Master Equation Description Research Articles

Statistical theory of nucleation, condensation and coagulation

Abstract Starting from a master-equation description of dense gases, binary mixtures, etc., we derive theories for nucleation, coagulation and droplet growth by reformulating the dynamics in terms of ‘clusters’. This treatment is shown to agree quantitatively with computer simulations of the nucleation kinetics in the lattice gas model, and also gives a much better account of recent nucleation experiments on CO2 than previous approaches. The possible definitions of clusters, the appropriate coordinates for their description and their relation to bulk equilibrium properties of the system are outlined, and the effects of fluctuations on the properties of the clusters are investigated. Near the critical point the crossover between ‘classical’ and ‘non-classical’ expressions for the droplet formation energy is described in terms of ‘scaling laws’. In contrast to the Cahn-Hilliard-Langer theories of nucleation based on the concept of a coarse-grained free energy, no significant changes of static or dynamic beh...

A master equation description of local fluctuations

A theory of fluctuations of macrovariables in nonequilibrium systems based on a nonlinear master equation is outlined. This equation takes into account, via a “mean field” type of approximation, the effect of the spatial extension of fluctuations. A comparison with the birth and death formalism reveals several unsatisfactory features of the latter.

The Master-Equation Formulation of Chromatography Theory

Abstract De Clerk et al. have recently proposed that if chromatography theory were based on a master equation rather than a Fokker-Planck equation, asymmetries could readily arise [Separation Sci., 1, 443(1966)]. It is shown here that the master-equation description of an infinitely long homogeneous column also leads to a Gaussian limiting distribution.