A Faraway Quasar in the Direction of the Highest Energy Auger Event

The highest energy cosmic ray event reported by the Auger Observatory has an energy of 148 EeV. It does not correlate with any nearby (z$<$0.024) object capable of originating such a high energy event. Intrigued by the fact that the highest energy event ever recorded (by the Fly's Eye collaboration) points to a faraway quasar with very high radio luminosity and large Faraday rotation measurement, we have searched for a similar source for the Auger event. We find that the Auger highest energy event points to a quasar with similar characteristics to the one correlated to the Fly's Eye event. We also find the same kind of correlation for one of the highest energy AGASA events. We conclude that so far these types of quasars are the best source candidates for both Auger and Fly's Eye highest energy events. We discuss a few exotic candidates that could reach us from gigaparsec distances.Comment: 13 pages (version to be published in JCAP

Coupled vortex shedding and acoustic resonances in a duct

Undesirable sound generation in the combustion chambers of solid propellant rocket motors previously has been attributed to vortex shedding from obstructions that are uncovered as the propellant burns back. An experimental investigation of the phenomenon has re-conf irmed this observation and extended the understanding of the mechanism by which the process is self-sustaining. A pair of aluminum baffles within a lucite duct through which air is drawn models the important aspects which enable the sound generation mechanism to operate. The baffles form an edgetone system which interacts with the longitudinal acoustic modes of the chamber. Pure acoustic tones occur spontaneously, at frequencies equal to the acoustic resonances, when the spacing between the baffles satisfies certain criteria. Flow visualization using smoke and a strobe light triggered by the pressure oscillation indicates that vortex shedding occurs at the upstream baffle in phase with the acoustic velocity oscillation there. Based on the results of the present experiments and others reported in the literature, a mechanism is postulated which explains the observed behavior. It is suggested that pressures induced on the downstream baffle by the vortices convected past by the freestream drive the acoustic resonance. In turn, the acoustic velocity at the upstream baffle serves as the perturbation triggering the formation of vortices in the shear layer growing from the separation point at that location. The amplitude is limited by the nonlinearity in the growth of the vortices in the shear layer. A lIodel based on the proposed mechanism is formulated and written as a computer program. The results predict the behavior of the experilllental apparatus well, confirming that the postulated mechanism is correct

On the Andreadakis-Johnson filtration of the automorphism group of a free group

The Johnson filtration of the automorphism group of a free group is composed of those automorphisms which act trivially on nilpotent quotients of the free group. We compute cohomology classes as follows: (i) we analyze analogous classes for a subgroup of the pure symmetric automorphism group of a free group, and (ii) we analyze features of these classes which are preserved by the Johnson homomorphism. One consequence is that the ranks of the cohomology groups in any fixed dimension between 1 and n-1 increase without bound for terms deep in the Johnson filtraton.Comment: Corrections; revisions to proof of main theore