Linking Backlund and Monodromy Charges for Strings on AdS_5 x S^5

We find an explicit relation between the two known ways of generating an infinite set of local conserved charges for the string sigma model on AdS_5 x S^5: the Backlund and monodromy approaches. We start by constructing the two-parameter family of Backlund transformations for the string with an arbitrary world-sheet metric. We then show that only for a special value of one of the parameters the solutions generated by this transformation are compatible with the Virasoro constraints. By solving the Backlund equations in a non-perturbative fashion, we finally show that the generating functional of the Backlund conservation laws is equal to a certain sum of the quasi-momenta. The positions of the quasi-momenta in the complex spectral plane are uniquely determined by the real parameter of the Backlund transform.Comment: 25 pages, 1 figur

THE RATE OF BINARY BLACK HOLE MERGERS INFERRED FROM ADVANCED LIGO OBSERVATIONS SURROUNDING GW150914

A transient gravitational-wave signal, GW150914, was identi fi ed in the twin Advanced LIGO detectors on 2015 September 2015 at 09:50:45 UTC. To asse ss the implications of this discovery, the detectors remained in operation with unchanged con fi gurations over a period of 39 days around the time of t he signal. At the detection statistic threshold corresponding to that observed for GW150914, our search of the 16 days of simultaneous two-detector observational data is estimated to have a false-alarm rate ( FAR ) of < ́ -- 4.9 10 yr 61 , yielding a p -value for GW150914 of < ́ - 210 7 . Parameter estimation follo w-up on this trigger identi fi es its source as a binary black hole ( BBH ) merger with component masses ( )( ) = - + - + mm M ,36,29 12 4 5 4 4 at redshift = - + z 0.09 0.04 0.03 ( median and 90% credible range ) . Here, we report on the constraints these observations place on the rate of BBH coalescences. Considering only GW150914, assuming that all BBHs in the universe have the same masses and spins as this event, imposing a search FAR threshold of 1 per 100 years, and assuming that the BBH merger rate is constant in the comoving frame, we infer a 90% credible range of merger rates between – -- 2 53 Gpc yr 31 ( comoving frame ) . Incorporating all search triggers that pass a much lower threshold while accounting for the uncerta inty in the astrophysical origin of each trigger, we estimate a higher rate, ranging from – -- 13 600 Gpc yr 31 depending on assumptions about the BBH mass distribution. All together, our various rate estimat es fall in the conservative range – -- 2 600 Gpc yr 31

Lifetime enhancement of scroll rings by spatiotemporal fluctuations

The dynamics of three-dimensional scroll rings with spatiotemporal random excitability is investigated numerically using the FitzHugh-Nagumo model. Depending on the correlation time and length scales of the fluctuations, the lifetime of the ring filament is enlarged and a resonance effect between the time scale of the scroll ring and the time correlation of the noise is observed. Numerical results are interpreted in terms of a simplified stochastic model derived from the kinematical equations for three-dimensional excitable waves

Lifetime enhancement of scroll rings by spatiotemporal fluctuations

The dynamics of three-dimensional scroll rings with spatiotemporal random excitability is investigated numerically using the FitzHugh-Nagumo model. Depending on the correlation time and length scales of the fluctuations, the lifetime of the ring filament is enlarged and a resonance effect between the time scale of the scroll ring and the time correlation of the noise is observed. Numerical results are interpreted in terms of a simplified stochastic model derived from the kinematical equations for three-dimensional excitable waves