Approach to a rational rotation number in a piecewise isometric system

We study a parametric family of piecewise rotations of the torus, in the limit in which the rotation number approaches the rational value 1/4. There is a region of positive measure where the discontinuity set becomes dense in the limit; we prove that in this region the area occupied by stable periodic orbits remains positive. The main device is the construction of an induced map on a domain with vanishing measure; this map is the product of two involutions, and each involution preserves all its atoms. Dynamically, the composition of these involutions represents linking together two sector maps; this dynamical system features an orderly array of stable periodic orbits having a smooth parameter dependence, plus irregular contributions which become negligible in the limit.Comment: LaTeX, 57 pages with 13 figure

Improving LIGO calibration accuracy by tracking and compensating for slow temporal variations

Calibration of the second-generation LIGO interferometric gravitational-wave detectors employs a method that uses injected periodic modulations to track and compensate for slow temporal variations in the differential length response of the instruments. These detectors utilize feedback control loops to maintain resonance conditions by suppressing differential arm length variations. We describe how the sensing and actuation functions of these servo loops are parameterized and how the slow variations in these parameters are quantified using the injected modulations. We report the results of applying this method to the LIGO detectors and show that it significantly reduces systematic errors in their calibrated outputs.Comment: 13 pages, 8 figures. This is an author-created, un-copyedited version of an article published in Classical and Quantum Gravity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from i

The Properties of Large Amplitude Whistler Mode Waves in the Magnetosphere: Propagation and Relationship with Geomagnetic Activity

Wepresent resultsof a studyof the characteristicsof very large amplitude whistler mode waves inside the terrestrial magnetosphere at radial distances of less than 15 RE using waveform capture data from the Wind spacecraft. We observed 247 whistler mode waves with at least one electric field component (105/247 had !80 mV/m peak!to!peak amplitudes) and 66 whistler mode waves with at least one search coil magnetic field component (38/66 had !0.8 nT peak!to!peak amplitudes). Wave vectors determined from events with three magnetic field components indicate that 30/46 propagate within 20 of the ambient magnetic field, though some are more oblique (up to "50 ). No relationship was observed between wave normal angle and GSM latitude. 162/247 of the large amplitude whistler mode waves were observed during magnetically active periods (AE > 200 nT). 217 out of 247 total whistler mode waves examined were observed inside the radiation belts. We present a waveform capture with the largest whistler wave magnetic field amplitude (^8 nT peak!to!peak) ever reported in the radiation belts. The estimated Poynting flux magnitude associated with this wave is ^300 mW/m2, roughly four orders of magnitude above estimates from previous satellite measurements. Such large Poynting flux values are consistent with rapid energization of electrons

Interplanetary and Interstellar Dust Observed by the Wind/WAVES Electric Field Instrument

Observations of hypervelocity dust particles impacting the Wind spacecraft are reported here for the first time using data from the WindWAVES electric field instrument. A unique combination of rotating spacecraft, amplitude-triggered high-cadence waveform collection, and electric field antenna configuration allow the first direct determination of dust impact direction by any spacecraft using electric field data. Dust flux and impact direction data indicate that the observed dust is approximately micron-sized with both interplanetary and interstellar populations. Nanometer radius dust is not detected by Wind during times when nanometer dust is observed on the STEREO spacecraft and both spacecraft are in close proximity. Determined impact directions suggest that interplanetary dust detected by electric field instruments at 1 AU is dominated by particles on bound trajectories crossing Earths orbit, rather than dust with hyperbolic orbits

Reconstructing the calibrated strain signal in the Advanced LIGO detectors

Advanced LIGO's raw detector output needs to be calibrated to compute dimensionless strain h(t). Calibrated strain data is produced in the time domain using both a low-latency, online procedure and a high-latency, offline procedure. The low-latency h(t) data stream is produced in two stages, the first of which is performed on the same computers that operate the detector's feedback control system. This stage, referred to as the front-end calibration, uses infinite impulse response (IIR) filtering and performs all operations at a 16384 Hz digital sampling rate. Due to several limitations, this procedure currently introduces certain systematic errors in the calibrated strain data, motivating the second stage of the low-latency procedure, known as the low-latency gstlal calibration pipeline. The gstlal calibration pipeline uses finite impulse response (FIR) filtering to apply corrections to the output of the front-end calibration. It applies time-dependent correction factors to the sensing and actuation components of the calibrated strain to reduce systematic errors. The gstlal calibration pipeline is also used in high latency to recalibrate the data, which is necessary due mainly to online dropouts in the calibrated data and identified improvements to the calibration models or filters.Comment: 20 pages including appendices and bibliography. 11 Figures. 3 Table

Very Extended X-ray and H-alpha Emission in M82: Implications for the Superwind Phenomenon

We discuss the properties and implications of a 3.7x0.9 kpc region of spatially-coincident X-ray and H-alpha emission about 11.6 kpc to the north of the galaxy M82 previously discussed by Devine and Bally (1999). The PSPC X-ray spectrum is fit by thermal plasma (kT=0.80+-0.17 keV) absorbed by only the Galactic foreground column density. We evaluate the relationship of the X-ray/H-alpha ridge to the M82 superwind. The main properties of the X-ray emission can all be explained as being due to shock-heating driven as the superwind encounters a massive ionized cloud in the halo of M82. This encounter drives a slow shock into the cloud, which contributes to the excitation of the observed H-alpha emission. At the same time, a fast bow-shock develops in the superwind just upstream of the cloud, and this produces the observed X-ray emission. This interpretation would imply that the superwind has an outflow speed of roughly 800 km/s, consistent with indirect estimates based on its general X-ray properties and the kinematics of the inner kpc-scale region of H-alpha filaments. The gas in the M82 ridge is roughly two orders-of-magnitude hotter than the minimum "escape temperature" at this radius, so this gas will not be retained by M82. (abridged)Comment: 24 pages (latex), 3 figures (2 gif files and one postscript), accepted for publication in Part 1 of The Astrophysical Journa

Accurate calibration of test mass displacement in the LIGO interferometers

We describe three fundamentally different methods we have applied to calibrate the test mass displacement actuators to search for systematic errors in the calibration of the LIGO gravitational-wave detectors. The actuation frequencies tested range from 90 Hz to 1 kHz and the actuation amplitudes range from 1e-6 m to 1e-18 m. For each of the four test mass actuators measured, the weighted mean coefficient over all frequencies for each technique deviates from the average actuation coefficient for all three techniques by less than 4%. This result indicates that systematic errors in the calibration of the responses of the LIGO detectors to differential length variations are within the stated uncertainties.Comment: 10 pages, 6 figures, submitted on 31 October 2009 to Classical and Quantum Gravity for the proceedings of 8th Edoardo Amaldi Conference on Gravitational Wave

Discretized rotation has infinitely many periodic orbits

For a fixed k in (-2,2), the discretized rotation on Z^2 is defined by (x,y)->(y,-[x+ky]). We prove that this dynamics has infinitely many periodic orbits.Comment: Revised after referee reports, and added a quantitative statemen