A Note on the Injection Distance

Koetter and Kschischang showed in [R. Koetter and F.R. Kschischang, "Coding for Errors and Erasures in Random Network Coding," IEEE Trans. Inform. Theory, {54(8), 2008] that the network coding counterpart of Gabidulin codes performs asymptotically optimal with respect to the subspace distance. Recently, Silva and Kschischang introduced in [D. Silva and F.R. Kschischang, "On Metrics for Error Correction in Network Coding," To appear in IEEE Trans. Inform. Theory, ArXiv: 0805.3824v4[cs.IT], 2009] the injection distance to give a detailed picture of what happens in noncoherent network coding. We show that the above codes are also asymptotically optimal with respect to this distance

On the possibility of sub-TeV Gamma-ray emission from Cyg X-3

The compact X-ray binary system Cyg X-3 has been recently discovered as a source of GeV gamma-rays by the AGILE and the {\it Fermi} satellites. It shows emission features in the GeV gamma-rays similar to other gamma-ray binaries which were also observed in the TeV gamma-rays (LS 5039 and LSI +61 303). The question appears whether Cyg X-3 can be also detected in the TeV gamma-rays by the Cherenkov telescopes. Here we discuss this problem in detail based on the anisotropic inverse Compton (IC) e-p pair cascade model successfully applied to TeV gamma-ray binaries. We calculate the gamma-ray light curves and gamma-ray spectra expected from the cascade process occurring inside the Cyg X-3 binary system. It is found that the gamma-ray light curves at GeV energies can be consistent with the gamma-ray light curve observed by the Fermi for reasonable parameters of the orbit of the injection source of relativistic electrons. Moreover, we show that in such a model the sub-TeV gamma-ray emission (above 100 GeV) is expected to be below sensitivities of the present Cherenkov telescopes assuming that electrons are accelerated in Cyg X-3 to TeV energies. The next stage Cherenkov telescopes (MAGIC II, HESS II) should have the energy threshold in the range 20-30 GeV, in order to have a chance to detect the signal from Cyg X-3. Otherwise, the positive detection of gamma-rays at energies above a few tens of GeV requires a telescope with the sensitivity of ~0.1% of Crab Units. We conclude that detection of sub-TeV gamma-rays from Cyg X-3 by on-ground telescopes has to probably wait for construction of the Cherenkov Telescope Array (CTA).Comment: 13 pages, 8 figures, small changes in the text and discussion extended, accepted to MNRA

Charge carrier injection into insulating media: single-particle versus mean-field approach

Self-consistent, mean-field description of charge injection into a dielectric medium is modified to account for discreteness of charge carriers. The improved scheme includes both the Schottky barrier lowering due to the individual image charge and the barrier change due to the field penetration into the injecting electrode that ensures validity of the model at both high and low injection rates including the barrier dominated and the space-charge dominated regimes. Comparison of the theory with experiment on an unipolar ITO/PPV/Au-device is presented.Comment: 32 pages, 9 figures; revised version accepted to PR

A Sufficient Condition for Power Flow Insolvability with Applications to Voltage Stability Margins

For the nonlinear power flow problem specified with standard PQ, PV, and slack bus equality constraints, we present a sufficient condition under which the specified set of nonlinear algebraic equations has no solution. This sufficient condition is constructed in a framework of an associated feasible, convex optimization problem. The objective employed in this optimization problem yields a measure of distance (in a parameter set) to the power flow solution boundary. In practical terms, this distance is closely related to quantities that previous authors have proposed as voltage stability margins. A typical margin is expressed in terms of the parameters of system loading (injected powers); here we additionally introduce a new margin in terms of the parameters of regulated bus voltages.Comment: 12 pages, 7 figure

Optical depths for gamma-rays in the radiation field of a star heated by external X-ray source in LMXBs: Application to Her X-1 and Sco X-1

The surface of a low mass star inside a compact low mass X-ray binary system (LMXB) can be heated by the external X-ray source which may appear due to the accretion process onto a companion compact object (a neutron star or a black hole). As a result, the surface temperature of the star can become significantly higher than it is in the normal state resulting from thermonuclear burning. We wonder whether high energy electrons and gamma-rays, injected within the binary system, can efficiently interact with this enhanced radiation field. To decide this, we calculate the optical depths for the gamma-ray photons in the radiation field of such irradiated star as a function of the phase of the binary system. Based on these calculations, we conclude that compact low mass X-ray binary systems may also become sources of high energy gamma-rays since conditions for interaction of electrons and gamma-rays are quite similar to these ones observed within the high mass TeV gamma-ray binaries such as LS 5039 and LSI 303 +61. However, due to differences in the soft radiation field, the expected gamma-ray light curves can significantly differ between low mass and high mass X-ray binaries. As an example, we apply such calculations to two well known LMXBs: Her X-1 and Sco X-1. It is concluded that electrons accelerated to high energies inside these binaries should find enough soft photon target from the companion star for efficient gamma-ray production.Comment: 10 pages, 8 figures, accepted to A&

Ultra-High Energy Heavy Nuclei Propagation in Extragalactic Magnetic Fields

We extend existing work on the propagation of ultra-high energy cosmic rays in extragalactic magnetic fields to a possible component of heavy nuclei, taking into account photodisintegration, pion production, and creation of e+e- pairs. We focus on the influence of the magnetic field on the spectrum and chemical composition of observed ultra-high energy cosmic rays. We apply our simulations to the scenarios proposed by Anchordoqui et al, in which Iron nuclei are accelerated in nearby starburst galaxies, and show that it is in marginal agreement with the data. We also show that it is highly unlikely to detect He nuclei from M87 at the highest energies observed $\sim3 10^{20}$eV as required for the scenario of Ahn et al. in which the highest energy cosmic rays originate from M87 and are deflected in a Parker spiral Galactic magnetic field.Comment: 10 pages, 16 figures, submitted to PR