1,680 research outputs found
Spectral Properties of the Ruelle Operator for Product Type Potentials on Shift Spaces
We study a class of potentials on one sided full shift spaces over finite
or countable alphabets, called potentials of product type. We obtain explicit
formulae for the leading eigenvalue, the eigenfunction (which may be
discontinuous) and the eigenmeasure of the Ruelle operator. The uniqueness
property of these quantities is also discussed and it is shown that there
always exists a Bernoulli equilibrium state even if does not satisfy
Bowen's condition. We apply these results to potentials of the form with . For , we obtain the existence of
two different eigenfunctions. Both functions are (locally) unbounded and exist
a.s. (but not everywhere) with respect to the eigenmeasure and the measure of
maximal entropy, respectively.Comment: To appear in the Journal of London Mathematical Societ
Ergodicity of avalanche transformations
PublishedIn this paper, we study dynamical systems of product type and some particular inducing scheme motivated by neural dynamics (called avalanche transformation). We derive the distribution of avalanche sizes and give sufficient conditions such that the avalanche transformation is ergodic. Moreover, we deduce a multivariate central limit theorem as a corollary.We would like to thank Ira Gessel and Wlodek Bryc for some helpful remarks concerning Section 2.
The research of M. Denker was supported by the National Science Foundation grant DMS-
1008538. The research of A. Rodrigues is supported by the Swedish Research Council (VR Grant
2010/5905). The authors would like to thank the Goran Gustafsson Foundation UU/KTH for the ¨
financial support
The Thermal Environment of the Fiber Glass Dome for the New Solar Telescope at Big Bear Solar Observatory
The New Solar Telescope (NST) is a 1.6-meter off-axis Gregory-type telescope
with an equatorial mount and an open optical support structure. To mitigate the
temperature fluctuations along the exposed optical path, the effects of
local/dome-related seeing have to be minimized. To accomplish this, NST will be
housed in a 5/8-sphere fiberglass dome that is outfitted with 14 active vents
evenly spaced around its perimeter. The 14 vents house louvers that open and
close independently of one another to regulate and direct the passage of air
through the dome. In January 2006, 16 thermal probes were installed throughout
the dome and the temperature distribution was measured. The measurements
confirmed the existence of a strong thermal gradient on the order of 5 degree
Celsius inside the dome. In December 2006, a second set of temperature
measurements were made using different louver configurations. In this study, we
present the results of these measurements along with their integration into the
thermal control system (ThCS) and the overall telescope control system (TCS).Comment: 12 pages, 11 figures, submitted to SPIE Optics+Photonics, San Diego,
U.S.A., 26-30 August 2007, Conference: Solar Physics and Space Weather
Instrumentation II, Proceedings of SPIE Volume 6689, Paper #2
Utilizing weak pump depletion to stabilize squeezed vacuum states
We propose and demonstrate a pump-phase locking technique that makes use of
weak pump depletion (WPD) - an unavoidable effect that is usually neglected -
in a sub-threshold optical parametric oscillator (OPO). We show that the phase
difference between seed and pump beam is imprinted on both light fields by the
non-linear interaction in the crystal and can be read out without disturbing
the squeezed output. Our new locking technique allows for the first
experimental realization of a pump-phase lock by reading out the pre-existing
phase information in the pump field. There is no degradation of the detected
squeezed states required to implement this scheme.Comment: 11 pages, 7 figure
Two-Dimensional Spectroscopy of Photospheric Shear Flows in a Small delta Spot
In recent high-resolution observations of complex active regions,
long-lasting and well-defined regions of strong flows were identified in major
flares and associated with bright kernels of visible, near-infrared, and X-ray
radiation. These flows, which occurred in the proximity of the magnetic neutral
line, significantly contributed to the generation of magnetic shear. Signatures
of these shear flows are strongly curved penumbral filaments, which are almost
tangential to sunspot umbrae rather than exhibiting the typical radial
filamentary structure. Solar active region NOAA 10756 was a moderately complex,
beta-delta sunspot group, which provided an opportunity to extend previous
studies of such shear flows to quieter settings. We conclude that shear flows
are a common phenomenon in complex active regions and delta spots. However,
they are not necessarily a prerequisite condition for flaring. Indeed, in the
present observations, the photospheric shear flows along the magnetic neutral
line are not related to any change of the local magnetic shear. We present
high-resolution observations of NOAA 10756 obtained with the 65-cm vacuum
reflector at Big Bear Solar Observatory (BBSO). Time series of
speckle-reconstructed white-light images and two-dimensional spectroscopic data
were combined to study the temporal evolution of the three-dimensional vector
flow field in the beta-delta sunspot group. An hour-long data set of consistent
high quality was obtained, which had a cadence of better than 30 seconds and
sub-arcsecond spatial resolution.Comment: 23 pages, 6 gray-scale figures, 4 color figures, 2 tables, submitted
to Solar Physic
Limit theorems for von Mises statistics of a measure preserving transformation
For a measure preserving transformation of a probability space
we investigate almost sure and distributional convergence
of random variables of the form where (called the \emph{kernel})
is a function from to and are appropriate normalizing
constants. We observe that the above random variables are well defined and
belong to provided that the kernel is chosen from the projective
tensor product with We establish a form of the individual ergodic theorem for such
sequences. Next, we give a martingale approximation argument to derive a
central limit theorem in the non-degenerate case (in the sense of the classical
Hoeffding's decomposition). Furthermore, for and a wide class of
canonical kernels we also show that the convergence holds in distribution
towards a quadratic form in independent
standard Gaussian variables . Our results on the
distributional convergence use a --\,invariant filtration as a prerequisite
and are derived from uni- and multivariate martingale approximations
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