2,528 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
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
Beam propagation in a Randomly Inhomogeneous Medium
An integro-differential equation describing the angular distribution of beams
is analyzed for a medium with random inhomogeneities. Beams are trapped because
inhomogeneities give rise to wave localization at random locations and random
times. The expressions obtained for the mean square deviation from the initial
direction of beam propagation generalize the "3/2 law".Comment: 4 page
Deterministic Walks in Quenched Random Environments of Chaotic Maps
This paper concerns the propagation of particles through a quenched random
medium. In the one- and two-dimensional models considered, the local dynamics
is given by expanding circle maps and hyperbolic toral automorphisms,
respectively. The particle motion in both models is chaotic and found to
fluctuate about a linear drift. In the proper scaling limit, the cumulative
distribution function of the fluctuations converges to a Gaussian one with
system dependent variance while the density function shows no convergence to
any function. We have verified our analytical results using extreme precision
numerical computations.Comment: 18 pages, 9 figure
Heat transport in stochastic energy exchange models of locally confined hard spheres
We study heat transport in a class of stochastic energy exchange systems that
characterize the interactions of networks of locally trapped hard spheres under
the assumption that neighbouring particles undergo rare binary collisions. Our
results provide an extension to three-dimensional dynamics of previous ones
applying to the dynamics of confined two-dimensional hard disks [Gaspard P &
Gilbert T On the derivation of Fourier's law in stochastic energy exchange
systems J Stat Mech (2008) P11021]. It is remarkable that the heat conductivity
is here again given by the frequency of energy exchanges. Moreover the
expression of the stochastic kernel which specifies the energy exchange
dynamics is simpler in this case and therefore allows for faster and more
extensive numerical computations.Comment: 21 pages, 5 figure
Upgrading the Local Ergodic Theorem for planar semi-dispersing billiards
The Local Ergodic Theorem (also known as the `Fundamental Theorem') gives
sufficient conditions under which a phase point has an open neighborhood that
belongs (mod 0) to one ergodic component. This theorem is a key ingredient of
many proofs of ergodicity for billiards and, more generally, for smooth
hyperbolic maps with singularities. However the proof of that theorem relies
upon a delicate assumption (Chernov-Sinai Ansatz), which is difficult to check
for some physically relevant models, including gases of hard balls. Here we
give a proof of the Local Ergodic Theorem for two dimensional billiards without
using the Ansatz.Comment: 17 pages, 2 figure
A simple piston problem in one dimension
We study a heavy piston that separates finitely many ideal gas particles
moving inside a one-dimensional gas chamber. Using averaging techniques, we
prove precise rates of convergence of the actual motions of the piston to its
averaged behavior. The convergence is uniform over all initial conditions in a
compact set. The results extend earlier work by Sinai and Neishtadt, who
determined that the averaged behavior is periodic oscillation. In addition, we
investigate the piston system when the particle interactions have been
smoothed. The convergence to the averaged behavior again takes place uniformly,
both over initial conditions and over the amount of smoothing.Comment: Accepted by Nonlinearity. 27 pages, 2 figure
Circularly polarized modes in magnetized spin plasmas
The influence of the intrinsic spin of electrons on the propagation of
circularly polarized waves in a magnetized plasma is considered. New eigenmodes
are identified, one of which propagates below the electron cyclotron frequency,
one above the spin-precession frequency, and another close to the
spin-precession frequency.\ The latter corresponds to the spin modes in
ferromagnets under certain conditions. In the nonrelativistic motion of
electrons, the spin effects become noticeable even when the external magnetic
field is below the quantum critical\ magnetic field strength, i.e.,
and the electron density
satisfies m. The importance of electron
spin (paramagnetic) resonance (ESR) for plasma diagnostics is discussed.Comment: 10 page
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