20,718 research outputs found
Central limit theorems for the spectra of classes of random fractals
We discuss the spectral asymptotics of some open subsets of the real line
with random fractal boundary and of a random fractal, the continuum random
tree. In the case of open subsets with random fractal boundary we establish the
existence of the second order term in the asymptotics almost surely and then
determine when there will be a central limit theorem which captures the
fluctuations around this limit. We will show examples from a class of random
fractals generated from Dirichlet distributions as this is a relatively simple
setting in which there are sets where there will and will not be a central
limit theorem. The Brownian continuum random tree can also be viewed as a
random fractal generated by a Dirichlet distribution. The first order term in
the spectral asymptotics is known almost surely and here we show that there is
a central limit theorem describing the fluctuations about this, though the
positivity of the variance arising in the central limit theorem is left open.
In both cases these fractals can be described through a general
Crump-Mode-Jagers branching process and we exploit this connection to establish
our central limit theorems for the higher order terms in the spectral
asymptotics. Our main tool is a central limit theorem for such general
branching processes which we prove under conditions which are weaker than those
previously known
Spin-orbit resonances and rotation of coorbital bodies in quasi-circular orbits
The rotation of asymmetric bodies in eccentric Keplerian orbits can be
chaotic when there is some overlap of spin-orbit resonances. Here we show that
the rotation of two coorbital bodies (two planets orbiting a star or two
satellites of a planet) can also be chaotic even for quasi-circular orbits
around the central body. When dissipation is present, the rotation period of a
body on a nearly circular orbit is believed to always end synchronous with the
orbital period. Here we demonstrate that for coorbital bodies in quasi-circular
orbits, stable non-synchronous rotation is possible for a wide range of mass
ratios and body shapes. We further show that the rotation becomes chaotic when
the natural rotational libration frequency, due to the axial asymmetry, is of
the same order of magnitude as the orbital libration frequency
Unconditional security proof of long-distance continuous-variable quantum key distribution with discrete modulation
We present a continuous-variable quantum key distribution protocol combining
a discrete modulation and reverse reconciliation. This protocol is proven
unconditionally secure and allows the distribution of secret keys over long
distances, thanks to a reverse reconciliation scheme efficient at very low
signal-to-noise ratio.Comment: 4 pages, 2 figure
Improved Parameters and New Lensed Features for Q0957+561 from WFPC2 Imaging
New HST WFPC2 observations of the lensed double QSO 0957+561 will allow
improved constraints on the lens mass distribution and hence will improve the
derived value of H. We first present improved optical positions and
photometry for the known components of this lens. The optical separation
between the A and B quasar images agrees with VLBI data at the 10 mas level,
and the optical center of the primary lensing galaxy G1 coincides with the VLBI
source G' to within 10 mas. The best previous model for this lens (Grogin and
Narayan 1996) is excluded by these data and must be reevaluated.
Several new resolved features are found within 10\arcsec of G1, including an
apparent fold arc with two bright knots. Several other small galaxies are
detected, including two which may be multiple images of each other. We present
positions and crude photometry of these objects.Comment: 7 pages including 2 postscript figures, LaTeX, emulateapj style. Also
available at
http://www.astro.lsa.umich.edu:80/users/philf/www/papers/list.htm
A nonlinear model for rotationally constrained convection with Ekman pumping
It is a well established result of linear theory that the influence of
differing mechanical boundary conditions, i.e., stress-free or no-slip, on the
primary instability in rotating convection becomes asymptotically small in the
limit of rapid rotation. This is accounted for by the diminishing impact of the
viscous stresses exerted within Ekman boundary layers and the associated
vertical momentum transport by Ekman pumping. By contrast, in the nonlinear
regime recent experiments and supporting simulations are now providing evidence
that the efficiency of heat transport remains strongly influenced by Ekman
pumping in the rapidly rotating limit. In this paper, a reduced model is
developed for the case of low Rossby number convection in a plane layer
geometry with no-slip upper and lower boundaries held at fixed temperatures. A
complete description of the dynamics requires the existence of three distinct
regions within the fluid layer: a geostrophically balanced interior where fluid
motions are predominately aligned with the axis of rotation, Ekman boundary
layers immediately adjacent to the bounding plates, and thermal wind layers
driven by Ekman pumping in between. The reduced model uses a classical Ekman
pumping parameterization to alleviate the need for spatially resolving the
Ekman boundary layers. Results are presented for both linear stability theory
and a special class of nonlinear solutions described by a single horizontal
spatial wavenumber. It is shown that Ekman pumping allows for significant
enhancement in the heat transport relative to that observed in simulations with
stress-free boundaries. Without the intermediate thermal wind layer the
nonlinear feedback from Ekman pumping would be able to generate a heat
transport that diverges to infinity. This layer arrests this blowup resulting
in finite heat transport at a significantly enhanced value.Comment: 38 pages, 14 figure
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