Ionic strength and pH as control parameters for spontaneous surface oscillations

A system far from equilibrium, where the surfactant transfer from a small drop located in the aqueous bulk to the air-water interface results in spontaneous nonlinear oscillations of surface tension, is theoretically and experimentally considered. The oscillations in this system are the result of periodically arising and terminating Marangoni instability. The surfactant under consideration is octanoic acid, the dissociated form of which is much less surface-active than the protonated form. Numerical simulations show how the system behavior can be controlled by changes in pH and ionic strength of the aqueous phase. The results of numerical simulations are in good agreement with experimental data.     

Construction of analytically tractable mean-field theories for quantum models

A general theoretical framework for the construction of maximally complex, yet analytically tractable mean-field theories for quantum-mechanical models is presented. These mean-field theories fulfil several strict conditions which are derived from analogous theories in classical statistical mechanics. In particular, they are thermodynamically consistent, conserving approximations and provide exact bounds on the free energy of the original model. The formalism is used to construct a mean-field theory for the Hubbard model in thestrong-coupling limit.