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We present a numerical study of mixed boson-fermion systems at zero temperature in isotropic and anisotropic harmonic traps. We investigate the phenomenon of component separation as function of the strength of the inter-particle interaction. While solving a Gross-Pitaevskii mean field equation for the boson distribution in the trap, we utilize two different methods to extract the density profile of the fermion component; a semiclassical Thomas-Fermi approximation and a quantum mechanical Slater determinant Schr\"{o}dinger equation.Comment: 21 pages, 5 figures, To appear in Physical Review

We present two new models for wind turbine interaction effects and a recipe for combining them. The first model is an extension of the Park model, which explicitly incorporates turbulence, both the ambient atmospheric turbulence and the turbulence generated in the wake itself. This Turbulence Optimized Park model is better equipped to describe wake recovery over long distances such as between wind farms, where the wake expansion slows down as the turbine-generated turbulence decays. The second model is a first version of a full engineering wind farm blockage model. In the same vein as the wake model it adds blockage contributions from the individual wind turbines to form an aggregated wind farm scale blockage effect that can be incorporated directly into the park power curve and annual energy calculations. The wake model and the blockage model describe downstream and upstream turbine interaction effects, respectively. They are coupled as the outputs of one model are the inputs to the other model and vice versa. We describe how this coupling is achieved through an iterative process. We give early stage examples of the validation of the two models and discuss how they might be further validated and improved in the future.

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We analyze the scattering and bound state physics of a pair of atoms in a one-dimensional optical lattice interacting via a narrow Feshbach resonance. The lattice provides a structured continuum allowing for the existence of bound dimer states both below and above the continuum bands, with pairs above the continuum stabilized by either repulsive interactions or their center of mass motion. Inside the band the Feshbach coupling to a closed channel bound state leads to a Fano resonance profile for the transmission, which may be mapped out by RF-or photodissociative spectroscopy. We generalize the scattering length concept to the one-dimensional lattice, where a scattering length may be defined at both the lower and the upper continuum thresholds. As a function of the applied magnetic field the scattering length at either band edge exhibits the usual Feshbach divergence when a bound state enters or exits the continuum. Near the scattering length divergences the binding energy and wavefunction of the weakly bound dimer state acquires a universal form reminiscent of those of free-space Feshbach molecules. We give numerical examples of our analytic results for a specific Feshbach resonance, which has been studied experimentally.