1,925 research outputs found
Experimental setup for muon diagnostics of the Earth's atmosphere and magnetosphere (the URAGAN project)
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
From Discrete Hopping to Continuum Modeling on Vicinal Surfaces with Applications to Si(001) Electromigration
Coarse-grained modeling of dynamics on vicinal surfaces concentrates on the
diffusion of adatoms on terraces with boundary conditions at sharp steps, as
first studied by Burton, Cabrera and Frank (BCF). Recent electromigration
experiments on vicinal Si surfaces suggest the need for more general boundary
conditions in a BCF approach. We study a discrete 1D hopping model that takes
into account asymmetry in the hopping rates in the region around a step and the
finite probability of incorporation into the solid at the step site. By
expanding the continuous concentration field in a Taylor series evaluated at
discrete sites near the step, we relate the kinetic coefficients and
permeability rate in general sharp step models to the physically suggestive
parameters of the hopping models. In particular we find that both the kinetic
coefficients and permeability rate can be negative when diffusion is faster
near the step than on terraces. These ideas are used to provide an
understanding of recent electromigration experiment on Si(001) surfaces where
step bunching is induced by an electric field directed at various angles to the
steps.Comment: 10 pages, 4 figure
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
Results and prospects on registration of reflected Cherenkov light of EAS from cosmic particles above 10^{15} eV
We give an overview of the SPHERE experiment based on detection of reflected
Vavilov-Cherenkov radiation (Cherenkov light) from extensive air showers in the
energy region E>10^{15} eV. A brief history of the reflected Cherenkov light
technique is given; the observations carried out with the SPHERE-2 detector are
summarized; the methods of the experimental datasample analysis are described.
The first results on the primary cosmic ray all-nuclei energy spectrum and mass
composition are presented. Finally, the prospects of the SPHERE experiment and
the reflected Cherenkov light technique are given.Comment: 4 pages, 3 figures, Proc. PANIC-201
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
The wave function of a gravitating shell
We have calculated a discrete spectrum and found an exact analytical solution
in the form of Meixner polynomials for the wave function of a thin gravitating
shell in the Reissner-Nordstrom geometry. We show that there is no extreme
state in the quantum spectrum of the gravitating shell, as in the case of
extreme black hole.Comment: 7 pages, 1 figur
Possible types of the evolution of vacuum shells around the de Sitter space
All possible evolution scenarios of a thin vacuum shell surrounding the
spherically symmetric de Sitter space have been determined and the
corresponding global geometries have been constructed. Such configurations can
appear at the final stage of the cosmological phase transition, when isolated
regions (islands) of the old vacuum remain. The islands of the old vacuum are
absorbed by the new vacuum, expand unlimitedly, or form black holes and
wormholes depending on the sizes of the islands as well as on the density and
velocity of the shells surrounding the islands.Comment: 3 pages, 1 figur
Prediction with Expert Advice under Discounted Loss
We study prediction with expert advice in the setting where the losses are
accumulated with some discounting---the impact of old losses may gradually
vanish. We generalize the Aggregating Algorithm and the Aggregating Algorithm
for Regression to this case, propose a suitable new variant of exponential
weights algorithm, and prove respective loss bounds.Comment: 26 pages; expanded (2 remarks -> theorems), some misprints correcte
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