A universal phenomenological approach to study evolution of long-wave fluctuations caused by the external random force is developed. The Furutzu–Novikov theorem is generalized for non-Gaussian processes. General kinetic and hydrodynamic equations that include the effect of long-wave...

In the present work we derive hydrodynamic equations for the infinite, rarified, smooth, non-homogeneous spherical granular gas. The long-time behavior of these equations is analyzed and we show that the diffusive modes become negligible compared to the propagating modes of the system. This...

Nonlinear equations governing the relaxation of some macroscopic quantities, a(r,t) are derived using Kubo's response theory, in isolated inhomogeneous systems. The resulting equations contain microcanonical time correlation functions. It is shown how to express these in terms of arbitrary...

We have derived, starting from the Liouville equation and using projection operators, the three-dimensional Langevin and Fokker-Planck equations for the time dependence of the momenta and position of two Brownian particles of mass M interacting with a harmonic potential (i.e., a harmonic...

The coupled diffusion equations recently proposed by Tokuyama for concentrated hard-sphere suspensions are numerically solved, starting from nonequilibrium initial configurations. The most important feature of those equations is that the self-diffusion coefficient DS(Φ) becomes zero at the...

The convergence properties of the integral corresponding to the three-body cyclic collisions in the two-dimensional density expansion of transport coefficients are investigated. It is shown exactly that the integral considered by Oppenheim et al. and by Eu diverges logarithmically in the...

Local order effects on the dynamical properties of critical fluids are taken into account by introducing a new slowly varying tensorial quantity which is related to the angular momentum of a group of correlated molecules. The theory is applied to an analysis of ultrasonic and light scattering...

We consider a system consisting of two immiscible fluids and their interface. The equilibrium interface is assumed to be planar. The velocity fields in the fluids are described by the linearized Navier-Stokes equations with appropriate boundary conditions at the interface. Explicit expressions...

In this paper we lay the groundwork for the molecular derivation of the macroscopic equations describing the temporal behavior of two-phase systems. A description of the system in terms of the bulk densities and the multipole moments of the surface excess densities is developed. The exact...

It is shown how a fairly simple random walk on a lattice provides insight into the nature of hydrodynamic boundary conditions. In a flow parallel to the boundary, collisions of up and downward moving particles induce lateral bulk diffusion. At the wall the model accounts essentially for 1)...