3,416 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
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
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
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