Related papers: Fractal Electromagnetic Showers
The generic properties of the emission of coherent radiation from a moving charge distribution are discussed. The general structure of the charge and current distributions in an extensive air shower are derived. These are subsequently used…
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…
Small-angle scattering (SAS) of X-rays, neutrons or light from ensembles of randomly oriented and placed deterministic fractal structures are studied theoretically. In the standard analysis, a very few parameters can be determined from SAS…
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…
In the single-scattering theory of electromagnetic radiation, the {\it fractal regime} is a definite range in the photon momentum-transfer $q$, which is characterized by the scaling-law behavior of the structure factor: $S(q) \propto…
\emph{Fractal percolation} or \emph{Mandelbrot percolation} is one of the most well studied families of random fractals. In this paper we study some of the geometric measure theoretical properties (dimension of projections and structure of…
Large scale airshower simulations around the GZK cutoff are performed. An extensive analysis of the behaviour of the various subcomponents of the cascade is presented. We focus our investigation both on the study of total and partial…
Ultra-high energy cosmic rays impinge on the atmosphere and induce air shower cascades, in which huge numbers of particles are produced. By travelling through the Earth's atmosphere and magnetic field, these particles create a noticeable…
We consider the fragmentation process with mass loss and discuss self-similar properties of the arising structure both in time and space focusing on dimensional analysis. This exhibits a spectrum of mass exponents $\theta$, whose exact…
The present status of extensive air shower (EAS) simulation procedures is reviewed. The advantages of combining numerical and Monte Carlo methods for the description of EAS development are discussed. Physics content of cosmic ray…
Ultra high energy (UHE) photons can initiate electromagnetic showers in magnetic field. We analyze the two processes that determine the development of the shower, $e^+ e^-$ pair creation and synchrotron radiation, and derive formulae for…
Experiments on fracture surface morphologies offer increasing amounts of data that can be analyzed using methods of statistical physics. One finds scaling exponents associated with correlation and structure functions, indicating a rich…
In the parameter spaces of nonlinear dynamical systems, we investigate the boundaries between periodicity and chaos and unveil the existence of fractal sets characterized by a singular fractal dimension. This dimension stands out from the…
Inspired by the similarity between the fractal Weierstrass function and quantum systems with discrete scaling symmetry, we establish general conditions under which the dynamics of a quantum system will exhibit fractal structure in the time…
There are various notions of dimension in fractal geometry to characterise (random and non-random) subsets of $\mathbb R^d$. In this expository text, we discuss their analogues for infinite subsets of $\mathbb Z^d$ and, more generally, for…
Fractals have been at the heart of geophysical and geospatial studies in the recent past. We examine the emergent fractal character of water vapor distributions above the surface of the Earth as a function of both image resolution (number…
The fractal properties of models of randomly placed $n$-dimensional spheres ($n$=1,2,3) are studied using standard techniques for calculating fractal dimensions in empirical data (the box counting and Minkowski-sausage techniques). Using…
We present a new idea to understand the structure of nuclei, which is comparing to the liquid drop model. After discussing the probability that the nuclear system may be a fractal object with the characteristic of self-similarity, the…
Theoretical predictions for lateral distribution function of electrons in extensive air showers based on scaling formalism are presented. Our results are tested by comparison with AGASA experimental data taking into account the contribution…
Radio Cherenkov emission underlines detection of high energy particles via a signal growing like the particle-energy-squared. Cosmic ray-induced electromagnetic showers are a primary application. While many studies have treated the…