2,255 research outputs found
Exponential speed of mixing for skew-products with singularities
Let be the
endomorphism given by where is a positive real number. We prove that is
topologically mixing and if then is mixing with respect to Lebesgue
measure. Furthermore we prove that the speed of mixing is exponential.Comment: 23 pages, 3 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
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
Oseledets' Splitting of Standard-like Maps
For the class of differentiable maps of the plane and, in particular, for
standard-like maps (McMillan form), a simple relation is shown between the
directions of the local invariant manifolds of a generic point and its
contribution to the finite-time Lyapunov exponents (FTLE) of the associated
orbit. By computing also the point-wise curvature of the manifolds, we produce
a comparative study between local Lyapunov exponent, manifold's curvature and
splitting angle between stable/unstable manifolds. Interestingly, the analysis
of the Chirikov-Taylor standard map suggests that the positive contributions to
the FTLE average mostly come from points of the orbit where the structure of
the manifolds is locally hyperbolic: where the manifolds are flat and
transversal, the one-step exponent is predominantly positive and large; this
behaviour is intended in a purely statistical sense, since it exhibits large
deviations. Such phenomenon can be understood by analytic arguments which, as a
by-product, also suggest an explicit way to point-wise approximate the
splitting.Comment: 17 pages, 11 figure
The Lyapunov exponent in the Sinai billiard in the small scatterer limit
We show that Lyapunov exponent for the Sinai billiard is with where
is the radius of the circular scatterer. We consider the disk-to-disk-map
of the standard configuration where the disks is centered inside a unit square.Comment: 15 pages LaTeX, 3 (useful) figures available from the autho
Stages of steady diffusion growth of a gas bubble in strongly supersaturated gas-liquid solution
Gas bubble growth as a result of diffusion flux of dissolved gas molecules
from the surrounding supersaturated solution to the bubble surface is studied.
The condition of the flux steadiness is revealed. A limitation from below on
the bubble radius is considered. Its fulfillment guarantees the smallness of
fluctuation influence on bubble growth and irreversibility of this process.
Under the conditions of steadiness of diffusion flux three stages of bubble
growth are marked out. With account for Laplace forces in the bubble intervals
of bubble size change and time intervals of these stages are found. The trend
of the third stage towards the self-similar regime of the bubble growth, when
Laplace forces in the bubble are completely neglected, is described
analytically.Comment: 22 page
Proving The Ergodic Hypothesis for Billiards With Disjoint Cylindric Scatterers
In this paper we study the ergodic properties of mathematical billiards
describing the uniform motion of a point in a flat torus from which finitely
many, pairwise disjoint, tubular neighborhoods of translated subtori (the so
called cylindric scatterers) have been removed. We prove that every such system
is ergodic (actually, a Bernoulli flow), unless a simple geometric obstacle for
the ergodicity is present.Comment: 24 pages, AMS-TeX fil
Escape Rates and Physically Relevant Measures for Billiards with Small Holes
We study the billiard map corresponding to a periodic Lorentz gas in
2-dimensions in the presence of small holes in the table. We allow holes in the
form of open sets away from the scatterers as well as segments on the
boundaries of the scatterers. For a large class of smooth initial
distributions, we establish the existence of a common escape rate and
normalized limiting distribution. This limiting distribution is conditionally
invariant and is the natural analogue of the SRB measure of a closed system.
Finally, we prove that as the size of the hole tends to zero, the limiting
distribution converges to the smooth invariant measure of the billiard map.Comment: 39 pages, 4 figure
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