arXiv subjects

Claudio Cremaschini

Publications and source records attributed to Claudio Cremaschini.

41 records · Page 3Linked to original sources

arXiv2010

Mathematical properties of the Navier-Stokes dynamical system for incompressible Newtonian fluids

A remarkable feature of fluid dynamics is its relationship with classical dynamics and statistical mechanics. This has motivated in the past mathematical investigations concerning, in a special way, the "derivation" based on kinetic theory, and in particular the Boltzmann equation, of the incompressible Navier-Stokes equations (INSE). However, the connection determined in this way is usually merely asymptotic (i.e., it can be reached only for suitable limit functions) and therefore presents difficulties of its own. This feature has suggested the search of an alternative approach, based on the construction of a suitable inverse kinetic theory (IKT; Tessarotto et al., 2004-2007), which can avoid them. IKT, in fact, permits to achieve an exact representation of the fluid equations by identifying them with appropriate moment equations of a suitable (inverse) kinetic equation. The latter can be identified with a Liouville equation advancing in time a phase-space probability density function (PDF), in terms of which the complete set of fluid fields (prescribing the state of the fluid) are determined. In this paper we intend to investigate the mathematical properties of the underlying \textit{finite-dimensional} phase-space classical dynamical system, denoted \textit{Navier-Stokes dynamical system}, which can be established in this way. The result we intend to establish has fundamental implications both for the mathematical investigation of Navier-Stokes equations as well as for diverse consequences and applications in fluid dynamics and applied sciences.

physics.flu-dyn↗

arXiv2009

Lagrangian dynamics of thermal tracer particles in Navier-Stokes fluids

A key issue in fluid dynamics is the definition of the phase-space Lagrangian dynamics characterizing prescribed ideal fluids (i.e., continua), which is related to the dynamics of so-called \textit{ideal tracer particles} moving in the same fluids. These are by definition particles of infinitesimal size which do not produce significant perturbations of the fluid fields and do not interact among themselves. In this work we point out that the phase-space Lagrangian description of incompressible Navier-Stokes fluids can be achieved by means of a particular subset of ideal tracer particles, denoted as thermal particles. For these particles the magnitude of their relative velocities - with respect to the local fluid velocity - is solely determined by the kinetic pressure, in turn, uniquely related to the fluid pressure. The dynamics of thermal tracer particles is shown to generate the time-evolution of the fluid fields by means of a suitable statistical model. The result is reached introducing a 1-D statistical description of the fluid exclusively based on the ensemble of thermal tracer particles. In particular, it is proven that the statistic of thermal particles can be uniquely defined requiring that for these particles the directions of their initial relative velocities are defined by a suitable family of random coplanar unit vectors.

physics.flu-dyn↗

arXiv2009

Phase-space Lagrangian dynamics of incompressible thermofluids

Phase-space Lagrangian dynamics in ideal fluids (i.e, continua) is usually related to the so-called {\it ideal tracer particles}. The latter, which can in principle be permitted to have arbitrary initial velocities, are understood as particles of infinitesimal size which do not produce significant perturbations of the fluid and do not interact among themselves. An unsolved theoretical problem is the correct definition of their dynamics in ideal fluids. The issue is relevant in order to exhibit the connection between fluid dynamics and the classical dynamical system, underlying a prescribed fluid system, which uniquely generates its time-evolution. \ The goal of this paper is to show that the tracer-particle dynamics can be {\it exactly} established for an arbitrary incompressible fluid uniquely based on the construction of an inverse kinetic theory (IKT) (Tessarotto \textit{et al.}, 2000-2008). As an example, the case of an incompressible Newtonian thermofluid is here considered.

physics.flu-dyn↗

arXiv2008

Lagrangian dynamics of incompressible thermofluids

A key aspect of fluid dynamics is the correct definition of the \textit{% phase-space} Lagrangian dynamics which characterizes arbitrary fluid elements of an incompressible fluid. Apart being an unsolved theoretical problem of fundamental importance, the issue is relevant to exhibit the connection between fluid dynamics and the classical dynamical systems underlying incompressible and non-isothermal fluid, typically founded either on: a) a \textit{configuration-space} Lagrangian description of the dynamics of fluid elements; b) a kinetic description of the molecular dynamics, based on a discrete representation of the fluid. The goal of this paper is to show that the exact Lagrangian dynamics can be established based on the inverse kinetic theory (IKT) for incompressible fluids recently pointed out (Ellero \textit{et al.}, 2004-2006, \cite{Ellero2004}). The result is reached by adopting an IKT approach based on a \textit{restricted phase-space representation} of the fluid, in which the configuration space coincides with the physical fluid domain. The result appears of potential importance in applied fluid dynamics and CFD.

physics.flu-dyn↗

arXiv2006

Non-linear gyrokinetic theory of magnetoplasmas

A crucial issue in relativistic plasma, particularly relevant in the astrophysical context, is the description of highly magnetized plasmas based on a covariant formulation of gyrokinetic dynamics. An interesting case in question is that in which the background electric field (produced either by the same plasma of by other sources) results suitably small (or vanishing) with respect to the magnetic field, while at the same time short-wavelength EM perturbations can be present. The purpose of this work is to extend the relativistic gyrokinetic theory developed by Beklemishev \textit{et al.} [1999-2005] to include, in particular, also the treatment of such a case. We intend to show that this requires the development of a perturbative expansion involving simultaneously both the particle 4-position vector and the corresponding \textit{4-velocity vector}. For this purpose a synchronous form of the relativistic Hamilton variational principle is adopted.

physics.plasm-ph↗