Universality in Three-Frequency Resonances

We investigate the hierarchical structure of three-frequency resonances in nonlinear dynamical systems with three interacting frequencies. We hypothesize an ordering of these resonances based on a generalization of the Farey tree organization from two frequencies to three. In experiments and numerical simulations we demonstrate that our hypothesis describes the hierarchies of three-frequency resonances in representative dynamical systems. We conjecture that this organization may be universal across a large class of three-frequency systems

Burridge-Knopoff Models as Elastic Excitable Media

We construct a model of an excitable medium with elastic rather than the usual diffusive coupling. We explore the dynamics of elastic excitable media, which we find to be dominated by low dimensional structures, including global oscillations, period-doubled pacemakers, and propagating fronts. We suggest that examples of elastic excitable media are to be found in such diverse physical systems as Burridge-Knopoff models of frictional sliding, electronic transmission lines, and active optical waveguides

Events in the life of a cocoon surrounding a light, collapsar jet

According to the collapsar model, gamma-ray bursts are thought to be produced in shocks that occur after the relativistic jet has broken free from the stellar envelope. If the mass density of the collimated outflow is less than that of the stellar envelope, the jet will then be surrounded by a cocoon of relativistic plasma. This material would itself be able to escape along the direction of least resistance, which is likely to be the rotation axis of the stellar progenitor, and accelerate in approximately the same way as an impulsive fireball. We discuss how the properties of the stellar envelope have a decisive effect on the appearance of a cocoon propagating through it. The relativistic material that accumulated in the cocoon would have enough kinetic energy to substantially alter the structure of the relativistic outflow, if not in fact provide much of the observed explosive power. Shock waves within this plasma can produce gamma-ray and X-ray transients, in addition to the standard afterglow emission that would arise from the deceleration shock of the cocoon fireball.Comment: 16 pages, 5 figures, slightly revised version, accepted for publication in MNRA

Synchronization of Chaotic Systems by Common Random Forcing

We show two examples of noise--induced synchronization. We study a 1-d map and the Lorenz systems, both in the chaotic region. For each system we give numerical evidence that the addition of a (common) random noise, of large enough intensity, to different trajectories which start from different initial conditions, leads eventually to the perfect synchronization of the trajectories. The largest Lyapunov exponent becomes negative due to the presence of the noise terms.Comment: 5 pages, uses aipproc.cls and aipproc.sty (included). Five double figures are provided as ten separate gif files. Version with (large) postscript figures included available from http://www.imedea.uib.es/PhysDept/publicationsDB/date.htm

On Spectral and Temporal Variability in Blazars and Gamma Ray Bursts

A simple model for variability in relativistic plasma outflows is studied, in which nonthermal electrons are continuously and uniformly injected in the comoving frame over a time interval dt. The evolution of the electron distribution is assumed to be dominated by synchrotron losses, and the energy- and time-dependence of the synchrotron and synchrotron self-Compton (SSC) fluxes are calculated for a power-law electron injection function with index s = 2. The mean time of a flare or pulse measured at photon energy E with respect to the onset of the injection event varies as E^{-1/2} and E^{-1/4} for synchrotron and SSC processes, respectively, until the time approaches the limiting intrinsic mean time (1+z)dt/(2 D), where z is the redshift and D is the Doppler factor. This dependence is in accord with recent analyses of blazar and GRB emissions, and suggests a method to discriminate between external Compton and SSC models of high-energy gamma radiation from blazars and GRBs. The qualititative behavior of the X-ray spectral index/flux relation observed from BL Lac objects can be explained with this model. This demonstrates that synchrotron losses are primarily responsible for the X-ray variability behavior and strengthens a new test for beaming from correlated hard X-ray/TeV observations.Comment: 10 pages, 2 figures, accepted for publication in Astrophysical Journal Letters; uses aaspp4.sty, epsf.st

A search for x-ray counterparts of gamma-ray bursts with the ROSAT PSPC

We search for faint X-ray bursts with duration 10--300 seconds in the ROSAT PSPC pointed observations with a total exposure of 1.6e7 seconds. We do not detect any events shorter than ~100s, i.e. those that could be related to the classic gamma-ray bursts. At the same time, we detect a number of long flares with durations of several hundred seconds. Most, but not all, of the long flares are associated with stars. If even a small number of those long flares, that cannot identified with stars, are X-ray afterglows of GRB, the number of X-ray afterglows greatly exceeds the number of BATSE GRB. This would imply that the beaming factor of gamma-rays from the burst should be >100. The non-detection of any short bursts in our data constrains the GRB counts at the fluences 1--2.5 orders of magnitude below the BATSE limit. The constrained burst counts are consistent with the extrapolation of the BATSE log N - log S relation. Finally, our results do not confirm a reality of short X-ray flashes found in the Einstein IPC data by Gotthelf, Hamilton and Helfand.Comment: Accepted to ApJ Letters. 4 pages with 3 figures, LaTeX2

Analysis and Visualization of 3D Motion Data for UPDRS Rating of Patients with Parkinson's Disease

Remote monitoring of Parkinson's Disease (PD) patients with inertia sensors is a relevant method for a better assessment of symptoms. We present a new approach for symptom quantification based on motion data: the automatic Unified Parkinson Disease Rating Scale (UPDRS) classification in combination with an animated 3D avatar giving the neurologist the impression of having the patient live in front of him. In this study we compared the UPDRS ratings of the pronation-supination task derived from: (a) an examination based on video recordings as a clinical reference;(b) an automatically classified UPDRS;and (c) a UPDRS rating from the assessment of the animated 3D avatar. Data were recorded using Magnetic, Angular Rate, Gravity (MARG) sensors with 15 subjects performing a pronation- supination movement of the hand. After preprocessing, the data were classified with a J48 classifier and animated as a 3D avatar. Video recording of the movements, as well as the 3D avatar, were examined by movement disorder specialists and rated by UPDRS. The mean agreement between the ratings based on video and (b) the automatically classified UPDRS is 0.48 and with (c) the 3D avatar it is 0.47. The 3D avatar is similarly suitable for assessing the UPDRS as video recordings for the examined task and will be further developed by the research team