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

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

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

New models for two real scalar fields and their kinklike solutions

In this work we study the presence of kinks in models described by two real scalar fields in bi-dimensional space-time. We generate new two-field models, constructed from distinct but important one-field models, and we solve them with techniques that we introduce in the current work. We illustrate the results with several examples of current interest to high energy physics.Comment: 8 pages, 6 figures; To appear in Adv. High Energy Phy