5,183 research outputs found
Convex Dynamics and Applications
This paper proves a theorem about bounding orbits of a time dependent
dynamical system. The maps that are involved are examples in convex dynamics,
by which we mean the dynamics of piecewise isometries where the pieces are
convex. The theorem came to the attention of the authors in connection with the
problem of digital halftoning. \textit{Digital halftoning} is a family of
printing technologies for getting full color images from only a few different
colors deposited at dots all of the same size. The simplest version consist in
obtaining grey scale images from only black and white dots. A corollary of the
theorem is that for \textit{error diffusion}, one of the methods of digital
halftoning, averages of colors of the printed dots converge to averages of the
colors taken from the same dots of the actual images. Digital printing is a
special case of a much wider class of scheduling problems to which the theorem
applies. Convex dynamics has roots in classical areas of mathematics such as
symbolic dynamics, Diophantine approximation, and the theory of uniform
distributions.Comment: LaTex with 9 PostScript figure
A Closing Lemma for a Class of Symplectic Diffeomorphisms
We prove a closing lemma for a class of partially hyperbolic symplectic
diffeomorphisms. We show that for a generic symplectic diffeomorphism, , with two dimensional center and close to a product map, the set
of all periodic points is dense
Properties of quasi-periodic pulsations in solar flares from a single active region
We investigate the properties of a set of solar flares originating from a
single active region (AR) that exhibit QPPs, and look for signs of the QPP
periods relating to AR properties. The AR studied, best known as NOAA 12192,
was unusually long-lived and produced 181 flares. Data from the GOES, EVE,
Fermi, Vernov and NoRH observatories were used to determine if QPPs were
present in the flares. For the soft X-ray GOES and EVE data, the time
derivative of the signal was used. Power spectra of the time series data
(without any form of detrending) were inspected, and flares with a peak above
the 95% confidence level in the spectrum were labelled as having candidate
QPPs. The confidence levels were determined taking account of uncertainties and
the possible presence of red noise. AR properties were determined using HMI
line of sight magnetograms. A total of 37 flares (20% of the sample) show good
evidence of having QPPs, and some of the pulsations can be seen in data from
multiple instruments and in different wavebands. The QPP periods show a weak
correlation with the flare amplitude and duration, but this may be due to an
observational bias. A stronger correlation was found between the QPP period and
duration of the QPP signal, which can be partially but not entirely explained
by observational constraints. No correlations were found with the AR area,
bipole separation, or average magnetic field strength. The fact that a
substantial fraction of the flare sample showed evidence of QPPs using a strict
detection method with minimal processing of the data demonstrates that these
QPPs are a real phenomenon, which cannot be explained by the presence of red
noise or the superposition of multiple unrelated flares. The lack of
correlation between the QPP periods and AR properties implies that the
small-scale structure of the AR is important, and/or that different QPP
mechanisms act in different cases.Comment: 23 pages, 57 figures. Accepted for publication by Astronomy &
Astrophysic
Cataphoresis in rotating electric fields
A new method of making cataphoresis measurements on colloid particles has been developed and tested. The method makes use of a rotating electric field which causes the particles to move in circles. In this way it is easily possible to test the effect of variable speed of the particle on the distribution of the diffuse electric double layer surrounding it. The results obtained indicate that this effect is negligible. Furthermore, it has been discovered that the mobility of the small particles (below 10^-4 cm in diameter) fluctuates widely and this is made very evident to the eye by the fluctuations in the circular paths of the particles. The fluctuations are quite violent with particles as small as 10^-6 cm in diameter. Considerable study of these variations has been made as well as an attempt to explain them qualitatively
Generation of internal stress and its effects
Internal stresses may be generated continually in many polycrystalline materials. Their existence is manifested by changes in crystal defect concentration and arrangement, by surface observations, by macroscopic shape changes and particularly by alteration of mechanical properties when external stresses are simultaneously imposed
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