Long continuous seismic data recorded at five broadband seismic stations during 2006 at Campi Flegrei caldera have been analyzed. Introducing a coarse‐grained method, we evaluate the time evolution of amplitude and polarization of the seismic noise in the frequency band common to long‐period events. The series are modulated on tidal time scales: the root‐mean square is basically dominated by solar contribution, while the azimuth of the polarization vector shows lunar diurnal and semidiurnal constituents. In addition, we find that in the frequency band common to long‐period events the azimuths are polarized toward a specific area, suggesting that these persistent oscillations can be induced by the activity of the shallow geothermal reservoir.

A not trivial problem for every experimental time series associated to a natural system is to individuate the significant variables to describe the dynamics, i.e., the effective degrees of freedom. The application of independent component analysis (ICA) has provided interesting results in this direction, e.g., in the seismological and atmospheric field. Since all natural phenomena can be represented by dynamical systems, our aim is to check the performance of ICA in this general context to avoid ambiguities when investigating an unknown experimental system. We show many examples, representing linear, nonlinear, and stochastic processes, in which ICA seems to be an efficacious preanalysis able to give information about the complexity of the dynamics.

We introduce a description of the collective transverse dynamics of charged (proton) beams in the stability regime by suitable classical stochastic fluctuations. In this scheme, the collective beam dynamics is described by time-reversal invariant diffusion processes deduced by stochastic variational principles (Nelson processes). By general arguments, we show that the diffusion coefficient, expressed in units of length, is given by ${\lambda }_c\sqrt{N},$ where N is the number of particles in the beam and ${\lambda }_c$ the Compton wavelength of a single constituent. This diffusion coefficient represents an effective unit of beam emittance. The hydrodynamic equations of the stochastic dynamics can be easily recast in the form of a Schrödinger equation, with the unit of emittance replacing the Planck action constant. This fact provides a natural connection to the so-called “quantum-like approaches” to beam dynamics. The transition probabilities associated to Nelson processes can be exploited to model evolutions suitable to control the transverse beam dynamics. In particular we show how to control, in the quadrupole approximation to the beam-field interaction, both the focusing and the transverse oscillations of the beam, either together or independently.

We analyze time series of Strombolian volcanic tremor, focusing our attention on the frequency band [0.1–0.5] Hz (very long period (VLP) tremor). Although this frequency band is largely affected by noise, we evidence two significant components by using Independent Component Analysis with the frequencies, respectively, of ~0.2 and ~0.4 Hz. We show that these components display wavefield features similar to those of the high frequency Strombolian signals (>0.5 Hz). In fact, they are radially polarised and located within the crater area. This characterization is lost when an enhancement of energy appears. In this case, the presence of microseismic noise becomes relevant. Investigating the entire large data set available, we determine how microseismic noise influences the signals. We ascribe the microseismic noise source to Scirocco wind. Moreover, our analysis allows one to evidence that the Strombolian conduit vibrates like the asymmetric cavity associated with musical instruments generating self-sustained tones.

We consider satellite time series concerning the atmospheric aerosol content. We prove that these time series are well described by a stochastic dynamical model. The principal peak in the power spectrum of these signals can be explained by stochastic resonance, linking variable external factors, such as Sun-Earth radiation budget and local insolation, to fluctuations on smaller spatial and temporal scale due to internal weather and antrophic components.