Interdependent networks with correlated degrees of mutually dependent nodes

We study a problem of failure of two interdependent networks in the case of correlated degrees of mutually dependent nodes. We assume that both networks (A and B) have the same number of nodes $N$ connected by the bidirectional dependency links establishing a one-to-one correspondence between the nodes of the two networks in a such a way that the mutually dependent nodes have the same number of connectivity links, i.e. their degrees coincide. This implies that both networks have the same degree distribution $P(k)$. We call such networks correspondently coupled networks (CCN). We assume that the nodes in each network are randomly connected. We define the mutually connected clusters and the mutual giant component as in earlier works on randomly coupled interdependent networks and assume that only the nodes which belong to the mutual giant component remain functional. We assume that initially a $1-p$ fraction of nodes are randomly removed due to an attack or failure and find analytically, for an arbitrary $P(k)$, the fraction of nodes $\mu(p)$ which belong to the mutual giant component. We find that the system undergoes a percolation transition at certain fraction $p=p_c$ which is always smaller than the $p_c$ for randomly coupled networks with the same $P(k)$. We also find that the system undergoes a first order transition at $p_c>0$ if $P(k)$ has a finite second moment. For the case of scale free networks with $2<\lambda \leq 3$, the transition becomes a second order transition. Moreover, if $\lambda<3$ we find $p_c=0$ as in percolation of a single network. For $\lambda=3$ we find an exact analytical expression for $p_c>0$. Finally, we find that the robustness of CCN increases with the broadness of their degree distribution.Comment: 18 pages, 3 figure

Electron-Ion Recombination Rate Coefficients and Photoionization Cross Sections for Astrophysically Abundant Elements. V. Relativistic calculations for Fe XXIV and Fe XXV for X-ray modeling

Photoionization and recombination cross sections and rate coefficients are calculated for Li-like Fe XXIV and He-like Fe XXV using the Breit-Pauli R-matrix (BPRM) method. A complete set of total and level-specific parameters is obtained to enable X-ray photoionization and spectral modeling. The ab initio calculations for the unified (e + ion) recombination rate coefficients include both the non-resonant and the resonant recombination (radiative and di-electronic recombination, RR and DR, respectively) for (e + Fe XXV) -> Fe XXIV and (e + Fe XXVI) -> Fe XXV. The level specific rates are computed for all fine structure levels up to n = 10, enabling accurate computation of recombination-cascade matrices and effective rates for the X-ray lines. The total recombination rate coefficients for both Fe XXIV and Fe XXV differ considerably, by several factors, from the sum of RR and DR rates currently used to compute ionization fractions in astrophysical models. As the photoionization/recombination calculations are carried out using an identical eigenfunction expansion, the cross sections for both processes are theoretically self-consistent; the overall uncertainty is estimated to be about 10-20%. All data for Fe XXIV and Fe XXV (and also for H-like Fe XXVI, included for completeness) are available electronically.Comment: 31 pages, 10fug

Variability of the X-ray P Cygni Line Profiles from Circinus X-1 Near Zero Phase

The luminous X-ray binary Circinus X-1 has been observed twice near zero orbital phase using the High-Energy Transmission Grating Spectrometer (HETGS) onboard Chandra. The source was in a high-flux state during a flare for the first observation, and it was in a low-flux state during a dip for the second. Spectra from both flux states show clear P Cygni lines, predominantly from H-like and He-like ion species. These indicate the presence of a high-velocity outflow from the Cir X-1 system which we interpret as an equatorial accretion-disk wind, and from the blueshifted resonance absorption lines we determine outflow velocities of 200 - 1900 km/s with no clear velocity differences between the two flux states. The line strengths and profiles, however, are strongly variable both between the two observations as well as within the individual observations. We characterize this variability and suggest that it is due to both changes in the amount of absorbing material along the line of sight as well as changes in the ionization level of the wind. We also refine constraints on the accretion-disk wind model using improved plasma diagnostics such as the He-like Mg XI triplet, and we consider the possibility that the X-ray absorption features seen from superluminal jet sources can generally be explained via high-velocity outflows.Comment: 12 pages, 8 figures, accepted by ApJ (Main

