Salvatore De Martino

Radon emanation and exhalation rates from soils measured with an electrostatic collector

Abstract The radon emanation and exhalation rates from soil samples were measured using an electrostatic collector coupled to a silicon detector. The radon progenitor activities ( 226 Ra and 232 Th) of soil samples were determined using γ-ray spectroscopy with a germanium detector. The radon emanation and exhalation rates have been measured accurately and rapidly. Measurements of soil samples having different physical properties were performed. Data analysis methods were developed to identify the effect of grain size and porosity of soil samples. The results confirm interesting dependencies of emanated radon as a function of two soil parameters.

Analogical model for mechanical vibrations in flue organ pipes inferred by independent component analysis

Several experiments have been performed to investigate the mechanical vibrations associated with an organ pipe. The measurements have been made by using laser Doppler vibrometry, a well-known not-invasive optical measurement technique that is very widely used in structural dynamics. The recorded signals are analyzed by using a well-established decomposition method in time domain, i.e., independent component analysis. Asymptotic dynamics methods to recognize low-dimensional dynamic system associated with this wave field is then considered. The full-toned recorded signals appear decomposed into three independent components. The independent components are nonlinear due to the fractal dimension of the attractor. These results for the mechanic vibrational field are compared with those of the acoustic one. It is interesting to note that the two fields have many common characteristics. Finally, a low-dimensional dynamic system that reproduces the main characteristics of the mechanical wave field in the time and frequency domains is introduced.

NON-NEWTONIAN GRAVITY, FLUCTUATIVE HYPOTHESIS AND THE SIZES OF ASTROPHYSICAL STRUCTURES

We show that the characteristic sizes of astrophysical and cosmological structures, where gravity is the only overall relevant interaction assembling the system, have a phenomenological relation to the microscopic scales whose order of magnitude is essentially ruled by the Compton wavelength of the proton. This result agrees with the absence of screening mechanisms for the gravitational interaction and could be connected to the presence of Yukawa correcting terms in the Newtonian potential which introduces typical interaction lengths. Furthermore, we are able to justify, in a straightforward way, the Sanders-postulated mass of a vector boson considered in order to obtain the characteristic sizes of galaxies.

ICA based identification of dynamical systems generating synthetic and real world time series

Independent Component Analysis (ICA) is a recent and well known technique used to separate mixtures of signals. While in general the researchers put their attention on the type of signals and of mixing, we focus our attention on a quite general class of models which act as sources of the time series, the dynamical systems. In this paper we focus our attention on the general problem to understand the behaviour of ICA methods with respect to the time series deriving from a specific dynamical system, selecting large classes of them, and using ICA to make separation. This study gives some interesting results that are very useful both to highlight some properties related to dynamical systems and to clarify some general aspects of ICA, by using both synthetic and real data.From one hand we study the features of the linear (simple and coupled) and non-linear (single and coupled) dynamical systems, stochastic resonances, chaotic and real dynamical systems. We have to stress that we obtain information about the separation of these systems and substantially how from the entropy of the complete system we can obtain the entropies of the single dynamical systems (so that we also could obtain a more realistic analogic circuit).On the other hand these results show the high capability of the ICA method to recognize the dynamical systems independently from their complexity and in the case of stochastic series ICA perfectly recognizes the different dynamical systems also where the Fourier Transform is irresolute.We also note that in the case of real dynamical systems we showed that ICA permits to recognize the information connected to the sources and to associate to it a phenomenological dynamical system that reproduce it (i.e. Organ Pipe, Stromboli Volcano, Aerosol Index).

Exact solutions of Fokker-Planck equations associated to quantum wave functions

Abstract We analyse the non-stationary solutions of the Fokker-Planck equations associated to quantum states by stochastic mechanics. In particular we study the exact solutions for the stationary states of the harmonic oscillator and the potentials which realize new possible evolutions ruled by the same equations.

Stochastic-hydrodynamic model of halo formation in charged particle beams

The formation of the beam halo in charged particle accelerators is studied in the framework of a stochastic-hydrodynamic model for the collective motion of the particle beam. In such a stochastic- hydrodynamic theory the density and the phase of the charged beam obey a set of coupled nonlinear hydrodynamic equations with explicit time-reversal invariance. This leads to a linearized theory that describes the collective dynamics of the beam in terms of a classical Schrodinger equation. Taking into account space-charge effects, we derive a set of coupled nonlinear hydrodynamic equations. These equations define a collective dynamics of self-interacting systems much in the same spirit as in the Gross-Pitaevskii and Landau-Ginzburg theories of the collective dynamics for interacting quantum many-body systems. Self-consistent solutions of the dynamical equations lead to quasistationary beam configurations with enhanced transverse dispersion and transverse emittance growth. In the limit of a frozen space-charge core it is then possible to determine and study the properties of stationary, stable core-plus-halo beam distributions. In this scheme the possible reproduction of the halo after its elimination is a consequence of the stationarity of the transverse distribution which plays the role of an attractor for every other distribution.

Controlled quantum evolutions and transitions

We study the nonstationary solutions of Fokker-Planck equations associated to either stationary or non stationary quantum states. In particular, we discuss the stationary states of quantum systems with singular velocity fields. We introduce a technique that allows arbitrary evolutions ruled by these equations to account for controlled quantum transitions. As a first signficant application we present a detailed treatment of the transition probabilities and of the controlling time-dependent potentials associated to the transitions between the stationary, the coherent, and the squeezed states of the harmonic oscillator.

DIFFUSION PROCESSES AND COHERENT STATES

It is shown that uncertanity relations, as well as coherent and squeezed states, are structural properties of stochastic processes with Fokker–Planck dynamics. The quantum mechanical coherent and squeezed states are explicitly constructed via Nelson stochastic quantization. The method is applied to derive new minimum uncertainty states in time-dependent oscillator potentials.

Lévy-Student distributions for halos in accelerator beams

We describe the transverse beam distribution in particle accelerators within the controlled, stochastic dynamical scheme of stochastic mechanics (SM) which produces time reversal invariant diffusion processes. This leads to a linearized theory summarized in a Schrödinger-like (SL) equation. The space charge effects have been introduced in recent papers by coupling this S-L equation with the Maxwell equations. We analyze the space-charge effects to understand how the dynamics produces the actual beam distributions, and in particular we show how the stationary, self-consistent solutions are related to the (external and space-charge) potentials both when we suppose that the external field is harmonic (constant focusing), and when we a priori prescribe the shape of the stationary solution. We then proceed to discuss a few other ideas by introducing generalized Student distributions, namely, non-Gaussian, Lévy infinitely divisible (but not stable) distributions. We will discuss this idea from two different standpoints: (a) first by supposing that the stationary distribution of our (Wiener powered) SM model is a Student distribution; (b) by supposing that our model is based on a (non-Gaussian) Lévy process whose increments are Student distributed. We show that in the case (a) the longer tails of the power decay of the Student laws and in the case (b) the discontinuities of the Lévy-Student process can well account for the rare escape of particles from the beam core, and hence for the formation of a halo in intense beams.

Inference of Planck action constant by a classical fluctuative postulate holding for stable microscopic and macroscopic dynamical systems

The possibility is discussed of inferring or simulating some aspects of quantum dynamics by adding classical statistical fluctuations to classical mechanics. We introduce a general principle of mechanical stability and derive a necessary condition for classical chaotic fluctuations to affect confined dynamical systems, on all scales ranging from microscopic to macroscopic domains. As a consequence we obtain, both for microscopic and macroscopic aggregates, dimensional relations defining the minimum unit of action of individual constituents, yielding in all cases Planck action constant.