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We consider long-time recorded seismic signals of Stromboli volcano to determine the inter-time distribution function of the Strombolian explosion-quakes. We show that it is Poissonian. Hence, the apparently observed periodic recurrence of the explosions is actually described by the constant rate of a Poisson process. Moreover, combining a diffusive model with the experimental inter-time distribution, we can determine the size distributions of the bubbles and infer the observed slug sizes.

Self-organized criticality (SOC) successfully describes power law behaviour of size distribution in many natural phenomena. However, it does not consider time correlations between events and therefore it is unable to reproduce the time occurrence behaviour, namely the inter-event time distribution, extremely relevant for many problems. We present a SOC model with memory: events are nucleated not only as a consequence of the instantaneous value of the local field with respect to the. ring threshold, but on the basis of the whole history of the system. We apply the model to the study of earthquake occurrence and we obtain, without any parameter tuning, excellent agreement with inter-event time and magnitude distributions from the Southern California Catalog.

In this paper we perform a linear stability analysis of the equilibrium solution of a suitable Korteweg model for a two-phase fluid modeling a magma transport in a volcanic conduit. By perturbing the fluid at rest and applying the principle of exchange of stabilities, we prove that at the onset of instability, a stationary cellular convection of bubbles prevails. This behavior could be a reasonable description of the transition from the two-phase system magma-dissolved gas in the chamber to the rising foam in the conduit, due to rapid decompression at the initial stage of a volcano's eruption. We analyze the disturbances in normal modes and show that the dimension of the cells, given by a suitable critical value of the wavelength, corresponds, consistently with the model, to the width of the Gaussian-shaped solitary wave solution found in the dynamical case. The implication of the model is to furnish the threshold value of the perturbations normal mode in order to trigger magma fragmentation, and as a consequence, we obtain the dimension value of the early cells of bubbles at the conduit's base.

The stick-slip is investigated in a seismic fault model made of a con fined granular system under shear stress via three dimensional Molecular Dynamics simulations. We study the statistics of slipping events and, in particular, the dependence of the distribution on model parameters. The distribution consistently exhibits two regimes: an initial power law and a bump at large slips. The initial power law decay is in agreement with the the Gutenberg-Richter law characterizing real seismic occurrence. The exponent of the initial regime is quite independent of model parameters and its value is in agreement with experimental results. Conversely, the position of the bump is solely controlled by the ratio of the drive elastic constant and the system size. Large slips also become less probable in absence of fault gouge and tend to disappear for stiff drives. A two{time force{force correlation function, and a susceptibility related to the system response to pressure changes, characterize the micromechanics of slipping events. The correlation function unveils the micromechanical changes occurring both during microslips and slips. The mechanical susceptibility encodes the magnitude of the incoming microslip. Numerical results for the cellular-automaton version of the spring block model con firm the parameter dependence observed for size distribution in the granular model.