Off-axis vortices in trapped Bose-condensed gases: Angular momentum and frequency splitting

We consider noncentered vortices and their arrays in a cylindrically trapped Bose-Einstein condensate at zero temperature. We study the kinetic energy and the angular momentum per particle in the Thomas-Fermi regime and their dependence on the distance of the vortices from the center of the trap. Using a perturbative approach with respect to the velocity field of the vortices, we calculate, to first order, the frequency shift of the collective low-lying excitations due to the presence of an off-center vortex or a vortex array, and compare these results with predictions that would be obtained by the application of a simple sum-rule approach, previously found to be very successful for centered vortices. It turns out that the simple sum-rule approach fails for off-centered vortices.

Duration-frequency relationships of heavy rainfall in Santa Catarina, Brazil

The purpose of this study was to adjust equations that establish relationships between rainfall events with different duration and data from weather stations in the state of Santa Catarina, Brazil. In this study, the relationships between different duration heavy rainfalls from 13 weather stations of Santa Catarina were analyzed. From series of maximum annual rainfalls, and using the Gumbel-Chow distribution, the maximum rainfall for durations between 5 min and 24 h were estimated considering return periods from 2 to 100 years. The data fit to the Gumbel-Chow model was verified by the Kolmogorov-Smirnov test at 5 % significance. The coefficients of Bell's equation were adjusted to estimate the relationship between rainfall duration t (min) and the return period T (y) in relation to the maximum rainfall with a duration of 1 hour and a 10 year return period. Likewise, the coefficients of Bell's equation were adjusted based on the maximum rainfall with a duration of 1 day and a 10 year return period. The results showed that these relationships are viable to estimate short-duration rainfall events at locations where there are no rainfall records.