We use a modified Thomas-Fermi approximation to estimate analytically the critical velocity for the formation of vortices in harmonically trapped BEC. We compare this analytical estimate to numerical calculations and to recent experiments on trapped alkali condensates.

We find a limit cycle in a quasi-equilibrium model of evaporative cooling of a two-component trapped fermion gas. The existence of such a limit cycle represents an obstruction to reaching the quantum ground state evaporatively. We show that evaporatively βµ ∼ O(1). We speculate that one may be able to cool an atomic fermi gas further by photoassociating dimers near the bottom of the fermi sea.

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