212 research outputs found
Critical percolation of free product of groups
In this article we study percolation on the Cayley graph of a free product of
groups.
The critical probability of a free product of groups
is found as a solution of an equation involving only the expected subcritical
cluster size of factor groups . For finite groups these
equations are polynomial and can be explicitly written down. The expected
subcritical cluster size of the free product is also found in terms of the
subcritical cluster sizes of the factors. In particular, we prove that
for the Cayley graph of the modular group (with the
standard generators) is , the unique root of the polynomial
in the interval .
In the case when groups can be "well approximated" by a sequence of
quotient groups, we show that the critical probabilities of the free product of
these approximations converge to the critical probability of
and the speed of convergence is exponential. Thus for residually finite groups,
for example, one can restrict oneself to the case when each free factor is
finite.
We show that the critical point, introduced by Schonmann,
of the free product is just the minimum of for the factors
High resolution general purpose D-layer experiment for EISCAT incoherent scatter radars using selected set of random codes
International audienceThe ionospheric D-layer is a narrow bandwidth radar target often with a very small scattering cross section. The target autocorrelation function can be obtained by transmitting a series of relatively short coded pulses and computing the correlation between data obtained from different pulses. The spatial resolution should be as high as possible and the spatial side lobes of the codes used should be as small as possible. However, due to the short pulse repetition period (in the order of milliseconds) at any instant, the radar receives detectable scattered signals not only from the pulse illuminating the D-region but also from 3?5 ambiguous-range pulses, which makes it difficult to produce a reliable estimate near zero lag of the autocorrelation function. A new experimental solution to this measurement problem, using a selected set of 40-bit random codes with 4 µs elements giving 600 m spatial resolution is presented. The zero lag is approximated by dividing the pulse into two 20-bit codes and computing the correlation between those two pulses. The lowest altitudes of the E-layer are measured by dividing the pulse into 5 pieces of 8 bits, which allows for computation of 4 lags. In addition, coherent integration of data from four pulses is used for obtaining separately the autocorrelation function estimate for the lowest altitudes and in cases when the target contains structures with a long coherence time. Design details and responses of the experiment are given, and analysed test data are shown
Study on spatiotemporal variations of ionospheric trough in auroral/subauroral region
第3回極域科学シンポジウム/第36回極域宙空圏シンポジウム 11月26日(月)、27日(火) 国立極地研究所 2階ラウン
Convergence towards an asymptotic shape in first-passage percolation on cone-like subgraphs of the integer lattice
In first-passage percolation on the integer lattice, the Shape Theorem
provides precise conditions for convergence of the set of sites reachable
within a given time from the origin, once rescaled, to a compact and convex
limiting shape. Here, we address convergence towards an asymptotic shape for
cone-like subgraphs of the lattice, where . In particular, we
identify the asymptotic shapes associated to these graphs as restrictions of
the asymptotic shape of the lattice. Apart from providing necessary and
sufficient conditions for - and almost sure convergence towards this
shape, we investigate also stronger notions such as complete convergence and
stability with respect to a dynamically evolving environment.Comment: 23 pages. Together with arXiv:1305.6260, this version replaces the
old. The main results have been strengthened and an earlier error in the
statement corrected. To appear in J. Theoret. Proba
Percolation in invariant Poisson graphs with i.i.d. degrees
Let each point of a homogeneous Poisson process in R^d independently be
equipped with a random number of stubs (half-edges) according to a given
probability distribution mu on the positive integers. We consider
translation-invariant schemes for perfectly matching the stubs to obtain a
simple graph with degree distribution mu. Leaving aside degenerate cases, we
prove that for any mu there exist schemes that give only finite components as
well as schemes that give infinite components. For a particular matching scheme
that is a natural extension of Gale-Shapley stable marriage, we give sufficient
conditions on mu for the absence and presence of infinite components
The dynamical background of polar mesosphere winter echoes from simultaneous EISCAT and ESRAD observations
On 30 October 2004 during a strong solar proton event, layers of enhanced backscatter from altitudes between 55 and 75km have been observed by both ESRAD (52MHz) and the EISCAT VHF (224MHz) radars. These echoes have earlier been termed Polar Mesosphere Winter Echoes, PMWE. After considering the morphology of the layers and their relation to observed atmospheric waves, we conclude that the radars have likely seen the same phenomenon even though the radars' scattering volumes are located about 220km apart and that the most long-lasting layer is likely associated with wind-shear in an inertio-gravity wave. An ion-chemistry model is used to determine parameters necessary to relate wind-shear induced turbulent energy dissipation rates to radar backscatter. The model is verified by comparison with electron density profiles measured by the EISCAT VHF radar. Observed radar signal strengths are found to be 2-3 orders of magnitude stronger than the maximum which can be expected from neutral turbulence alone, assuming that previously published results relating radar signal scatter to turbulence parameters, and turbulence parameters to wind shear, are correct. The possibility remains that some additional or alternative mechanism may be involved in producing PMWE, such as layers of charged dust/smoke particles or large cluster ions
The Extending of Observing Altitudes of Plasma and Ion Lines During Ionospheric Heating
Source at https://doi.org/10.1002/2017JA024809. The ultrahigh-frequency observation during an ionospheric heating experiment on 11 March 2014 at the European Incoherent Scatter Scientific Association Tromsø site illustrated a remarkable extension of observing altitudes of the enhanced plasma line and the ion line, implying that the enhanced ion acoustic wave and Langmuir wave should satisfy the Bragg condition within the extending altitude range. An analysis shows that the dependence of the wave number of the traveling ion acoustic wave on the profiles of enhanced electron temperature and ion mass, as are expected from the dispersion relation of the ion acoustic wave, leads to the extension of observing altitudes of the enhanced ion line. In addition, the altitude extension of the enhanced plasma line is dependent mainly on the profile of the electron density, although it is not independent of the profile of the electron temperature. Considering a small gradient profile of electron density, however, the enhanced electron temperature, as well as the thermal conduction along the magnetic field, may lead to the altitude extension of the enhanced plasma line
Palm pairs and the general mass-transport principle
We consider a lcsc group G acting properly on a Borel space S and measurably
on an underlying sigma-finite measure space. Our first main result is a
transport formula connecting the Palm pairs of jointly stationary random
measures on S. A key (and new) technical result is a measurable disintegration
of the Haar measure on G along the orbits. The second main result is an
intrinsic characterization of the Palm pairs of a G-invariant random measure.
We then proceed with deriving a general version of the mass-transport principle
for possibly non-transitive and non-unimodular group operations first in a
deterministic and then in its full probabilistic form.Comment: 26 page
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