Related papers: Fractal Electromagnetic Showers
Recently, we pointed out that on a class on non exactly decimable fractals two different parameters are required to describe diffusive and vibrational dynamics. This phenomenon we call dynamical dimension splitting is related to the lack of…
Fractal percolation exhibits a dramatic topological phase transition, changing abruptly from a dust-like set to a system spanning cluster. The transition points are unknown and difficult to estimate. In many classical percolation models the…
The evolution and spatial structure of displacement fronts in fractures with self-affine rough walls are studied by numerical simulations. The fractures are open and the two faces are identical but shifted along their mean plane, either…
We have studied the effect of changing the density and magnetic field strength in the coherent pulses that are emitted as energetic showers develop in the atmosphere. For this purpose we have developed an extension of ZHS, a program to…
Detailed theoretical study of the mean square radius of extensive air shower electrons has been made in connection with further development of scaling formalism for electron lateral distribution function. A very simple approximation…
The domain morphology of weakly disordered ferromagnets, quenched from the high-temperature phase to the low-temperature phase, is studied using numerical simulations. We find that the geometrical properties of the coarsening domain…
In a recent work on fluid infiltration in a Hele-Shaw cell with the pore-block geometry of Sierpinski carpets (SCs), the area filled by the invading fluid was shown to scale as F~t^n, with n<1/2, thus providing a macroscopic realization of…
Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…
Propagation of elastic waves along the axis of cylindrical shells is of great current interest due to their ubiquitous presence and technological importance. Geometric imperfections and spatial variations of properties are inevitable in…
Anomalous short- and long-time self-diffusion of non-overlapping fractal particles on a percolation cluster with spreading dimension $1.67(2)$ is studied by dynamic Monte Carlo simulations. As reported in Phys. Rev. Lett. 115, 097801…
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…
Energy techniques can be used to study the structure of fractal sets; the existence of a measure with finite Riesz energy supported on a set gives information about its dimension, distribution, and density. In this paper, we study…
The properties of cosmic rays with energies above 10**6 GeV have to be deduced from the spacetime structure and particle content of the air showers which they initiate. In this review we summarize the phenomenology of these giant air…
A computer simulation technique, suited to replicate real adsorption experiments, was applied to pure simulated silica in order to gain insight into the fractal regime of its surface. The previously reported experimental fractal dimension…
Recently, attempts have been made to take into account the fractal properties of seismicity when mapping the long-term rate of earthquakes. The paper touches upon the theoretical aspects of fractality and provides a critical analysis of its…
We study the scaling properties of two-dimensional turbulence using dimensional analysis. In particular, we consider the energy spectrum both at large and small scales and in the "inertial ranges" for the cases of freely decaying and forced…
The interstellar medium seems to have an underlying fractal structure which can be characterized through its fractal dimension. However, interstellar clouds are observed as projected two-dimensional images, and the projection of a…
The concept of self-similarity on subsets of algebraic varieties is defined by considering algebraic endomorphisms of the variety as `similarity' maps. Self-similar fractals are subsets of algebraic varieties which can be written as a…
Self-projective sets are natural fractal sets which describe the action of a semigroup of matrices on projective space. In recent years there has been growing interest in studying the dimension theory of self-projective sets, as well as…
Research done during the previous century established our Standard Cosmological Model. There are many details still to be filled in, but few would seriously doubt the basic premise. Past surveys have revealed that the large-scale…