7,678 research outputs found
Dynamical Sieve of Eratosthenes
In this document, prime numbers are related as functions over time, mimicking
the Sieve of Eratosthenes. For this purpose, the mathematical representation is
a uni-dimentional time line depicting the number line for positive natural
numbers N, where each number n represents a time t. In the same way as the
Eratosthenes' sieve, which iteratively mark as composite the multiples of each
prime, starting at each prime. This dynamical prime number function P(s)
zero-cross all composite numbers departing from primes, following a linear
progression over time.Comment: 9 page
One-dimensional solitary waves in singular deformations of SO(2) invariant two-component scalar field theory models
In this paper we study the structure of the manifold of solitary waves in
some deformations of SO(2) symmetric two-component scalar field theoretical
models in two-dimensional Minkowski space. The deformation is chosen in order
to make the analogous mechanical system Hamilton-Jacobi separable in polar
coordinates and displays a singularity at the origin of the internal plane. The
existence of the singularity confers interesting and intriguing properties to
the solitary waves or kink solutions.Comment: 25 pages, 18 figure
Statistical evaluation of the flux cross-calibration of the XMM-Newton EPIC cameras
The second XMM-Newton serendipitous source catalogue, 2XMM, provides the
ideal data base for performing a statistical evaluation of the flux
cross-calibration of the XMM-Newton European Photon Imaging Cameras (EPIC). We
aim to evaluate the status of the relative flux calibration of the EPIC cameras
on board XMM-Newton (MOS1, MOS2, and pn) and investigate the dependence of the
calibration on energy, position in the field of view of the X-ray detectors,
and lifetime of the mission. We compiled the distribution of flux percentage
differences for large samples of 'good quality' objects detected with at least
two of the EPIC cameras. The mean offset of the fluxes and dispersion of the
distributions was then found by Gaussian fitting. Count rate to flux conversion
was performed with a fixed spectral model. The impact on the results of varying
this model was investigated. Excellent agreement was found between the two EPIC
MOS cameras to better than 4% from 0.2 keV to 12.0 keV. MOS cameras register
7-9% higher flux than pn below 4.5 keV and 10-13% flux excess above 4.5 keV. No
evolution of the flux ratios is seen with time, except at energies below 0.5
keV, where we found a strong decrease in the MOS to pn flux ratio with time.
This effect is known to be due to a gradually degrading MOS redistribution
function. The flux ratios show some dependence on distance from the optical
axis in the sense that the MOS to pn flux excess increases with off-axis angle.
Furthermore, in the 4.5-12.0 keV band there is a strong dependence of the MOS
to pn excess flux on the azimuthal-angle. These results strongly suggest that
the calibration of the Reflection Grating Array (RGA) blocking factors is
incorrect at high energies. Finally, we recommend ways to improve the
calculation of fluxes in future versions of XMM-Newton source catalogues.Comment: 11 pages, 10 figures, 3 tables. Abridged Abstract. Accepted for
publication in Astronomy and Astrophysic
The Kink variety in systems of two coupled scalar fields in two space-time dimensions
In this paper we describe the moduli space of kinks in a class of systems of
two coupled real scalar fields in (1+1) Minkowskian space-time. The main
feature of the class is the spontaneous breaking of a discrete symmetry of
(real) Ginzburg-Landau type that guarantees the existence of kink topological
defects.Comment: 12 pages, 5 figures. To appear in Phys. Rev.
Tachyons, Supertubes and Brane/Anti-Brane Systems
We find supertubes with arbitrary (and not necessarily planar) cross section;
the stability against the D2-brane tension is due to a compensation by the
local momentum generated by Born-Infeld fields. Stability against long-range
supergravity forces is also established. We find the corresponding solutions of
the infinite-N M(atrix) model. The supersymmetric D2/anti-D2 system is a
special case of the general supertube, and we show that there are no
open-string tachyons in this system via a computation of the open-string
one-loop vacuum energy.Comment: 1+23 pages, 2 figures, LaTeX. V2, 1+28 pages: Further generalization
to non-planar cross-sections and addition of an entirely new section with the
explicit supergravity solutions. V3, 1+30 pages: Bound on the angular
momentum added, other minor changes in Section
Anticipated synchronization in coupled inertia ratchets with time-delayed feedback: a numerical study
We investigate anticipated synchronization between two periodically driven
deterministic, dissipative inertia ratchets that are able to exhibit directed
transport with a finite velocity. The two ratchets interact through an
unidirectional delay coupling: one is acting as a master system while the other
one represents the slave system. Each of the two dissipative deterministic
ratchets is driven externally by a common periodic force. The delay coupling
involves two parameters: the coupling strength and the (positive-valued) delay
time. We study the synchronization features for the unbounded, current carrying
trajectories of the master and the slave, respectively, for four different
strengths of the driving amplitude. These in turn characterize differing phase
space dynamics of the transporting ratchet dynamics: regular, intermittent and
a chaotic transport regime. We find that the slave ratchet can respond in
exactly the same way as the master will respond in the future, thereby
anticipating the nonlinear directed transport
Synopsis of a computer program designed to interface a personal computer with the fast data acquisition system of a time-of-flight mass spectrometer
Briefly described are the essential features of a computer program designed to interface a personal computer with the fast, digital data acquisition system of a time-of-flight mass spectrometer. The instrumentation was developed to provide a time-resolved analysis of individual vapor pulses produced by the incidence of a pulsed laser beam on an ablative material. The high repetition rate spectrometer coupled to a fast transient recorder captures complete mass spectra every 20 to 35 microsecs, thereby providing the time resolution needed for the study of this sort of transient event. The program enables the computer to record the large amount of data generated by the system in short time intervals, and it provides the operator the immediate option of presenting the spectral data in several different formats. Furthermore, the system does this with a high degree of automation, including the tasks of mass labeling the spectra and logging pertinent instrumental parameters
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