29 research outputs found
Interpretation of percolation in terms of infinity computations
In this paper, a number of traditional models related to the percolation
theory has been considered by means of new computational methodology that does
not use Cantor's ideas and describes infinite and infinitesimal numbers in
accordance with the principle `The part is less than the whole'. It gives a
possibility to work with finite, infinite, and infinitesimal quantities
numerically by using a new kind of a computer - the Infinity Computer -
introduced recently in by Ya.D. Sergeyev in a number of patents. The new
approach does not contradict Cantor. In contrast, it can be viewed as an
evolution of his deep ideas regarding the existence of different infinite
numbers in a more applied way. Site percolation and gradient percolation have
been studied by applying the new computational tools. It has been established
that in an infinite system the phase transition point is not really a point as
with respect of traditional approach. In light of new arithmetic it appears as
a critical interval, rather than a critical point. Depending on "microscope" we
use this interval could be regarded as finite, infinite and infinitesimal short
interval. Using new approach we observed that in vicinity of percolation
threshold we have many different infinite clusters instead of one infinite
cluster that appears in traditional consideration.Comment: 22 pages, 7 figures. arXiv admin note: substantial text overlap with
arXiv:1203.4140, arXiv:1203.316
Spiral attractor created by vector solitons
Mode-locked lasers emitting a train of femtosecond pulses called dissipative solitons are an enabling technology for metrology, high-resolution spectroscopy, fibre optic communications, nano-optics and many other fields of science and applications. Recently, the vector nature of dissipative solitons has been exploited to demonstrate mode locked lasing with both locked and rapidly evolving states of polarisation. Here, for an erbium-doped fibre laser mode locked with carbon nanotubes, we demonstrate the first experimental and theoretical evidence of a new class of slowly evolving vector solitons characterized by a double-scroll chaotic polarisation attractor substantially different from Lorenz, Rössler and Ikeda strange attractors. The underlying physics comprises a long time scale coherent coupling of two polarisation modes. The observed phenomena, apart from the fundamental interest, provide a base for advances in secure communications, trapping and manipulation of atoms and nanoparticles, control of magnetisation in data storage devices and many other areas
The astrometric Gaia-FUN-SSO observation campaign of 99 942 Apophis
Astrometric observations performed by the Gaia Follow-Up Network for Solar
System Objects (Gaia-FUN-SSO) play a key role in ensuring that moving objects
first detected by ESA's Gaia mission remain recoverable after their discovery.
An observation campaign on the potentially hazardous asteroid (99 942) Apophis
was conducted during the asteroid's latest period of visibility, from
12/21/2012 to 5/2/2013, to test the coordination and evaluate the overall
performance of the Gaia-FUN-SSO . The 2732 high quality astrometric
observations acquired during the Gaia-FUN-SSO campaign were reduced with the
Platform for Reduction of Astronomical Images Automatically (PRAIA), using the
USNO CCD Astrograph Catalogue 4 (UCAC4) as a reference. The astrometric
reduction process and the precision of the newly obtained measurements are
discussed. We compare the residuals of astrometric observations that we
obtained using this reduction process to data sets that were individually
reduced by observers and accepted by the Minor Planet Center. We obtained 2103
previously unpublished astrometric positions and provide these to the
scientific community. Using these data we show that our reduction of this
astrometric campaign with a reliable stellar catalog substantially improves the
quality of the astrometric results. We present evidence that the new data will
help to reduce the orbit uncertainty of Apophis during its close approach in
2029. We show that uncertainties due to geolocations of observing stations, as
well as rounding of astrometric data can introduce an unnecessary degradation
in the quality of the resulting astrometric positions. Finally, we discuss the
impact of our campaign reduction on the recovery process of newly discovered
asteroids.Comment: Accepted for publication in A&
Long-range corrected DFT calculations of charge-transfer integrals in model metal-free phthalocyanine complexes
An assessment of several widely used exchange--correlation potentials in computing charge-transfer integrals is performed. In particular, we employ the recently proposed Coulomb-attenuated model which was proven by other authors to improve upon conventional functionals in the case of charge-transfer excitations. For further validation, two distinct approaches to compute the property in question are compared for a phthalocyanine dimer