5,436 research outputs found
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
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
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
UCLA Intermediate Energy Nuclear and Particle Physics Research: Final Report
This project covers the following research: (a) Investigations into the structure of the proton and neutron. This is done by investigating the different resonance states of nucleons with beams of tagged, polarized photons, linearly as well as circularly, incident on polarized hydrogen/deuterium targets and measuring the production of {pi}{sup #25;0}, 2{pi}{sup #25;}0, 3{pi}{sup #25;0}, {eta}#17;, {eta}', {omega}, etc. The principal detector is the Crystal Ball multiphoton spectrometer which has an acceptance of nearly 4#25;. It has been moved to the MAMI accelerator facility of the University of Mainz, Germany. We investigate the conversion of electromagnetic energy into mesonic matter and conversely. (b) We investigate the consequences of applying the "standard" symmetries of isospin, GâÂÂparity, charge conjugation, C, P, T, and chirality using rare and forbidden decays of light mesons such as the {eta}#17;,{eta}' and {omega}. We also investigate the consequences of these symmetries being slightly broken symmetries. We do this by studying selected meson decays using the Crystal Ball detector. (c) We determine the mass, or more precisely the mass difference of the three light quarks (which are inputs to Quantum Chromodynamics) by measuring the decay rate of specially selected {eta}#17; and {eta}' decay modes, again we use the Crystal Ball. (d)We have started a new program to search for the 33 missing cascade baryons using the CLAS detector at the Thomas Jefferson Laboratory. Cascade resonances are very special: they have double strangeness and are quite narrow. This implies that they can be discovered by the missing mass technique in photoproduction reactions such as in {gamma}p{yields}{Xi}{sup #4;âÂÂ}K{sup +}K{sup +}. The cascade program is of particular importance for the upgrade to 12 GeV of the CLAS detector and for design of the Hall D at JLab. (e) Finally, we are getting more involved in a new program to measure the hadronic matter form factor of complex nuclei, in particular the "neutron skin" of {sup 208}Pb, which is of great interest to astroparticle physics for determining the properties of neutron stars. Processes of study are coherent and nonâÂÂcoherent #25;0 photoproduction. The Crystal Ball is uniquely suited for these studies because of the large acceptance, good direction and energy resolution and it is an inclusive detector for the #25;{pi}{sup 0} final state and exclusive for background such as 2#25;{pi}{sup 0}
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
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