6,024 research outputs found
Descending Dungeons and Iterated Base-Changing
For real numbers a, b> 1, let as a_b denote the result of interpreting a in
base b instead of base 10. We define ``dungeons'' (as opposed to ``towers'') to
be numbers of the form a_b_c_d_..._e, parenthesized either from the bottom
upwards (preferred) or from the top downwards. Among other things, we show that
the sequences of dungeons with n-th terms 10_11_12_..._(n-1)_n or
n_(n-1)_..._12_11_10 grow roughly like 10^{10^{n log log n}}, where the
logarithms are to the base 10. We also investigate the behavior as n increases
of the sequence a_a_a_..._a, with n a's, parenthesized from the bottom upwards.
This converges either to a single number (e.g. to the golden ratio if a = 1.1),
to a two-term limit cycle (e.g. if a = 1.05) or else diverges (e.g. if a =
frac{100{99).Comment: 11 pages; new version takes into account comments from referees;
version of Sep 25 2007 inculdes a new theorem and several small improvement
Modeling of the saturation current of a fission chamber taking into account the distorsion of electric field due to space charge effects
Fission chambers were first made fifty years ago for neutron detection. At
the moment, the French Atomic Energy Commission \textsf{(CEA-Cadarache)} is
developing a sub-miniature fission chamber technology with a diameter of 1.5 mm
working in the current mode (Bign). To be able to measure intense fluxes, it is
necessary to adjust the chamber geometry and the gas pressure before testing it
under real neutron flux. In the present paper, we describe a theoretical method
to foresee the current-voltage characteristics (sensitivity and saturation
plateau) of a fission chamber whose geometrical features are given, taking into
account the neutron flux to be measured (spectrum and intensity). The proposed
theoretical model describes electric field distortion resulting from charge
collection effect. A computer code has been developed on this model basis. Its
application to 3 kinds of fission chambers indicates excellent agreement
between theoretical model and measured characteristics
Open TURNS: An industrial software for uncertainty quantification in simulation
The needs to assess robust performances for complex systems and to answer
tighter regulatory processes (security, safety, environmental control, and
health impacts, etc.) have led to the emergence of a new industrial simulation
challenge: to take uncertainties into account when dealing with complex
numerical simulation frameworks. Therefore, a generic methodology has emerged
from the joint effort of several industrial companies and academic
institutions. EDF R&D, Airbus Group and Phimeca Engineering started a
collaboration at the beginning of 2005, joined by IMACS in 2014, for the
development of an Open Source software platform dedicated to uncertainty
propagation by probabilistic methods, named OpenTURNS for Open source Treatment
of Uncertainty, Risk 'N Statistics. OpenTURNS addresses the specific industrial
challenges attached to uncertainties, which are transparency, genericity,
modularity and multi-accessibility. This paper focuses on OpenTURNS and
presents its main features: openTURNS is an open source software under the LGPL
license, that presents itself as a C++ library and a Python TUI, and which
works under Linux and Windows environment. All the methodological tools are
described in the different sections of this paper: uncertainty quantification,
uncertainty propagation, sensitivity analysis and metamodeling. A section also
explains the generic wrappers way to link openTURNS to any external code. The
paper illustrates as much as possible the methodological tools on an
educational example that simulates the height of a river and compares it to the
height of a dyke that protects industrial facilities. At last, it gives an
overview of the main developments planned for the next few years
The IBIS view of the galactic centre: INTEGRAL's imager observations simulations
The Imager on Board Integral Satellite (IBIS) is the imaging instrument of
the INTEGRAL satellite, the hard-X/soft-gamma ray ESA mission to be launched in
2001. It provides diagnostic capabilities of fine imaging (12' FWHM), source
identification and spectral sensitivity to both continuum and broad lines over
a broad (15 keV--10 MeV) energy range. It has a continuum sensitivity of
