Dynamics of fully coupled rotators with unimodal and bimodal frequency distribution

We analyze the synchronization transition of a globally coupled network of N phase oscillators with inertia (rotators) whose natural frequencies are unimodally or bimodally distributed. In the unimodal case, the system exhibits a discontinuous hysteretic transition from an incoherent to a partially synchronized (PS) state. For sufficiently large inertia, the system reveals the coexistence of a PS state and of a standing wave (SW) solution. In the bimodal case, the hysteretic synchronization transition involves several states. Namely, the system becomes coherent passing through traveling waves (TWs), SWs and finally arriving to a PS regime. The transition to the PS state from the SW occurs always at the same coupling, independently of the system size, while its value increases linearly with the inertia. On the other hand the critical coupling required to observe TWs and SWs increases with N suggesting that in the thermodynamic limit the transition from incoherence to PS will occur without any intermediate states. Finally a linear stability analysis reveals that the system is hysteretic not only at the level of macroscopic indicators, but also microscopically as verified by measuring the maximal Lyapunov exponent.Comment: 22 pages, 11 figures, contribution for the book: Control of Self-Organizing Nonlinear Systems, Springer Series in Energetics, eds E. Schoell, S.H.L. Klapp, P. Hoeve

Conductance of Open Quantum Billiards and Classical Trajectories

We analyse the transport phenomena of 2D quantum billiards with convex boundary of different shape. The quantum mechanical analysis is performed by means of the poles of the S-matrix while the classical analysis is based on the motion of a free particle inside the cavity along trajectories with a different number of bounces at the boundary. The value of the conductance depends on the manner the leads are attached to the cavity. The Fourier transform of the transmission amplitudes is compared with the length of the classical paths. There is good agreement between classical and quantum mechanical results when the conductance is achieved mainly by special short-lived states such as whispering gallery modes (WGM) and bouncing ball modes (BBM). In these cases, also the localization of the wave functions agrees with the picture of the classical paths. The S-matrix is calculated classically and compared with the transmission coefficients of the quantum mechanical calculations for five modes in each lead. The number of modes coupled to the special states is effectively reduced.Comment: 19 pages, 6 figures (jpg), 2 table

Extraction of black hole coalescence waveforms from noisy data

We describe an independent analysis of LIGO data for black hole coalescence events. Gravitational wave strain waveforms are extracted directly from the data using a filtering method that exploits the observed or expected time-dependent frequency content. Statistical analysis of residual noise, after filtering out spectral peaks (and considering finite bandwidth), shows no evidence of non-Gaussian behaviour. There is also no evidence of anomalous causal correlation between noise signals at the Hanford and Livingston sites. The extracted waveforms are consistent with black hole coalescence template waveforms provided by LIGO. Simulated events, with known signals injected into real noise, are used to determine uncertainties due to residual noise and demonstrate that our results are unbiased. Conceptual and numerical differences between our RMS signal-to-noise ratios (SNRs) and the published matched-filter detection SNRs are discussed.Comment: 15 pages, 11 figures. Version accepted for publicatio

The estimation of geoacoustic properties from broadband acoustic data, focusing on instantaneous frequency techniques

The compressional wave velocity and attenuation of marine sediments are fundamental to marine science. In order to obtain reliable estimates of these parameters it is necessary to examine in situ acoustic data, which is generally broadband. A variety of techniques for estimating the compressional wave velocity and attenuation from broadband acoustic data are reviewed. The application of Instantaneous Frequency (IF) techniques to data collected from a normal-incidence chirp profiler is examined. For the datasets examined the best estimates of IF are obtained by dividing the chirp profile into a series of sections, estimating the IF of each trace in the section using the first moments of the Wigner Ville distribution, and stacking the resulting IF to obtain a composite IF for the section. As the datasets examined cover both gassy and saturated sediments, this is likely to be the optimum technique for chirp datasets collected from all sediment environments

Techniques for targeted Fermi-GBM follow-up of gravitational-wave events

The Advanced LIGO and Advanced Virgo ground-based gravitational-wave detectors are projected to come online 2015-2016, reaching a final sensitivity sufficient to observe dozens of binary neutron star mergers per year by 2018. We present a fully-automated, targeted search strategy for prompt gamma-ray counterparts in offline Fermi-GBM data. The multi-detector method makes use of a detailed model response of the instrument, and benefits from time and sky location information derived from the gravitational-wave signal.Comment: 2012 Fermi Symposium proceedings - eConf C12102

On the precision of noise correlation interferometry

Long duration noisy-looking waveforms such as those obtained in randomly multiply scattering and reverberant media are complex; they resist direct interpretation. Nevertheless, such waveforms are sensitive to small changes in the source of the waves or in the medium in which they propagate. Monitoring such waveforms, whether obtained directly or obtained indirectly by noise correlation, is emerging as a technique for detecting changes in media. Interpretation of changes is in principle problematic; it is not always clear whether a change is due to sources or to the medium. Of particular interest is the detection of small changes in propagation speeds. An expression is derived here for the apparent, but illusory, waveform dilation due to a change of source. The expression permits changes in waveforms due to changes in wavespeed to be distinguished with high precision from changes due to other reasons. The theory is successfully compared with analysis of a laboratory ultrasonic data set and a seismic data set from Parkfield California