Alexander Balankin

SEISMIC ACTIVITY SEEN THROUGH EVOLUTION OF THE HURST EXPONENT MODEL IN 3D

The dynamics seismic activity occurred in the Cocos Plate—Mexico is analyzed through the evolution of Hurst exponent and 3D fractal dimension, under the mathematical fractal structure based on seismic activity time series, taking into account the magnitude (M) as the main parameter to be estimated. The seismic activity time series and, annual intervals are considered first for finding the Hurst exponent of each year since 1988 (the year in which the database is consistent) until 2012, and then the following years are accumulated describing the cumulative Hurst exponent. The seismic activity description is based on Cocos Plate data information; during a period conform from 1 January 1988 to 31 December 2012. Analyses were performed following methods, mainly considering that the Hurst exponent analysis provides the ability to find the seismicity behavior time–space, described by parameters obtained under the fractal dimension and complex systems.

Anomalous roughness with system-size-dependent local roughness exponent.

We note that in a system far from equilibrium the interface roughening may depend on the system size which plays the role of control parameter. To detect the size effect on the interface roughness, we study the scaling properties of rough interfaces formed in paper combustion experiments. Using paper sheets of different width lambda L0, we found that the turbulent flame fronts display anomalous multiscaling characterized by nonuniversal global roughness exponent alpha and the system-size-dependent spectrum of local roughness exponents zeta(q) (lambda) = zeta(1) (1) q(-omega) lambda(phi) <alpha, whereas the burning fronts possess conventional multiaffine scaling. The structure factor of turbulent flame fronts also exhibit unconventional scaling dependence on lambda. These results are expected to apply to a broad range of far from equilibrium systems, when the kinetic energy fluctuations exceed a certain critical value.