Related papers: Fractal Electromagnetic Showers
We review some of the properties of extensive cosmic ray air showers and describe a simple model of the radio-frequency radiation generated by shower electrons and positrons as they bend in the Earth's magnetic field. We perform simulations…
The dimensionality of an electronic quantum system is decisive for its properties. In 1D electrons form a Luttinger liquid and in 2D they exhibit the quantum Hall effect. However, very little is known about the behavior of electrons in…
We discuss the definition and measurability questions of random fractals and find under certain conditions a formula for upper and lower Minkowski dimensions. For the case of a random self-similar set we obtain the packing dimension.
In this article we study the energy level spectrum of fractals which have block-hierarchical structures. We develop a method to study the spectral properties in terms of linearization of spectral decimation procedure and verify it…
In this article, I will review how observations performed with extensive air showers are being used to probe hadronic interactions at high energy. I will briefly overview the new studies exploring the connection between the dynamics of air…
The increasing efforts are still in progress to establish existence and to investigate the properties of pairs of Extensive Air Showers (EAS) that can be considered as originated from a single event which produced the Cosmic Radiation (CR)…
In this work we argue that, in the interpretation of the energy dependence of the depth of the shower maximum and of the muon content in high energy cosmic ray showers ($E > 10^{17}$ eV), other variables besides the composition may play an…
The behavior of microgels near surfaces and their adsorption is studied by simple scaling theory. Two different types of microgels can be studied, i.e., fractal type microgels and randomly crosslinked polymer chains. In the first case the…
Urbanization is a phenomenon of concern for planning and public health: projections are difficult because of policy changes and natural events, and indicators are multiple. There are previous studies of development that used fractals, but…
We study the wave equation on one-dimensional self-similar fractal structures that can be analyzed by the spectral decimation method. We develop efficient numerical approximation techniques and also provide uniform estimates obtained by…
It is wellknown that the ordinary calculus is inadequate to handle fractal structures and processes and another suitable calculus needs to be developed for this purpose. Recently it was realized that fractional calculus with suitable…
We propose a definition for the similarity dimension of fractal curves with multiple generators.
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…
The properties of cosmic rays with energies above 1PeV have to be deduced from the spacetime structure and particle content of the air showers which they initiate. In this review, a summary of the phenomenology of these giant air showers is…
In a recently published paper (J. of Modern Optics 50 (9) (2003) 1477-1486) a qualitative analysis of the moire effect observed by superposing two grids containing Cantor fractal structures was presented. It was shown that the moire effect…
Electromagnetic showers developing from the collision of an ultra-intense laser pulse with a beam of high-energy electrons or photons are investigated under conditions relevant to future experiments on multi-petawatt laser facilities. A…
We study the conformal dimension of fractal percolation and show that, almost surely, the conformal dimension of a fractal percolation is strictly smaller than its Hausdorff dimension.
Fractal time series has been shown to be self-affine and are characterized by a roughness exponent H. The exponent H is a measure of the persistence of the fluctuations associated with the time series. We use a recently introduced method…
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…
The radiative properties of most structures are intimately connected to the way in which their constituents are ordered on the nano-scale. We have proposed a new representation for radiative heat transfer formalism in many-body systems. In…