Convolution-type derivatives, hitting-times of subordinators and time-changed C0C_0-semigroups

In this paper we will take under consideration subordinators and their inverse processes (hitting-times). We will present in general the governing equations of such processes by means of convolution-type integro-differential operators similar to the fractional derivatives. Furthermore we will discuss the concept of time-changed $C_0$-semigroup in case the time-change is performed by means of the hitting-time of a subordinator. We will show that such time-change give rise to bounded linear operators not preserving the semigroup property and we will present their governing equations by using again integro-differential operators. Such operators are non-local and therefore we will investigate the presence of long-range dependence.Comment: Final version, Potential analysis, 201

Supersonic plasma turbulence in the laboratory

The properties of supersonic, compressible plasma turbulence determine the behavior of many terrestrial and astrophysical systems. In the interstellar medium and molecular clouds, compressible turbulence plays a vital role in star formation and the evolution of our galaxy. Observations of the density and velocity power spectra in the Orion B and Perseus molecular clouds show large deviations from those predicted for incompressible turbulence. Hydrodynamic simulations attribute this to the high Mach number in the interstellar medium (ISM), although the exact details of this dependence are not well understood. Here we investigate experimentally the statistical behavior of boundary-free supersonic turbulence created by the collision of two laser-driven high-velocity turbulent plasma jets. The Mach number dependence of the slopes of the density and velocity power spectra agree with astrophysical observations, and supports the notion that the turbulence transitions from being Kolmogorov-like at low Mach number to being more Burgers-like at higher Mach numbers

Benford’s Law in Time Series Analysis of Seismic Clusters

Benford's analysis is applied to the recurrence times of approximately 17,000 seismic events in different geological contexts of Italy over the last 6 years, including the Mt. Etna volcanic area and the seismic series associated with the destructive M (w) 6.3, 2009 L'Aquila earthquake. A close conformity to Benford's law and a power-law probability distribution for the recurrence times of consecutive events is found, as typical of random multiplicative processes. The application of Benford's law to the recurrence event times in seismic series of specific seismogenic regions represents a novel approach, which enlarges the occurrence and relevance of Benford-like asymmetries, with implications on the physics of natural systems approaching a power law behaviour. Moreover, we propose that the shift from a close conformity of Benford's law to Brownian dynamics, observed for time separations among non-consecutive events in the study seismic series, may be ruled by a periodical noise factor, such as the effects of Earth tides on seismicity tuning