Extended Kalman filtering for vortex systems. Part II: Rankine vortices and observing-system design

Point-vortex systems with both regular and chaotic motion can be tracked by a combination of Lagrangian observations of vortex position and of Eulerian observations of fluid velocity at a few fixed points. If only Eulerian observations are available, singularities in the tracking can develop due to nonlinearity in the observing functions on two occasions: when point vortices pass very close to an observing station, and when the observed speed is small. In Part II of this two-part paper, the vorticity concentrations are approximated by Rankine vortices with finite core in solid-body rotation, while a cut-off criterion is imposed on the Eulerian observations; this removes the singularities and hence results in satisfactory tracking when the observations are judiciously chosen.The main result is that a number of observations comparable to that of the distinct vorticity concentrations suffices for very accurate tracking. The key elements for successful tracking of Rankine-vortex systems using nonlinear, Eulerian observations are: distribution of available stations, threshold criteria for the selection of stations used in each update, and the observing frequency. Simple analysis provides the optimal estimate for these key elements, together with the optimal size of the estimated Rankine vortices.     

Anomalous Ne enrichments in tektites

Abstract— We measured noble gases and Ne isotopic compositions of five tektites collected from three different strewn fields. The elemental abundance patterns of noble gases in all samples show anomalous Ne enrichments relative to air. Ne isotopic compositions in tektites are in good agreement with that of atmospheric Ne, suggesting that Ne has diffused in from the atmosphere. It is conceivable that the high relative Ne abundance is essentially an equilibrium effect, i.e., storage of Ne in vesicles rather than the glass itself, facilitated by the relatively high diffusion coefficient of Ne.