Related papers: The kinetic Holway-Shakhov equation
The dynamics of inelastic hard spheres is described in terms of the binary collision expansion, yielding the corresponding pseudo-Liouville equation and BBGKY hierarchy for the reduced distribution functions. Based on cluster expansion…
One key issue in the probability density function (PDF) approach for disperse two-phase turbulent flows is to close the diffusion term in the phase space. This study aimed to derive a kinetic equation for particle dispersion in turbulent…
Vlasov kinetic theory is the dynamics of a bunch of particles flowing according to symplectic Hamiltonian dynamics. More recently, this geometry has been extended to contact Hamiltonian dynamics. In this paper, we introduce geometric…
Self-diffusion along the longitudinal coordinate in a channel of varying cross section is considered. The starting point is the two-dimensional Enskog-Boltzmann-Lorentz kinetic equation with appropriated boundary conditions. It is…
In this work we present a new approach on studying dynamical systems. Combining the two ways of expressing the uncertainty, using probabilistic theory and credibility theory, we have research the generalized fractional hybrid equations. We…
We establish the explicit correspondence between the theory of soliton gases in classical integrable dispersive hydrodynamics, and generalized hydrodynamics (GHD), the hydrodynamic theory for many-body quantum and classical integrable…
Kinetic equations hold a very important place in physics and further their fractional generalization enhances the scope of their applicability and significance in describing the continuity of motion in materials. After the development of…
The physical quantities in a gas should vary continuously across a shock. However, the physics inherent in the compressible Euler equations is insufficient to describe the width or structure of the shock. We demonstrate the existence of…
We derive the hydrodynamic limit of a kinetic equation where the interactions in velocity are modelled by a linear operator (Fokker-Planck or Linear Boltzmann) and the force in the Vlasov term is a stochastic process with high amplitude and…
In the present paper we introduce generalized kinetic equations describing the dynamics of a system of interacting gas and photons obeying to a very general statistics. In the space homogeneous case we study the equilibrium state of the…
We introduce and study a new class of kinetic equations, which arise in the description of nonequilibrium macroscopic dynamics of soliton gases with elastic collisions between solitons. These equations represent nonlinear…
We compute the kinetic energy of the Langevin particle using different approaches. We build stochastic differential equations that describe this physical quantity based on both the It\^o and Stratonovich stochastic integrals. It is shown…
The equation of state for gas stream as analog of well-known equation of state of gas medium in the static conditions is submitted. The connection of parameters of state and motion, and also the volume-flow rate and the mass-flow rate of…
The dynamics of N point vortices in a fluid is described by the Helmholtz-Kirchhoff (HK) equations which lead to a completely integrable Hamiltonian system for N=2 or 3 but chaotic dynamics for N>3. Here we consider a generalization of the…
We consider the coupling between the equations of motion of a compressible fluid in two and three space dimensions with Christov's equation for the heat flux. Christov's equation is a frame indifferent formulation of the classical model of…
The subject of this paper is to derive the solution of generalized fractional kinetic equations. The results are obtained in a compact form containing the Mittag-Leffler function, which naturally occurs whenever one is dealing with…
A crucial issue in fluid dynamics is related to the knowledge of the fluid pressure. A new general pressure equation is derived from compressible Navier-Stokes equation. It is argued that this new pressure equation allows unifying…
A simple exactly solvable kinetic model for the non-linear inelastic hard sphere Boltzmann equation is used to explore the relevance of hydrodynamics for a granular gas. The equation predicts a non-trivial homogeneous cooling state (HCS),…
A framework for defining stochastic currents associated with diffusion processes on curved Riemannian manifolds is presented. This is achieved by introducing an overdamped Stratonovich-Langevin equation that remains fully covariant under…
The kinetic wave equation arises in wave turbulence to describe the Fourier spectrum of solutions to the cubic Schroedinger equation. The equation has two Kolmogorov-Zakharov steady states corresponding to out-of-equilibrium cascades…