Inverse kinetic theory for incompressible thermofluids

An interesting issue in fluid dynamics is represented by the possible existence of inverse kinetic theories (IKT) which are able to deliver, in a suitable sense, the complete set of fluid equations which are associated to a prescribed fluid. From the mathematical viewpoint this involves the formal description of a fluid by means of a classical dynamical system which advances in time the relevant fluid fields. The possibility of defining an IKT for the 3D incompressible Navier-Stokes equations (INSE), recently investigated (Ellero \textit{et al}, 2004-2007) raises the interesting question whether the theory can be applied also to thermofluids, in such a way to satisfy also the second principle of thermodynamics. The goal of this paper is to prove that such a generalization is actually possible, by means of a suitable \textit{extended phase-space formulation}. We consider, as a reference test, the case of non-isentropic incompressible thermofluids, whose dynamics is described by the Fourier and the incompressible Navier-Stokes equations, the latter subject to the conditions of validity of the Boussinesq approximation.Comment: Contributed paper at RGD26 (Kyoto, Japan, July 2008

Generalized covariant gyrokinetic dynamics of magnetoplasmas

A basic prerequisite for the investigation of relativistic astrophysical magnetoplasmas, occurring typically in the vicinity of massive stellar objects (black holes, neutron stars, active galactic nuclei, etc.), is the accurate description of single-particle covariant dynamics, based on gyrokinetic theory (Beklemishev et al.,1999-2005). Provided radiation-reaction effects are negligible, this is usually based on the assumption that both the space-time metric and the EM fields (in particular the magnetic field) are suitably prescribed and are considered independent of single-particle dynamics, while allowing for the possible presence of gravitational/EM perturbations driven by plasma collective interactions which may naturally arise in such systems. The purpose of this work is the formulation of a generalized gyrokinetic theory based on the synchronous variational principle recently pointed out (Tessarotto et al., 2007) which permits to satisfy exactly the physical realizability condition for the four-velocity. The theory here developed includes the treatment of nonlinear perturbations (gravitational and/or EM) characterized locally, i.e., in the rest frame of a test particle, by short wavelength and high frequency. Basic feature of the approach is to ensure the validity of the theory both for large and vanishing parallel electric field. It is shown that the correct treatment of EM perturbations occurring in the presence of an intense background magnetic field generally implies the appearance of appropriate four-velocity corrections, which are essential for the description of single-particle gyrokinetic dynamics.Comment: Contributed paper at RGD26 (Kyoto, Japan, July 2008

The exact radiation-reaction equation for a classical charged particle

An unsolved problem of classical mechanics and classical electrodynamics is the search of the exact relativistic equations of motion for a classical charged point-particle subject to the force produced by the action of its EM self-field. The problem is related to the conjecture that for a classical charged point-particle there should exist a relativistic equation of motion (RR equation) which results both non-perturbative, in the sense that it does not rely on a perturbative expansion on the electromagnetic field generated by the charged particle and non-asymptotic, i.e., it does not depend on any infinitesimal parameter. In this paper we intend to propose a novel solution to this well known problem, and in particular to point out that the RR equation is necessarily variational. The approach is based on two key elements: 1) the adoption of the relativistic hybrid synchronous Hamilton variational principle recently pointed out (Tessarotto et al, 2006). Its basic feature is that it can be expressed in principle in terms of arbitrary "hybrid" variables (i.e., generally non-Lagrangian and non-Hamiltonian variables); 2) the variational treatment of the EM self-field, taking into account the exact particle dynamics.Comment: Contributed paper at RGD26 (Kyoto, Japan, July 2008

SPATIO TEMPORAL DATA CUBE APPLIED TO AIS CONTAINERSHIPS TREND ANALYSIS IN THE EARLY YEARS OF THE BELT AND ROAD INITIATIVE – FROM GLOBAL TO LOCAL SCALE

Maritime trade represents a significant part of all global import-export trade. The traffic of containerships can be monitored through Automatic Identification System (AIS), due to the fact that the International Maritime Organization (IMO) regulation requires AIS to be fitted aboard all ships of 300 gross tonnage and upwards engaged on international voyages. The approach proposed by the authors aimed to extract value added information from an AIS dataset, with a focus on maritime economy. Using an AIS dataset of global position of containerships from 01/01/2012 to 31/12/2016, the paper focuses on space-time data cube creation and analysis for a better understanding of maritime trades trends. Data cube creation has been tested at different spatio-temporal bins dimension and on different specific topics (TEU classes, alliances, chokepoints and port areas), analysing the sensitivity on trend results, and highlighting how appropriate spatio-temporal bins dimensions are important to effectively highlight relevant trends. Results of the trend analysis are discussed and validated with the main data and information found over the period 2012–2016. The aim of this paper is to demonstrate the suitability of this approach applied to AIS data and to highlight its limitations. The authors can conclude that the approach used has proved to be adequate in describing the evolution of the global import-export trade

Generalized Grad-Shafranov equation for gravitational Hall-MHD equilibria

The consistent theoretical description of gravitational Hall-MHD (G-Hall-MHD) equilibria is of fundamental importance for understanding the phenomenology of accretion disks (AD) around compact objects (black holes, neutron stars, etc.). The very existence of these equilibria is actually suggested by observations, which show evidence of quiescent, and essentially non-relativistic, AD plasmas close to compact stars, thus indicating that accretion disks may be characterized by slowly varying EM and fluid fields. These (EM) fields, in particular the electric field, may locally be extremely intense, so that AD plasmas are likely to be locally non-neutral and therefore characterized by the presence of Hall currents. This suggests therefore that such equilibria should be described in the framework of the Hall-MHD theory. Extending previous approaches, holding for non-rotating plasmas or based on specialized single-species model equilibria which ignore the effect of space-time curvature, the purpose of this work is the formulation of a generalized Grad-Shafranov (GGS) equation suitable for the investigation of G-Hall-MHD equilibria in AD's where non-relativistic plasmas are present. For this purpose the equilibria are assumed to be generated by a strong axisymmetric stellar magnetic field and by the gravitating plasma characterizing the AD

Axisymmetric gravitational MHD equilibria in the presence of plasma rotation

In this paper, extending the investigation developed in an earlier paper (Cremaschini et al., 2008), we pose the problem of the kinetic description of gravitational Hall-MHD equilibria which may arise in accretion disks (AD) plasmas close to compact objects. When intense EM and gravitational fields, generated by the central object, are present, a convenient approach can be achieved in the context of the Vlasov-Maxwell description. In this paper the investigation is focused primarily on the following two aspects: 1) the formulation of the kinetic treatment of G-Hall-MHD equilibria. Based on the identification of the relevant first integrals of motion, we show that an explicit representation can be given for the equilibrium kinetic distribution function. For each species this is represented as a superposition of suitable generalized Maxwellian distributions; 2) the determination of the constraints to be placed on the fluid fields for the existence of the kinetic equilibria. In particular, this permits a unique determination of the functional form of the species number densities and of the fluid partial pressures, in terms of suitably prescribed flux functions.Comment: Contributed paper at RGD26 (Kyoto, Japan, July 2008