2,710 research outputs found
Billiards with polynomial mixing rates
While many dynamical systems of mechanical origin, in particular billiards,
are strongly chaotic -- enjoy exponential mixing, the rates of mixing in many
other models are slow (algebraic, or polynomial). The dynamics in the latter
are intermittent between regular and chaotic, which makes them particularly
interesting in physical studies. However, mathematical methods for the analysis
of systems with slow mixing rates were developed just recently and are still
difficult to apply to realistic models. Here we reduce those methods to a
practical scheme that allows us to obtain a nearly optimal bound on mixing
rates. We demonstrate how the method works by applying it to several classes of
chaotic billiards with slow mixing as well as discuss a few examples where the
method, in its present form, fails.Comment: 39pages, 11 figue
On the complexity of curve fitting algorithms
We study a popular algorithm for fitting polynomial curves to scattered data
based on the least squares with gradient weights. We show that sometimes this
algorithm admits a substantial reduction of complexity, and, furthermore, find
precise conditions under which this is possible. It turns out that this is,
indeed, possible when one fits circles but not ellipses or hyperbolas.Comment: 8 pages, no figure
Spectral and spatial observations of microwave spikes and zebra structure in the short radio burst of May 29, 2003
The unusual radio burst of May 29, 2003 connected with the M1.5 flare in AR
10368 has been analyzed. It was observed by the Solar Broadband Radio
Spectrometer (SBRS/Huairou station, Beijing) in the 5.2-7.6 GHz range. It
proved to be only the third case of a neat zebra structure appearing among all
observations at such high frequencies. Despite the short duration of the burst
(25 s), it provided a wealth of data for studying the superfine structure with
millisecond resolution (5 ms). We localize the site of emission sources in the
flare region, estimate plasma parameters in the generation sites, and suggest
applicable mechanisms for interpretating spikes and zebra-structure generation.
Positions of radio bursts were obtained by the Siberian Solar Radio Telescope
(SSRT) (5.7 GHz) and Nobeyama radioheliograph (NoRH) (17 GHz). The sources in
intensity gravitated to tops of short loops at 17 GHz, and to long loops at 5.7
GHz. Short pulses at 17 GHz (with a temporal resolution of 100 ms) are
registered in the R-polarized source over the N-magnetic polarity
(extraordinary mode). Dynamic spectra show that all the emission comprised
millisecond pulses (spikes) of 5-10 ms duration in the instantaneous band of 70
to 100 MHz, forming the superfine structure of different bursts, essentially in
the form of fast or slow-drift fibers and various zebra-structure stripes. Five
scales of zebra structures have been singled out. As the main mechanism for
generating spikes (as the initial emission) we suggest the coalescence of
plasma waves with whistlers in the pulse regime of interaction between
whistlers and ion-sound waves. In this case one can explain the appearance of
fibers and sporadic zebra-structure stripes exhibiting the frequency splitting.Comment: 11 pages, 5 figures, in press; A&A 201
Log-periodic drift oscillations in self-similar billiards
We study a particle moving at unit speed in a self-similar Lorentz billiard
channel; the latter consists of an infinite sequence of cells which are
identical in shape but growing exponentially in size, from left to right. We
present numerical computation of the drift term in this system and establish
the logarithmic periodicity of the corrections to the average drift
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