Related papers: Fractal Dimensionof the El Salvador Earthquake (20…
We study the self-similar structure of electromagnetic showers and introduce the notion of the fractal dimension of a shower. Studies underway of showers in various materials and at various energies are presented, and the range over which…
Scaling analysis reveals striking regularities in earthquake occurrence. The time between any one earthquake and that following it is random, but it is described by the same universal-probability distribution for any spatial region and…
An analysis of moments and spectra shows that, while the distribution of avalanche areas obeys finite size scaling, that of toppling numbers is universally characterized by a full, nonlinear multifractal spectrum. Rare, large avalanches…
We introduce here the two-fractal model of earthquake dynamics. As the fractured surfaces have self-affine properties, we consider the solid-solid interface of the earth's crust and the tectonic plate below as fractal surfaces. The overlap…
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…
Despite several experiments on chaotic quantum transport in two-dimensional systems such as semiconductor quantum dots, corresponding quantum simulations within a real-space model have been out of reach so far. Here we carry out quantum…
The possibility to constrain fractal space dimensionality from Astrophysics and other areas is briefly reviewed. Assuming such dimensionality to be $3 + \epsilon$, a limit to $\epsilon$ can be inferred from COBE satellite data. The…
This article deals with the estimation of fractal dimension of spatio-temporal patterns that are generated by numerically solving the Swift Hohenberg (SH) equation. The patterns were converted into a spatial series (analogous to time…
For any given set $E\subset [1,2]$, we discuss a fractal frequency-localized version of the $L^p$ local smoothing estimates for the half-wave propagator with times in $E$. A conjecture is formulated in terms of a quantity involving the…
Seismic risk estimates will be vastly improved with an increased understanding of historical (and pre-historical) seismic events. However the only existing data for these events is anecdotal and sparse. To address this we developed a…
We present a multifractal analysis of Mount St. Helens seismic activity during 1980-2002. The seismic time distribution is studied in relation to the eruptive activity, mainly marked by the 1980 major explosive eruptions and by the…
The optical spectra of fractal multilayer dielectric structures have been shown to possess spectral scalability, which has been found to be directly related to the structure's spatial (geometrical) self-similarity. Phase and amplitude…
\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…
For a long time, many methods are developed to make temporal signal analyses based on time series. However, for geographical systems, spatial signal analyses are as important as temporal signal analyses. Nonstationary spatial and temporal…
A recently proposed unified scaling law for interoccurrence times of earthquakes [P. Bak et al., Phys. Rev. Lett. {\bf 88}, 178501 (2002)] is analyzed, both theoretically and with data from Southern California. We decompose the…
In this work, we analyse the temperature fluctuations of the cosmic microwave background radiation observed by COBE and show that the distribution can be fitted by a fractal distribution with a fractal dimension $ D= 1.43 \pm 0.07 $. This…
The brain is a system operating on multiple time scales, and characterisation of dynamics across time scales remains a challenge. One framework to study such dynamics is that of fractal geometry. However, currently there exists no…
We review the developments of the statistical physics of fracture and earthquake over the last four decades. We argue that major progress has been made in this field and that the key concepts should now become integral part of the (under-)…
We show that when the standard techniques for calculating fractal dimensions in empirical data (such as the box counting) are applied on uniformly random structures, apparent fractal behavior is observed in a range between physically…
In this study, we present a method to measure changes over time of fractal dimension. We confirmed that our method can calculate the fractal dimension with the same precision as conventional methods, and tracking performance of our method…