A lattice Boltzmann model is introduced which simulates oil-water-surfactant mixtures. The model is based on a Ginzburg-Landau free energy with two scalar order parameters. Diffusive and hydrodynamic transport: is included. Results are presented showing how the surfactant diffuses to the oil-water interfaces thus lowering the surface tension and leading to spontaneous emulsification. The rate of emulsification depends on the viscosity of the ternary fluid.

The spinodal decomposition of binary mixtures in uniform shear flow is studied in the context of the time-dependent Ginzburg-Landau equation, approximated at one-loop order. We show that the structure factor obeys a generalized dynamical scaling with different growth exponents alpha(x) = 5/4 and alpha(y) = 1/4 in the flow and in the shear directions, respectively. The excess viscosity Delta eta after reaching a maximum relaxes to zero as gamma(-2)t(-3/2), gamma being the shear rate. Delta eta and other observables exhibit log-time periodic oscillations which can be interpreted as due to a growth mechanism where stretching and breakup of domains cyclically occur.

We show how a lattice-Boltzmann approach can be extended to ternary fluid mixtures with the aim of modeling the diverse behavior of oil-water-surfactant systems. We model the mixture using a Ginzburg-Landau free energy with two scalar order parameters which allows us to define a lattice-Boltzmann scheme in the spirit of the Cahn-Hilliard approach to nonequilibrium dynamics. Results are presented for the spontaneous emulsification of an oil-water droplet and for spinodal decomposition in the presence of a surfactant.

In this paper we analyze replica symmetry breaking in attractor neural networks with non-monotone activation function. We study the non-monotone version of the Edinburgh model, which allows the control of the domains of attraction by the stability parameter K, and we compute, at one step of symmetry breaking, storage capacity and, for the strongly dilute model, the domains of attraction of the stable fixed points.