2~10^{-7} ph cm^{-2} s^{-1} at 1 MeV for a 10^6 seconds observation and a
spectral resolution better than 7 % at 100 keV and of 6 % at 1 MeV. The imaging
capabilities of the IBIS are characterized by the coupling of the above quoted
source discrimination capability with a very wide field of view (FOV), namely 9
x 9 degrees fully coded, 29 x 29 degrees partially coded FOV. We present
simulations of IBIS observations of the Galactic Center based on the results of
the SIGMA Galactic Center survey. They show the capabilities of this instrument
in discriminating between different sources while at the same time monitoring a
huge FOV. It will be possible to simultaneously take spectra of all of these
sources over the FOV even if the sensitivity decreases out of the fully coded
area. It is envisaged that a proper exploitation of both the FOV dimension and
the source localization capability of the IBIS will be a key factor in
maximizing its scientific output.Comment: 5 pages, LaTeX, to be published in the 4th Compton Symposium
Conference Proceedings, uses aipproc.cls, aipproc.sty (included
Carryless Arithmetic Mod 10
We investigate what arithmetic would look like if carry digits into other
digit position were ignored, so that 9 + 4 = 3, 5 + 5 = 0, 9 X 4 = 6, 5 X 4 =
0, and so on. For example, the primes are now 21, 23, 25, 27, 29, 41, 43, 45,
47, ... .Comment: 7 pages. To the memory of Martin Gardner (October 21, 1914 -- May 22,
2010). Revised version (with a number of small improvements), July 7 201
Contact Moishezon threefolds with second Betti number one
We prove that the only contact Moishezon threefold having second Betti number
equal to one is the projective space.Comment: 5 pages. v2: exposition improved as suggested by the referee. To
appear in Archiv der Mat
An Estimate of the Spectral Intensity Expected from the Molecular Bremsstrahlung Radiation in Extensive Air Showers
A detection technique of ultra-high energy cosmic rays, complementary to the
fluorescence technique, would be the use of the molecular Bremsstrahlung
radiation emitted by low-energy electrons left after the passage of the showers
in the atmosphere. The emission mechanism is expected from quasi-elastic
collisions of electrons produced in the shower by the ionisation of the
molecules in the atmosphere. In this article, a detailed calculation of the
spectral intensity of photons at ground level originating from the transitions
between unquantised energy states of free ionisation electrons is presented. In
the absence of absorption of the emitted photons in the plasma, the obtained
spectral intensity is shown to be 5 10^{-26} W m^{-2}Hz^{-1} at 10 km from the
shower core for a vertical shower induced by a proton of 10^{17.5} eV.Comment: 16 pages, 6 figures, accepted in Astroparticle Physics. Compared to
v1 version: 1. Inclusion of ro-vibrational processes. 2. Use of more accurate
ionization potential values and energy distribution of the secondary
electron
Imaging extended sources with coded mask telescopes: Application to the INTEGRAL IBIS/ISGRI instrument
Context. In coded mask techniques, reconstructed sky images are
pseudo-images: they are maps of the correlation between the image recorded on a
detector and an array derived from the coded mask pattern. Aims. The
INTEGRAL/IBIS telescope provides images where the flux of each detected source
is given by the height of the local peak in the correlation map. As such, it
cannot provide an estimate of the flux of an extended source. What is needed is
intensity sky images giving the flux per solide angle as typically done at
other wavelengths. Methods. In this paper, we present the response of the
INTEGRAL IBIS/ISGRI coded mask instrument to extended sources. We develop a
general method based on analytical calculations in order to measure the
intensity and the associated error of any celestial source and validated with
Monte-Carlo simulations. Results. We find that the sensitivity degrades almost
linearly with the source extent. Analytical formulae are given as well as an
easy-to-use recipe for the INTEGRAL user. We check this method on IBIS/ISGRI
data but these results are general and applicable to any coded mask telescope.Comment: 9 pages, 6 figures, Accepted for publication in A&
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