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

Calibration of the LIGO displacement actuators via laser frequency modulation

We present a frequency modulation technique for calibration of the displacement actuators of the LIGO 4-km-long interferometric gravitational-wave detectors. With the interferometer locked in a single-arm configuration, we modulate the frequency of the laser light, creating an effective length variation that we calibrate by measuring the amplitude of the frequency modulation. By simultaneously driving the voice coil actuators that control the length of the arm cavity, we calibrate the voice coil actuation coefficient with an estimated 1-sigma uncertainty of less than one percent. This technique enables a force-free, single-step actuator calibration using a displacement fiducial that is fundamentally different from those employed in other calibration methods.Comment: 10 pages, 5 figures, submitted to Classical and Quantum Gravit

Biophysical, morphological, canopy optical property, and productivity data from the Superior National Forest

Described here are the results of a NASA field experiment conducted in the Superior National Forest near Ely, Minnesota, during the summers of 1983 and 1984. The purpose of the experiment was to examine the use of remote sensing to provide measurements of biophysical parameters in the boreal forests. Leaf area index, biomass, net primary productivity, canopy coverage, overstory and understory species composition data are reported for about 60 sites, representing a range of stand density and age for aspen and spruce. Leaf, needle, and bark high-resolution spectral reflectance and transmittance data are reported for the major boreal forest species. Canopy bidirectional reflectance measurements are provided from a helicopter-mounted Barnes Multiband Modular Radiometer (MMR) and the Thematic Mapper Simulator (TMS) on the NASA C-130 aircraft

On the Brightness and Waiting-time Distributions of a Type III Radio Storm observed by STEREO/WAVES

Type III solar radio storms, observed at frequencies below approximately 16 MHz by space borne radio experiments, correspond to the quasi-continuous, bursty emission of electron beams onto open field lines above active regions. The mechanisms by which a storm can persist in some cases for more than a solar rotation whilst exhibiting considerable radio activity are poorly understood. To address this issue, the statistical properties of a type III storm observed by the STEREO/WAVES radio experiment are presented, examining both the brightness distribution and (for the first time) the waiting-time distribution. Single power law behavior is observed in the number distribution as a function of brightness; the power law index is approximately 2.1 and is largely independent of frequency. The waiting-time distribution is found to be consistent with a piecewise-constant Poisson process. This indicates that during the storm individual type III bursts occur independently and suggests that the storm dynamics are consistent with avalanche type behavior in the underlying active region.Comment: 14 pages, 4 figures, 1 table. Accepted for publication in Astrophysical Journal Letter

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

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

The detection of geothermal areas from Skylab thermal data

Skylab-4 X-5 thermal data of the geysers area was analyzed to determine the feasibility of using midday Skylab images to detect geothermal areas. The hottest ground areas indicated on the Skylab image corresponded to south-facing barren or sparsely vegetated slopes. A geothermal area approximately 15 by 30 m coincided with one of the hottest areas indicated by Skylab. This area could not be unambiguously distinguished from the other areas which are believed to be hotter than their surroundings as a result of their topography, and micrometeorological conditions. A simple modification of a previous thermal model was performed and the predicted temperatures for the hottest slopes using representative values was in general agreement with the observed data. It is concluded that data from a single midday Skylab pass cannot be used to locate geothermal areas

Northern High-Latitude Ecosystems Respond to Climate Change

The northern high latitudes are an area of particular importance to global climate change. As a system dependent on freezing conditions, the top of the planet contains vast amounts of carbon in biomass, soils, and permafrost that have the potential to interact with the atmosphere through the biosphere, hydrosphere, lithosphere, and cryosphere. If released en masse, this carbon would greatly exacerbate the levels of greenhouse gases in the atmosphere. Over the past 2 years, a growing body of research has provided evidence of substantial but idiosyncratic environmental changes, with some surprising aspects, across the region. This article reviews some recent findings and presents a new analysis of northern vegetation photosynthetic and productivity trends tracked from Earth observing satellites