Coarse-Grained Probabilistic Automata Mimicking Chaotic Systems

Discretization of phase space usually nullifies chaos in dynamical systems. We show that if randomness is associated with discretization dynamical chaos may survive and be indistinguishable from that of the original chaotic system, when an entropic, coarse-grained analysis is performed. Relevance of this phenomenon to the problem of quantum chaos is discussed.Comment: 4 pages, 4 figure

Cyclotron-Bloch dynamics of a quantum particle in a 2D lattice

This paper studies the quantum dynamics of a charged particle in a 2D square lattice, under the influence of electric and magnetic fields, the former being aligned with one of the lattice axes and the latter perpendicular to the lattice plane. While in free space these dynamics consist of uniform motions in the direction orthogonal to the electric field vector, we find that, in a lattice, this directed drift takes place only for specific initial conditions and for electric field magnitudes smaller than a critical value. Otherwise, the quantum wave--packet spreads ballistically in both directions orthogonal to the electric field. We quantify this ballistic spreading and identify the subspace of initial conditions insuring directed transport with the drift velocity. We also describe the effect of disorder in the system.Comment: APS preprint format, 23 pages, 11 figure

Cosmological Perfect Fluids in Gauss-Bonnet Gravity

In a n-dimensional Friedmann-Robertson-Walker metric, it is rigorously shown that any analytical theory of gravity f(R,G), where R is the curvature scalar and G is the Gauss- Bonnet topological invariant, can be associated to a perfect-fluid stress-energy tensor. In this perspective, dark components of the cosmological Hubble flow can be geometrically interpreted

On the statistical distribution of first--return times of balls and cylinders in chaotic systems

We study returns in dynamical systems: when a set of points, initially populating a prescribed region, swarms around phase space according to a deterministic rule of motion, we say that the return of the set occurs at the earliest moment when one of these points comes back to the original region. We describe the statistical distribution of these "first--return times" in various settings: when phase space is composed of sequences of symbols from a finite alphabet (with application for instance to biological problems) and when phase space is a one and a two-dimensional manifold. Specifically, we consider Bernoulli shifts, expanding maps of the interval and linear automorphisms of the two dimensional torus. We derive relations linking these statistics with Renyi entropies and Lyapunov exponents.Comment: submitted to Int. J. Bifurcations and Chao

Ground state magnetic dipole moment of 35K

The ground state magnetic moment of 35K has been measured using the technique of nuclear magnetic resonance on beta-emitting nuclei. The short-lived 35K nuclei were produced following the reaction of a 36Ar primary beam of energy 150 MeV/nucleon incident on a Be target. The spin polarization of the 35K nuclei produced at 2 degrees relative to the normal primary beam axis was confirmed. Together with the mirror nucleus 35S, the measurement represents the heaviest T = 3/2 mirror pair for which the spin expectation value has been obtained. A linear behavior of gp vs. gn has been demonstrated for the T = 3/2 known mirror moments and the slope and intercept are consistent with the previous analysis of T = 1/2 mirror pairs.Comment: 14 pages, 5 figure

Elasto-viscoplastic modeling of subsidence above gas fields in the Adriatic Sea

Abstract. From the analysis of GPS monitoring data collected above gas fields in the Adriatic Sea, in a few cases subsidence responses have been observed not to directly correlate with the production trend. Such behavior, already described in the literature, may be due to several physical phenomena, ranging from simple delayed aquifer depletion to a much more complex time-dependent mechanical response of subsurface geomaterials to fluid withdrawal. In order to accurately reproduce it and therefore to be able to provide reliable forecasts, in the last years Eni has enriched its 3D finite element geomechanical modeling workflow by adopting an advanced constitutive model (Vermeer and Neher, 1999), which also considers the viscous component of the deformation. While the numerical implementation of such methodology has already been validated at laboratory scale and tested on synthetic hydrocarbon fields, the work herein presents its first application to a real gas field in the Adriatic Sea where the phenomenon has been observed. The results show that the model is capable to reproduce very accurately both GPS data and other available measurements. It is worth remarking that initial runs, characterized by the use of model parameter values directly obtained from the interpretation of mechanical laboratory tests, already provided very good results and only minor tuning operations have been required to perfect the model outcomes. Ongoing R&D projects are focused on a regional scale characterization of the Adriatic Sea basin in the framework of the Vermeer and Neher model approach

Implementation of an elasto-viscoplastic constitutive law in Abaqus/Standard for an improved characterization of rock materials

Subsidence modeling is an important activity in the oil and gas industry, for the environmental and operational implications associated to this phenomenon. Abaqus/Standard has been used for many years in Eni as the main numerical simulator for studying the geomechanical behavior of reservoirs. The results of a large campaign of acquisition of subsidence monitoring data in conjunction with the advanced analysis of laboratory experiments have shown that, in some cases, an improved mechanical characterization can be tailored to better capture the complex behavior of the reservoir rock under the effect of underground fluid withdrawal. In this work we first present an implementation in Abaqus/Standard of an elasto-viscoplastic model – namely the Vermeer and Neher model – as user defined material by means of the UMAT subroutine. Next, we provide the results of various simulations of laboratory tests that were performed to investigate its capability to identify the main features of the behavior of reservoir sands, also including time dependency. Finally, we show a preliminary application to a synthetic, nonetheless realistic, reservoir model that has been performed to assess the capabilities of the elasto-viscoplastic model in the simulation of subsidence evolution

Estimate of a spatially variable reservoir compressibility by assimilation of ground surface displacement data

Abstract. Fluid extraction from producing hydrocarbon reservoirs can cause anthropogenic land subsidence. In this work, a 3-D finite-element (FE) geomechanical model is used to predict the land surface displacements above a gas field where displacement observations are available. An ensemble-based data assimilation (DA) algorithm is implemented that incorporates these observations into the response of the FE geomechanical model, thus re- ducing the uncertainty on the geomechanical parameters of the sedimentary basin embedding the reservoir. The calibration focuses on the uniaxial vertical compressibility c M , which is often the geomechanical parameter to which the model response is most sensitive. The partition of the reservoir into blocks delimited by faults moti- vates the assumption of a heterogeneous spatial distribution of c M within the reservoir. A preliminary synthetic test case is here used to evaluate the effectiveness of the DA algorithm in reducing the parameter uncertainty associated with a heterogeneous c M distribution. A significant improvement in matching the observed data is obtained with respect to the case in which a homogeneous c M is hypothesized. These preliminary results are quite encouraging and call for the application of the procedure to real gas fields