Related papers: Post-Newtonian non-equilibrium kinetic theory
A novel formulation of second-order relativistic viscous fluid dynamics based on the effective Boltzmann equation for quasi-particles with medium-dependent masses is briefly reviewed.~The evolution equations for the shear and bulk…
After a brief account of the derivation of the first-order relativistic hydrodynamic equation as a construction of the invariant manifold of relativistic Boltzmann equation, we give a sketch of derivation of the second-order hydrodynamic…
We use covariant methods to analyse the nonlinear evolution of self-gravitating, non-relativistic media. The formalism is first applied to imperfect fluids, aiming at the kinematic effects of viscosity, before extended to inhomogeneous…
Experimental particle spectra can be successfully described by power-law tailed energy distributions characteristic to canonical equilibrium distributions associated to R\'enyi's or Tsallis' entropy formula - over a wide range of energies,…
The relativistic hydrodynamical equations are being examined with the aim of extracting the quantum-mechanical equations (the relativistic Klein-Gordon equation and the Schr\"odinger equation in the non-relativistic limit). In both cases it…
We derive multicomponent relativistic second-order dissipative fluid dynamics from the Boltzmann equations for a reactive mixture of $N_{\text{spec}}$ particle species with $N_q$ intrinsic quantum numbers (e.g. electric charge, baryon…
We derive equations for fluid dynamics from a non-extensive Boltzmann transport equation consistent with Tsallis' non-extensive entropy formula. We evaluate transport coefficients employing the relaxation time approximation and investigate…
Balance equations are derived from Enskog's kinetic equation for a two-dimensional system of hard disks using Grad's moment expansion method. This set of equations constitute an extended hydrodynamics for moderately dense bi-dimensional…
We are concerned with the energy equality for weak solutions to Newtonian and non-Newtonian incompressible fluids. In particular, the results obtained for non-Newtonian fluids, after restriction to the Newtonian case, equal or improve the…
In this work, we first derive the evolution equation for the general energy-momentum moment of $\delta f$, where $\delta f$ is the deviation from the local equilibrium phase space density. We then introduce a relativistic extension of…
A new formulation of second-order viscous hydrodynamics, based on an expansion around a locally anisotropic momentum distribution, is presented. It generalizes the previously developed formalism of anisotropic hydrodynamics (aHydro) to…
Starting with the relativistic Boltzmann equation where the collision term is generalized to include nonlocal effects via gradients of the phase-space distribution function, and using Grad's 14-moment approximation for the distribution…
New solutions are found for the non-relativistic hydrodynamical equations. These solutions describe expanding matter with a Gaussian density profile. In the simplest case, thermal equilibrium is maintained without any interaction, the…
Energy and momentum in Newtonian mechanics have the familiar relations, ($\mathrm{E}=mv^2/2$) and ($\mathbf{P}=m\mathbf{v}$), derived from the non-relativistic limit of special relativity. In this study, we find the corresponding relations…
Generalizing the collision term in the relativistic Boltzmann equation to include nonlocal effects, and using Grad's 14-moment approximation for the single-particle distribution function, we derive evolution equations for the relativistic…
We give a surface integral derivation of post-1-Newtonian translational equations of motion for a system of arbitrarily structured bodies, including the coupling to all the bodies' mass and current multipole moments. The derivation requires…
We use a macroscopic description of a system of relativistic particles based on adding a nonequilibrium tensor to the usual hydrodynamic variables. The nonequilibrium tensor is linked to relativistic kinetic theory through a nonlinear…
An internal energy function of the mass density, the volumetric entropy and their gradients at n-order generates the representation of multi-gradient fluids. Thanks to Hamilton's principle, we obtain a thermodynamical form of the equation…
We derive the relativistic non-resistive, viscous second-order magnetohydrodynamic equations for the dissipative quantities using the relaxation time approximation. The Boltzmann equation is solved for a system of particles and…
The non-linear dynamics of irrotational dust in General Relativity is studied in synchronous and comoving coordinates. All the equations are written in terms of the metric tensor of spatial sections orthogonal to the flow, which allows an…