Related papers: Fractal Electromagnetic Showers
In search for new methods of determining the primary energy spectrum of Cosmic Rays, the attention was paid to the density spectrum measurement. New methods available at present warrant an accurateness of conclusions derived from the…
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…
The fluorescence technique has been successfully used to detect ultrahigh energy cosmic rays by indirect measurements. The underlying idea is that the number of charged particles in the atmospheric shower, i.e, its longitudinal profile, can…
Air shower simulation programs are essential tools for the analysis of data from cosmic ray experiments and for planning the layout of new detectors. They are used to estimate the energy and mass of the primary particle. Unfortunately the…
In view of promising applications of fractal nanostructures, we analyze the spectra of quantum particles in the Sierpinski carpet and study the non-correlated electron gas in this geometry. We show that the spectrum exhibits scale…
Scaling properties of nuclei- and photon-initiated air showers are examined in wide primary energy range ($10^{14}\div 10^{22}$~eV) taking into account Landau-Pomeranchuk-Migdal and geomagnetic field effects. It is shown that the invariance…
Electric and magnetic fields of fractal distribution of charged particles are considered. The fractional integrals are used to describe fractal distribution. The fractional integrals are considered as approximations of integrals on…
Most of the known methods for estimating the fractal dimension of fractal sets are based on the evaluation of a single geometric characteristic, e.g. the volume of its parallel sets. We propose a method involving the evaluation of several…
We show that extended self-similarity, a scaling phenomenon firstly observed in classical turbulent flows, holds for a two-dimensional metal-insulator transition that belongs to the universality class of random Dirac fermions. Deviations…
We present the results concerning the main shower characteristics in a strong magnetic field obtained through shower simulation. The processes of magnetic bremsstrahlung and pair production were taken into account for values of the…
We examine the fractal structure of the physical universe from the large scale to the smallest scale, including the phenomenon of fractal scaling. This is explained in terms of a stochastic underpinning for the laws of physics. A picture in…
In this article we investigate the energy spectrum statistics of fractals at the quantum level. We show that the energy-level distribution of a fractal follows a power-law behaviour, if its energy spectrum is a limit set of piece-wise…
We study the kinetics of random sequential adsorption of a mixture of particles with continuous distribution of sizes for different deposition rules. It appears in the long time limit the resulting system can be described using the 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…
In the present article, the main attention is given to fractal sets whose elements have certain restrictions on using digits or combinations of digits in own nega-P-representation. Topological, metric, and fractal properties of images of…
It is shown that the shape of any electron distribution in a high energy air shower is the same in all such showers, if taken at the same age, independently of the primary energy, mass and thus, of the interaction model.
There are three important types of structural properties that remain unchanged under the structural transformation of condensed matter physics and chemistry. They are the properties that remain unchanged under the structural periodic…
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 study basic characteristics of distributions of the depths of shower maximum in air showers caused by cosmic rays with the highest energies. The consistency between their average values and widths, and their energy dependences are…
Fractals are measurable metric sets with non-integer Hausdorff dimensions. If electric and magnetic fields are defined on fractal and do not exist outside of fractal in Euclidean space, then we can use the fractional generalization of the…