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

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

Dynamic evolution of the source volumes of gradual and impulsive solar flare emissions

This study compares flare source volumes inferred from impulsive hard X-rays and microwaves with those derived from density sensitive soft X-ray line ratios in the O VII spectrum. The data for this study were obtained with the SMM Hard X-Ray Burst Spectrometer, Earth-based radio observatories, and the SOLEX-B spectrometer on the P78-1 satellite. Data were available for the flares of 1980 April 8, 1980 May 9, and 1981 February 26. The hard X-ray/microwave source volume is determined under the assumption that the same electron temperature or power law index characterizes both the source of hard X-rays and the source of microwaves. The O VII line ratios yield the density and volume of the 2 X 10 to the 6th K plasma. For all three flares, the O VII source volume is found to be smallest at the beginning of the flare, near the time when the impulsive hard X-ray/microwave volume reaches its first maximum. At this time, the O VII volume is three to four orders of magnitude smaller than that inferred from the hard X-ray/microwave analysis. Subsequently, the O VII source volume increases by one or two orders of magnitude then remains almost constant until the end of the flare when it apparently increases again

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

Cutting and Shuffling a Line Segment: Mixing by Interval Exchange Transformations

We present a computational study of finite-time mixing of a line segment by cutting and shuffling. A family of one-dimensional interval exchange transformations is constructed as a model system in which to study these types of mixing processes. Illustrative examples of the mixing behaviors, including pathological cases that violate the assumptions of the known governing theorems and lead to poor mixing, are shown. Since the mathematical theory applies as the number of iterations of the map goes to infinity, we introduce practical measures of mixing (the percent unmixed and the number of intermaterial interfaces) that can be computed over given (finite) numbers of iterations. We find that good mixing can be achieved after a finite number of iterations of a one-dimensional cutting and shuffling map, even though such a map cannot be considered chaotic in the usual sense and/or it may not fulfill the conditions of the ergodic theorems for interval exchange transformations. Specifically, good shuffling can occur with only six or seven intervals of roughly the same length, as long as the rearrangement order is an irreducible permutation. This study has implications for a number of mixing processes in which discontinuities arise either by construction or due to the underlying physics.Comment: 21 pages, 10 figures, ws-ijbc class; accepted for publication in International Journal of Bifurcation and Chao

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