arXiv subjects

M. Tessarotto

Publications and source records attributed to M. Tessarotto.

27 records · Page 2Linked to original sources

arXiv2008

Completeness of the Lattice-Boltzmann IKT approach for classical incompressible fluids

Despite the abundant literature on the subject appeared in the last few years, the lattice Boltzmann method (LBM) is probably the one for which a complete understanding is not yet available. As an example, an unsolved theoretical issue is related to the construction of a discrete kinetic theory which yields \textit{exactly} the fluid equations, i.e., is non-asymptotic (here denoted as \textit{LB inverse kinetic theory}). The purpose of this paper aims at investigating discrete inverse kinetic theories (IKT) for incompressible fluids. We intend to show that the discrete IKT can be defined in such a way to satisfy, in particular, the requirement of \emph{completeness}, i.e., {\it all} fluid fields are expressed as moments of the kinetic distribution function and {\it all} hydrodynamic equations can be identified with suitable moment equations of an appropriate inverse kinetic equation IKE.

physics.flu-dyn↗

arXiv2008

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.

astro-ph↗

arXiv2008

Inverse kinetic theory approach to turbulence theory

A fundamental aspect of turbulence theory is related to the identification of realizable phase-space statistical descriptions able to reproduce in some suitable sense the stochastic fluid equations of a turbulent fluid. In particular, a major open issue is whether a purely Markovian statistical description of hydrodynamic turbulence actually can be achieved. Based on the formulation of a \textit{deterministic inverse kinetic theory} (IKT) for the 3D incompressible Navier-Stokes equations, here we claim that such a \textit{Markovian statistical description actually exists}. The approach, which involves the introduction of the \textit{local velocity probability density} for the fluid (local pdf) - rather than the velocity-difference pdf adopted in customary approaches to homogeneous turbulence - relies exclusively on first principles. These include - in particular - the exact validity of the stochastic Navier-Stokes equations, the principle of entropy maximization and a constant H-theorem for the Shannon statistical entropy. As a result, the new approach affords an exact equivalence between Lagrangian and Eulerian formulations which permit local pdf's which are generally non-Maxwellian (i.e., non-Gaussian). The theory developed is quite general and applies in principle even to turbulence regimes which are non-stationary and non-uniform in a statistical sense.

physics.flu-dyn↗

arXiv2006

Nonlinear Debye screening in strongly-coupled plasmas

An ubiquitous property of plasmas is the so-called Debye shielding of the electrostatic potential. Important aspects of Debye screening concern, in particular, the investigation of non-linear charge screening effects taking place in strongly-coupled plasmas, that imply a reduction of the effective charge characterizing the Debye-Hückel potential. These effects are particularly relevant in dusty plasmas which are characterized by high-Z particles. The investigation of the effective interactions of these particles has attracted interest in recent years especially for numerical simulations. In this work we intend to analyze the consistency of the traditional mathematical model for the Debye screening. In particular, we intend to prove that the 3D Poisson equation involved in the DH model does not admit strong solutions. For this purpose a modified model is proposed which takes into account the effect of local plasma sheath (i.e., the local domain near test particles where the plasma must be considered discrete). Basic consequences of the model are discussed, which concern the asymptotic properties of the solutions determined both for weakly and strongly coupled plasmas. As an application the charge screening effect in strongly coupled plasmas is investigated and an explicit expression of the effective charge for the asymptotic DH potential is determined.

physics.plasm-ph↗

arXiv2006

Unique representation of an inverse-kinetic theory for incompressible Newtonian fluids

Fundamental aspects of inverse kinetic theories for the incompressible Navier-Stokes equations [Ellero and Tessarotto, 2004, 2005] include the possibility of defining uniquely the kinetic equation underlying such models and furthermore, the construction of a kinetic theory implying also the energy equation. The latter condition is consistent with the requirement that fluid fields result classical solutions of the fluid equations. These issues appear of potential relevance both from the mathematical viewpoint and for the physical interpretation of the theory. Purpose of this work is to prove that under suitable prescriptions the inverse kinetic theory can be determined to satisfy such requirements.

physics.flu-dyn↗

arXiv2006

An H-theorem for incompressible fluids

A basic aspect of the kinetic descriptions of incompressible fluids based on an inverse kinetic approaches is the possibility of satisfying an H-theorem. This property is in fact related to the identification of the kinetic distribution function with a probability density in an appropriate phase space. Goal of this investigation is to analyze the conditions of validity of an H-theorem for the inverse kinetic theory recently proposed by Ellero and Tessarotto [2004, 2005]. It is found that the time-dependent contribution to the kinetic pressure, characteristic of such a kinetic model, can always be uniquely defined in such a way to warrant the constancy of the entropy.

physics.flu-dyn↗

arXiv2006

Plasma-sheath effects on the Debye screening problem

The classical Debye-Hückel screening effect of the electrostatic field generated by isolated charged particles immersed in a plasma is reviewed. The validity of the underlying mathematical model, and particularly of the weak-field approximation, are analyzed. It is shown that the presence of the plasma sheath around test particles and the resulting effect of charge screening are essential for the description of plasmas which are strongly coupled.

physics.plasm-ph↗

arXiv2006

Non-linear charge reduction effect in strongly-coupled plasmas

The charge reduction effect, produced by the nonlinear Debye screening of high-Z charges occuring in strongly-coupled plasmas, is investigated. An analytic asymptotic expression is obtained for the charge reduction factor which determines the Debye-Hueckel potential generated by a charged test particle. Its relevant parametric dependencies are analyzed and shown to predict a strong charge reduction effect in strongly-coupled plasmas.

physics.plasm-ph↗

arXiv2004

Short waves and cyclotron losses in the relativistic gyrokinetic theory

Radiation damping of the motion of charged particles in relativistic, optically thin plasmas is described within the framework of the covariant gyrokinetic theory. It involves description of the collisionless single-particle dynamics as well as the Vlasov and Maxwell equations both written in the covariant formulation. The damping causes corrections to the phase-space trajectory of the particle, as well as to the form of the kinetic equation itself, due to the failure of conditions of the Liouville theorem. Both effects result independent of the gyrophase, which is retained as an ignorable variable. In addition, the applicability range of the covariant gyrokinetic theory is extended to describe short-wavelength perturbations with the background of zero parallel electric field. The presented theory is suitable for description of magnetized, relativistic, collisionless plasmas in the context of astrophysical or laboratory problems. Non-uniquenes of the gyrokinetic representation and consequences thereof are discussed.

physics.plasm-ph↗