A non-variational approach to nonlinear stability in stellar dynamics applied to the King model

In previous work by Y. Guo and G. Rein, nonlinear stability of equilibria in stellar dynamics, i.e., of steady states of the Vlasov-Poisson system, was accessed by variational techniques. Here we propose a different, non-variational technique and use it to prove nonlinear stability of the King model against a class of spherically symmetric, dynamically accessible perturbations. This model is very important in astrophysics and was out of reach of the previous techniques

Blow up solutions to a viscoelastic fluid system and a coupled Navier-Stokes/Phase-Field system in R^2

We find explicit solutions to both the Oldroyd-B model with infinite Weissenberg number and the coupled Navier-Stokes/Phase-Field system. The solutions blow up in finite time.Comment: 5 page

Effective generation of Ising interaction and cluster states in coupled microcavities

We propose a scheme for realizing the Ising spin-spin interaction and atomic cluster states utilizing trapped atoms in coupled microcavities. It is shown that the atoms can interact with each other via the exchange of virtual photons of the cavities. Through suitably tuning the parameters, an effective Ising spin-spin interaction can be generated in this optical system, which is used to produce the cluster states. This scheme does not need the preparation of initial states of atoms and cavity modes, and is insensitive to cavity decay.Comment: 11pages, 2 figures, Revtex