Related papers: Hydrodynamic Equations for Microscopic Phase Densi…
The problem of description of the evolution of the microscopic phase density and its generalizations is discussed. With this purpose, the sequence of marginal microscopic phase densities is introduced, and the appropriate BBGKY hierarchy…
On the basis of the sequence of marginal observables the evolution equations of the microscopic phase density and its generalizations is discussed. We introduced dual BBGKY hierarchy for these microscopic observables and their average…
Critical analyses of well-known methods of derivation of kinetic and hydrodynamic equations is presented. Another method of derivation of kinetic and hydrodynamic equations from classic mechanics is described. It is shown that equations of…
A hydrodynamic formulation of the evolution of large-scale structure in the Universe is presented. It relies on the spatially coarse-grained description of the dynamical evolution of a many-body gravitating system. Because of the assumed…
Relativistic hydrodynamics of classic plasmas is derived from the microscopic model in the limit of ideal plasmas. The chain of equations is constructed step by step starting from the concentration evolution. It happens that the energy…
We derive the Hydrodynamics for a system of N active, spherical, underdamped particles, interacting through conservative forces. At the microscopic level, we represent the evolution of the particles in terms of the Kramers equation for the…
The properties of dense granular systems are analyzed from a hydrodynamical point of view, based on conservation laws for the particle number density and linear momentum. We discuss averaging problems associated with the nature of such…
In this review, a theoretical description is provided for the solid (granular) phase of the gas-solid flows that are the focus of this book. Emphasis is placed on the fundamental concepts involved in deriving a macroscopic hydrodynamic…
We use the method of the microscopic phase density to get the kinetic equation for the system of self-propelled particles with Vicsek-like alignment rule. The hydrodynamic equations are derived for the ordered phase taking into account the…
The equations of continuum hydrodynamics can be derived from the Boltzmann equation, which describes rarefied gas dynamics at the kinetic level, by means of the Chapman-Enskog expansion. This expansion assumes a small Knudsen number, and as…
A new class of accelerating, exact, explicit and simple solutions of relativistic hydrodynamics is presented. Since these new solutions yield a finite rapidity distribution, they lead to an advanced estimate of the initial energy density…
We prove results on existence and uniqueness of solutions of a system of equations modeling the evolution of a generalized bioconvective flow. The mathematical model considered in the present work describes the convective motion generated…
We consider the hydrodynamic scaling behavior of the mass density with respect to a general class of mass conservative interacting particle systems on ${\mathbb Z}^n$, where the jump rates are asymmetric and long-range of order…
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…
We derive general depth-integrated model equations for overland flows featuring the evolution of suspended sediment that may be eroded from or deposited onto the underlying topography ('morphodynamics'). The resulting equations include…
The equation systems of generalized hydrodynamics, or generalized dynamics for simplicity, for soft-matter quasicrystals were established. Considering the fluidity of the matter with high order we introduced a new elementary…
A very early start up time of the hydrodynamic evolution is needed in order to reproduce observations from relativistic heavy-ion collisions experiments. At such early times the systems is still not locally equilibrated. Another source of…
We consider the generalized pure state density matrix which depends on different time moments. The evolution equation for this density matrix is obtained in case where the density matrix corresponds to the solutions of Gross-Pitaevskii…
Our review covers microscopic foundations of generalized hydrodynamics (GHD). As one generic approach we develop form factor expansions, for ground states and generalized Gibbs ensembles (GGE). In the latter case the so obtained results are…
The generalised hydrodynamic theory of an electron gas, which does not rely on an assumption of a local equilibrium, is derived as the long-wave limit of a kinetic equation. Apart from the common hydrodynamics variables the theory includes…