Related papers: An H-theorem for incompressible 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…
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…
Kinetic theory offers a promising alternative to conventional turbulence modelling by providing a mesoscopic perspective that naturally captures non-equilibrium physics such as non-Newtonian effects. In this work, we present an extension…
We develop a unified kinetic theory for ordered fluids, which systematically extends the phase space with the appropriate generalized angular momenta. Our theory yields a uniquely determined mesoscopic model for any continuum with…
Fundamental aspects of inverse kinetic theories for incompressible Navier-Stokes equations concern the possibility of defining uniquely the kinetic equation underlying such models and furthermore, the construction of a kinetic 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…
The kinetic theory for a fluid of hard spheres which undergo endothermic and/or exothermic reactions with mass transfer is developed. The exact balance equations for concentration, density, velocity and temperature are derived. The Enskog…
Many features of real granular fluids under rapid flow are exhibited as well by a system of smooth hard spheres with inelastic collisions. For such a system, it is tempting to apply standard methods of kinetic theory and hydrodynamics to…
A kinetic equation is derived for the phase density of a system of point particles, generating a system of integro-differential equations for distribution functions that have a deterministic meaning. The derivation took into account the…
In spite of the large number of papers appeared in the past which are devoted to the lattice Boltzmann (LB) methods, basic aspects of the theory still remain unchallenged. An unsolved theoretical issue is related to the construction of a…
In this note we survey some recent results for the Euler equations in compressible and incompressible fluid dynamics. The main point of all these theorems is the surprising fact that a suitable variant of Gromov's $h$-principle holds in…
These are notes prepared for presentation at the workshop "Challenges in Granular Matter" at the Abdus Salam Institute for Theoretical Physics, Trieste, August 2001. Revisions and figures will be added at a later date. Many features of real…
Highlights are presented regarding recent developments of the kinetic theory of granular matter. These concern the discovery of an exact kinetic equation and a related exact H-theorem both holding for finite $N-$body systems formed by…
A new kinetic theory Boltzmann-like collision term including correlations is proposed. In equilibrium it yields the one-particle distribution function in the form of a generalised-Lorentzian resembling but not being identical with the…
An important aspect of computational fluid dynamics is related to the determination of the fluid pressure in isothermal incompressible fluids. In particular this concerns the construction of an exact evolution equation for the fluid…
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…
H-theorem gives necessary conditions for a system to evolve in time with a non-diminishing entropy. In a quantum case the role of H-theorem plays the unitality criteria of a quantum channel transformation describing the evolution of the…
Extending the statistical approach proposed in a parallel paper \cite% {Tessarotto2008-aa}, purpose of this work is to propose a stochastic inverse kinetic theory for small-scale hydrodynamic turbulence based on the introduction of a…
Recent work in dynamical systems theory has shown that many properties that are associated with irreversible processes in fluids can be understood in terms of the dynamical properties of reversible, Hamiltonian systems. That is,…
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…