allows one to define calculus and algebra intrinsic to…
We theoretically and numerically demonstrate that completely integrable scattering processes may exhibit fractal transmission fluctuations, due to typical spectral properties of integrable systems. Similar properties also occur with…
Propagation of waves in the Cantor-set media is investigated by a renormalization-group type method. We find fixed points for complete reflection, $T^*=0$, and for complete transmission, $T^*=1$. In addition, the wave numbers for which…
We apply a theory of wave propagation through a turbulent medium to the scattering of radio waves in pulsar magnetospheres. We find that under conditions of strong density modulation the effects of magnetospheric scintillations in…
The main goal of this paper has a double purpose. On the one hand, we propose a new definition in order to compute the fractal dimension of a subset respect to any fractal structure, which completes the theory of classical box-counting…
The set of frequencies and angular properties of radiation emitted from a solid-state crystalline undulator based on the channeling effect are considered. High-frequency and low-frequency branches of the undulator radiation and the angular…
Statistical properties of the critical current distribution in superconductor with fractal clusters of a normal phase are considered. It is found that there is the range of fractal dimensions in which the variance and expectation for this…
A type of fractal dimension definition is based on the generalized entropy function. Both entropy and fractal dimension can be employed to characterize complex spatial systems such as cities and regions. Despite the inherent connect between…
Evidence is presented that the galaxy distribution can be described as a fractal system in the redshift range of the FDF galaxy survey. The fractal dimension $D$ was derived using the FDF galaxy volume number densities in the spatially…
The term fractal describes a class of complex structures exhibiting self-similarity across different scales. Fractal patterns can be created by using various techniques such as finite subdivision rules and iterated function systems. In this…
Linear binary fragmentation of synthetic fractal-like agglomerates composed of spherical, equal-size, touching monomers is numerically investigated. Agglomerates of different morphologies are fragmented via random bond removal. The…
A chaotic attractor is usually characterised by its multifractal spectrum which gives a geometric measure of its complexity. Here we present a characterisation using a minimal set of independant parameters which are uniquely determined by…
We consider a dimer formed by two particles with an attractive contact interaction in one dimension, colliding with a hard wall. We compute the scattering phase shifts and the reflection coefficients for various collision energies and…
The fractal properties of four-dimensional Euclidean simplicial manifold generated by the dynamical triangulation are analyzed on the geodesic distance D between two vertices instead of the usual scale between two simplices. In order to…