The development of a general theory of clustering is sketched. The primary focus is on the use of the pair connectedness function in problems of correlated clustering and on the Ornstein-Zernike formalism that has been developed to evaluate this function and relate it to observed mesoscopic and...

Some properties of the Boltzmann equation (BE) for a spatially uniform system of Maxwellian molecules are considered, including the explicit evaluation of the energy-space transition probability P(y, z; x), the evaluation of the constants λn and μn,i which enter in the moment equations, the...

The self-consistent Ornstein-Zernike approach (SCOZA) developed earlier by the authors for the lattice gas and Ising model as well as simple continuum fluids is extended to the D-vector spin model that includes the classical rotator model (D = 2), the classical Heisenberg model (D = 3), and the...

Our earlier work applying the self-consistent Ornstein-Zernike approach (SCOZA) to the D-vector model is extended to a more general class of continuous-spin models for which the constraint of a single-spin magnitude is relaxed.

Standard statistical mechanical approximations (e.g. mean-field approximations) for pair-correlation functions of strongly interacting systems that yield adequate thermodynamics away from critical points typically break down badly in critical regions. The self-consistent Ornstein–Zernike...

An Ornstein–Zernike approximation for the two-body correlation function embodying thermodynamic consistency is applied to a system of classical Heisenberg spins on a three-dimensional lattice. The consistency condition determined in a previous work is supplemented by introducing a simplified...