Stefano Vignolo

f(R) gravity with torsion: the metric-affine approach

The role of torsion in f(R) gravity is considered in the framework of metric-affine formalism. We discuss the field equations in empty space and in the presence of perfect fluid matter, taking into account the analogy with the Palatini formalism. As a result, the extra curvature and torsion degrees of freedom can be dealt as an effective scalar field of a fully geometric origin. From a cosmological point of view, such a geometric description could account for the whole dark side of the universe.

A Modified Theory of Gravity with Torsion and Its Applications to Cosmology and Particle Physics

In this paper we consider the most general least-order derivative theory of gravity in which not only curvature but also torsion is explicitly present in the Lagrangian, and where all independent fields have their own coupling constant: we will apply this theory to the case of ELKO fields, which is the acronym of the German Eigenspinoren des LadungsKonjugationsOperators designating eigenspinors of the charge conjugation operator, and thus they are a Majorana-like special type of spinors; and to the Dirac fields, the most general type of spinors. We shall see that because torsion has a coupling constant that is still undetermined, the ELKO and Dirac field equations are endowed with self-interactions whose coupling constant is undetermined: we discuss different applications according to the value of the coupling constants and the different properties that consequently follow. We highlight that in this approach, the ELKO and Dirac field’s self-interactions depend on the coupling constant as a parameter that may even make these non-linearities manifest at subatomic scales.

Dirac spinors in Bianchi-I f(R)-cosmology with torsion

We study Dirac spinors in Bianchi type-I cosmological models, within the framework of torsional f(R)-gravity. We find four types of results: the resulting dynamic behavior of the universe depends on the particular choice of function f(R); some f(R) models do not isotropize and have no Einstein limit, so that they have no physical significance, whereas for other f(R) models isotropization and Einsteinization occur, and so they are physically acceptable, suggesting that phenomenological arguments may select f(R) models that are physically meaningful; the singularity problem can be avoided, due to the presence of torsion; the general conservation laws holding for f(R)-gravity with torsion ensure the preservation of the Hamiltonian constraint, so proving that the initial value problem is well-formulated for these models.

Dirac fields in f(R)-gravity with torsion

We study f(R)-gravity with torsion in the presence of Dirac massive fields. Using the Bianchi identities, we formulate the conservation laws of the theory and we check the consistency with the matter field equations. Further, we decompose the field equations in torsionless and torsional terms: we show that the nonlinearity of the gravitational Lagrangian reduces to the presence of a scalar field that depends on the spinor field; this additional scalar field gives rise to an effective stress?energy tensor and plays the role of a scale factor modifying the normalization of Dirac fields. Problems for fermions regarding the positivity of energy and the particle?antiparticle duality are discussed.

Controllable pitch propeller actuating mechanism, modelling and simulation

This article focuses on the mathematical model of the pitch control mechanism for a marine controllable pitch propeller, with the aim of describing the dynamic behaviour of this kind of system and its influence on ship performance. Too great a load on the blades can result in high pressures in the actuating system, response delays and control system problems, which are ultimately responsible for most mechanism failures. The behaviour of the controllable pitch propeller actuating mechanism is considered in terms of blade position, oil pressures inside the controllable pitch propeller hub and magnitudes of the forces acting on the blades. In the proposed mathematical model, the forces acting on the propeller blade are evaluated taking into account the yaw motion of the ship, the propeller speed (including shaft accelerations and decelerations) and the turning of the blade during the pitch change. On the basis of the introduced procedure, a controllable pitch propeller numerical model as part of an overall propulsion and manoeuvrability simulator representing the dynamic behaviour of a twin-screw fast vessel is developed. The aim of this work is to represent the ship propulsion dynamics through time-domain simulation, based on which the designers can develop and test several design options, in order to avoid possible machinery overloads with their consequent failures and to obtain the best possible ship performances. In this aspect, the controllable pitch propeller model is an essential design tool.

On the well formulation of the Initial Value Problem of metric–affine f(R)-gravity

We study the well-formulation of the initial value problem of f(R)-gravity in the metric-affine formalism. The problem is discussed in vacuo and in presence of perfect-fluid matter, Klein–Gordon and Yang–Mills fields. Adopting Gaussian normal coordinates, it can be shown that the problem is always well-formulated. Our results refute some criticisms to the viability of f(R)-gravity recently appeared in literature.

Running coupling in electroweak interactions of leptons from f(R)-gravity with torsion

The f(R)-gravitational theory with torsion is considered for one family of leptons; it is found that the torsion tensor gives rise to interactions having the structure of the weak forces, while the intrinsic non-linearity of the f(R) function provides an energy-dependent coupling: in this way, torsional f(R) gravity naturally generates both structure and strength of the electroweak interactions among leptons. This implies that the weak interactions among the lepton fields could be addressed as a geometric effect due to the interactions among spinors induced by the presence of torsion in the most general f(R) gravity. Phenomenological considerations are given.

The most general ELKO matter in torsional f(R)-theories

We study f(R)-gravity with torsion in presence of the most general ELKO matter, checking the consistency of the conservation laws with the matter field equations; we discuss some mathematical features of the field equations in connection with a cosmological application.

Numerical modelling of propulsion, control and ship motions in 6 degrees of freedom

This work presents the main steps for the development of a multi-physic simulation platform, able to represent the dynamics of a twin-screw ship in 6 degrees of freedom, taking into account the complete propulsion system including automation effects. The simulation platform has to be used in the preliminary design phase in order to study and design the propulsion plant and its control system. The ship motion model has been developed including roll motion, in order to capture the ship heel angles during tight turning circles, which may be significant for a fast naval vessel. Moreover, the simulation model includes a simplified representation of the asymmetric behaviour of the two propeller shafts during manoeuvres, which cannot be neglected when dealing with the propulsion plant behaviour. Several sub-models have been developed and calibrated by means of a set of experimental tests, in model and full scale. The sea trial campaign is finally used to validate and tune the developed simulator; thus, the final version may be adopted as an optimization tool for other future designs (or sister ships) and training purposes. Although the presented case study has been validated on a specific ship, most of the discussed models have a general application.

The Cauchy problem for metric-affine f(R)-gravity in presence of a Klein-Gordon scalar field

We study the initial value formulation of metric-affine f(R)-gravity in presence of a Klein–Gordon scalar field acting as source of the field equations. Sufficient conditions for the well-posedness of the Cauchy problem are formulated. This result completes the analysis of the same problem already considered for other sources.