We consider a collection of droplets during the late stage of phase separation in a closed system. Its coarsening is driven by surface energy and leads asymptotically to a linear growth of the mean droplet volume with time (Ostwald ripening). The droplets grow either from the supersaturated...

The systematic procedure for deriving the Smoluchowski equation and successive corrections to it from the Fokker-Planck equation is modified and extended in such a way that it now also covers the case of several interacting Brownian particles with hydrodynamic interactions. This is done by means...

To test and to complement the moment method for solving kinetic equations in the space outside of a sphere that absorbs one component out of a gas mixture, we develop a solution method especially suitable for radii smaller or not much larger than a mean free path. The method is used to calculate...

We consider linear systems in which some of the variables evolve on a much faster time scale than the remaining ones. By means of a systematic perturbation theory in the time-scale ratio we extract a reduced dynamics in terms of the slow variables only, valid after an initial transient period....

We consider linear dynamical systems with motions characterized by two different time-scales. In practice the dynamical matrix in the phenomenological equations of motion often exhibits a strong coupling of the slow and fast variables. It is shown on the basis of the Onsager symmetry relations...

We study thermodynamic systems near equilibrium described by both slow and fast variables. A reduced relaxation matrix for the slow variables can be obtained from the full relaxation matrix by a systematic elimination of the fast variables. When the full relaxation matrix possesses...

A formal analogy between the linear Chapman-Enskog procedure and a variant of the perturbation theory of degenerate levels, as presented by C. Bloch, is established. The analogy is than exploited to obtain closed expressions for the Chapman-Enskog special solutions to all orders in the...

Recently we discussed the adiabatic elimination of fast variables from a many-dimensional Fokker-Planck equation linear in the fast variables. Here we show how the same results can be obtained by manipulation of the equivalent set of coupled Langevin equations. At first sight the Langevin...

The motion of a Brownian particle in an external field can be described on two levels: by a Fokker-Planck equation for the joint probability distribution of position and velocity, and by a Smoluchowski equation for the distribution in position space only. We derive the second description, with...

We study stationary solutions of the Fokker-Planck equation for velocity and position of a Brownian particle in the presence of a constant external field and a completely or selectively absorbing plane wall. Adapting a procedure used earlier for the field-free case, we determine analytically a...