Three-Dimensional FDTD Simulation of Biomaterial Exposure to Electromagnetic Nanopulses

Ultra-wideband (UWB) electromagnetic pulses of nanosecond duration, or nanopulses, have been recently approved by the Federal Communications Commission for a number of various applications. They are also being explored for applications in biotechnology and medicine. The simulation of the propagation of a nanopulse through biological matter, previously performed using a two-dimensional finite difference-time domain method (FDTD), has been extended here into a full three-dimensional computation. To account for the UWB frequency range, a geometrical resolution of the exposed sample was $0.25 mm$, and the dielectric properties of biological matter were accurately described in terms of the Debye model. The results obtained from three-dimensional computation support the previously obtained results: the electromagnetic field inside a biological tissue depends on the incident pulse rise time and width, with increased importance of the rise time as the conductivity increases; no thermal effects are possible for the low pulse repetition rates, supported by recent experiments. New results show that the dielectric sample exposed to nanopulses behaves as a dielectric resonator. For a sample in a cuvette, we obtained the dominant resonant frequency and the $Q$-factor of the resonator.Comment: 15 pages, 8 figure

Local and Global Distinguishability in Quantum Interferometry

A statistical distinguishability based on relative entropy characterises the fitness of quantum states for phase estimation. This criterion is employed in the context of a Mach-Zehnder interferometer and used to interpolate between two regimes, of local and global phase distinguishability. The scaling of distinguishability in these regimes with photon number is explored for various quantum states. It emerges that local distinguishability is dependent on a discrepancy between quantum and classical rotational energy. Our analysis demonstrates that the Heisenberg limit is the true upper limit for local phase sensitivity. Only the `NOON' states share this bound, but other states exhibit a better trade-off when comparing local and global phase regimes.Comment: 4 pages, in submission, minor revision

Effective action approach to strongly correlated fermion systems

We construct a new functional for the single particle Green's function, which is a variant of the standard Baym Kadanoff functional. The stability of the stationary solutions to the new functional is directly related to aspects of the irreducible particle hole interaction through the Bethe Salpeter equation. A startling aspect of this functional is that it allows a simple and rigorous derivation of both the standard and extended dynamical mean field (DMFT) equations as stationary conditions. Though the DMFT equations were formerly obtained only in the limit of infinite lattice coordination, the new functional described in the work, presents a way of directly extending DMFT to finite dimensional systems, both on a lattice and in a continuum. Instabilities of the stationary solution at the bifurcation point of the functional, signal the appearance of a zero mode at the Mott transition which then couples t o physical quantities resulting in divergences at the transition.Comment: 9 page

High-resolution X-ray Spectra Of The Symbiotic Star SS73 17

SS73 17 was an innocuous Mira-type symbiotic star until Integral and Swift discovered its bright hard X-ray emission, adding it to the small class of "hard X-ray emitting symbiotics." Suzaku observations in 2006 then showed it emits three bright iron lines as well, with little to no emission in the 0.3-2 keV bandpass. We present here followup observations with the Chandra HETG and Suzaku that confirm the earlier detection of strong emission lines of Fe Kalpha fluorescence, Fe XXV and Fe XXVI but also show significantly more soft X-ray emission. The high resolution spectrum also shows emission lines of other highly ionized ions as Si XIV and possibly S XVI. In addition, a reanalysis of the 2006 Suzaku data using the latest calibration shows that the hard (15-50 keV) X-ray emission is brighter than previously thought and remains constant in both the 2006 and 2008 data. The G ratio calculated from the Fe XXV lines shows that these lines are thermal, not photoionized, in origin. With the exception of the hard X-ray emission, the spectra from both epochs can be fit using thermal radiation assuming a differential emission measure based on a cooling flow model combined with a full and partial absorber. We show that acceptable fits can be obtained for all the data in the 1-10 keV band varying only the partial absorber. Based on the temperature and accretion rate, the thermal emission appears to be arising from the boundary layer between the accreting white dwarf and the accretion disk.Comment: 7 pages, 5 figures. Accepted by the Astrophysical Journa