Subgrid Parameterizations of the Eddy–Eddy, Eddy–Mean Field, Eddy–Topographic, Mean Field–Mean Field, and Mean Field–Topographic Interactions in Atmospheric Models

Optimization in mean field models

The non-rigorous cavity method of statistical mechanics, originally developed in the study of spin glasses and other disordered systems, has led to a number of purely mathematical predictions. Several of them can be found in the remarkable book [17] by Marc Mézard, Giorgio Parisi and Miguel Angel Virasoro. Establishing these predictions rigorously remains a challenge to probability theory. Impo...

Chains of Mean Field Models

We consider a collection of Curie-Weiss (CW) spin systems, possibly with a random field, each of which is placed along the positions of a one-dimensional chain. The CW systems are coupled together by a Kac-type interaction in the longitudinal direction of the chain and by an infinite range interaction in the direction transverse to the chain. Our motivations for studying this model come from re...

Tensor Interactions in Mean - Field Approaches

Basic properties of the nuclear tensor mean fields are reviewed, and their role in changing the shell structure and masses of nuclei is analyzed within the spherical Hartree-Fock-Bogolyubov approach.

Mean-field expansion for spin models with medium-range interactions

We study the critical crossover between the Gaussian and the Wilson-Fisher fixed point for general O(N)-invariant spin models with medium-range interactions. We perform a systematic expansion around the mean-field solution, obtaining the universal crossover curves and their leading corrections. In particular we show that, in three dimensions, the leading correction scales as R−3, R being the ra...

Exchangeability and Mean Field Models 3