Observations of the Vortex Ring State

This paper considers the vortex ring state, a flow condition usually associated with the descent of a rotor into its own wake. The phenomenon is investigated through experiments on simple rotor systems, and a comparison is then made with observations of a flow generated by a specially designed open core, annular jet that generates a mean flow velocity profile similar to the mean flow in a rotor wake in hover. In an experimentally simulated descent, the jet flow generates a flow state that shares many features of the rotor vortex ring state

On the local eigenvalue statistics for random band matrices in the localization regime

We study local eigenvalue statistics $\xi_{\omega,E}^N$ associated with one-dimensional, $(2N+1) \times (2N+1)$ random band matrices with independent, identically distributed, random variables and band width growing as $N^\alpha$, for $0 < \alpha < \frac{1}{2}$. We consider the limit points associated with the random variables $\xi_{\omega,E}^N [I]$, for $I \subset \mathbb{R}$. Our general result states that, under localization bounds and a weak Wegner estimate, any nontrivial limit points are distributed according to a compound Poisson point process. Furthermore, assuming localization bounds and strong Wegner and Minami estimates, we prove that this family of random variables has nontrivial limit points for almost every $E \in (-2,2)$, and that these limit points are Poisson distributed with positive intensities. The assumptions hold for Gaussian distributed random variables with $0 \leq \alpha < \frac{1}{7}$ (\cite{schenker, peled, et. al.}), although it is expected that localization bounds hold for $0 \leq \alpha < \frac{1}{2}$. Some related results under weaker hypotheses are presented

Convergence of resonances on thin branched quantum wave guides

We prove an abstract criterion stating resolvent convergence in the case of operators acting in different Hilbert spaces. This result is then applied to the case of Laplacians on a family X_\eps of branched quantum waveguides. Combining it with an exterior complex scaling we show, in particular, that the resonances on X_\eps approximate those of the Laplacian with ``free'' boundary conditions on $X_0$, the skeleton graph of X_\eps.Comment: 48 pages, 1 figur