Modeling The Time Variability of Accreting Compact Sources

We present model light curves for accreting Black Hole Candidates (BHC) based on a recently proposed model for their spectro-temporal properties. According to this model, the observed light curves and aperiodic variability of BHC are due to a series of soft photon injections at random (Poisson) intervals near the compact object and their reprocessing into hard radiation in an extended but non-uniform hot plasma corona surrounding the compact object. We argue that the majority of the timing characteristics of these light curves are due to the stochastic nature of the Comptonization process in the extended corona, whose properties, most notably its radial density dependence, are imprinted in them. We compute the corresponding Power Spectral Densities (PSD), autocorrelation functions, time skewness of the light curves and time lags between the light curves of the sources at different photon energies and compare our results to observation. Our model light curves compare well with observations, providing good fits to their overall morphology, as manifest by the autocorrelation and skewness functions. The lags and PSDs of the model light curves are also in good agreement with those observed (the model can even accommodate the presence of QPOs). Finally, while most of the variability power resides at time scales \gsim a few seconds, at the same time, the model allows also for shots of a few msec in duration, in accordance with observation. We suggest that refinements of this type of model along with spectral and phase lag information can be used to probe the structure of this class of high energy sources.Comment: 23 pages Latex, 15 encapsulated postscript figures, to appear in the Astrophysical Journa

Near-Optimal Distributed Approximation of Minimum-Weight Connected Dominating Set

This paper presents a near-optimal distributed approximation algorithm for the minimum-weight connected dominating set (MCDS) problem. The presented algorithm finds an $O(\log n)$ approximation in $\tilde{O}(D+\sqrt{n})$ rounds, where $D$ is the network diameter and $n$ is the number of nodes. MCDS is a classical NP-hard problem and the achieved approximation factor $O(\log n)$ is known to be optimal up to a constant factor, unless P=NP. Furthermore, the $\tilde{O}(D+\sqrt{n})$ round complexity is known to be optimal modulo logarithmic factors (for any approximation), following [Das Sarma et al.---STOC'11].Comment: An extended abstract version of this result appears in the proceedings of 41st International Colloquium on Automata, Languages, and Programming (ICALP 2014

Magnetic properties of a novel Pr Fe Ti phase

In a systematic study of the (Pr1−xTix)Fe5 alloy series, the (Pr0.65Ti0.35)Fe5 alloy has been found to have a dominant phase with either the rhombohedral Th2Zn17 structure or the newly discovered Nd2(Fe,Ti)19 (S. J. Collocott, R. K. Day, J. B. Dunlop, and R. L. Davis, in Proceedings of the Seventh International Symposium on Magnetic Anisotropy and Coercivity in R‐T Alloys, Canberra, July 1992, p. 437) structure, depending on the annealing procedure. Powder‐x‐ray‐diffraction patterns and scanning electron microscopy show that the sample annealed at a temperature of 850 °C followed by 1000 °C has the 2:17 structure whereas annealing at 1000 °C directly leads to the new 2:19 structure. Energy‐dispersive x‐ray analysis yields Pr:Fe:Ti ratios of 10.7:86.2:3.1 for the Pr2(Fe,Ti)17 phase and 9.2:85.9:4.9 for the Pr2(Fe,Ti)19 phase. 57 Fe Mössbauer spectroscopy (at 295 K) gives values for the average 57 Fe hyperfine field of 15.7 T for the 2:17 phase and 17.5 T for the 2:19 phase, respectively

Probing the Structure of Accreting Compact Sources Through X-Ray Time Lags and Spectra

We exhibit, by compiling all data sets we can acquire, that the Fourier frequency dependent hard X-ray lags, first observed in the analysis of aperiodic variability of the light curves of the black hole candidate Cygnus X-1, appear to be a property shared by several other accreting black hole candidate sources and also by the different spectral states of this source. We then present both analytic and numerical models of these time lags resulting by the process of Comptonization in a variety of hot electron configurations. We argue that under the assumption that the observed spectra are due to Comptonization, the dependence of the lags on the Fourier period provides a means for mapping the spatial density profile of the hot electron plasma, while the period at which the lags eventually level--off provides an estimate of the size of the scattering cloud. We further examine the influence of the location and spatial extent of the soft photon source on the form of the resulting lags for a variety of configurations; we conclude that the study of the X-ray hard lags can provide clues about these parameters of the Comptonization process too. Fits of the existing data with our models indicate that the size of the Comptonizing clouds are quite large in extent ($\sim$ 1 light second) with inferred radial density profiles which are in many instances inconsistent with those of the standard dynamical models, while the extent of the source of soft photons appears to be much smaller than those of the hot electrons by roughly two orders of magnitude and its location consistent with the center of the hot electron corona.Comment: 20 pages Latex, 11 postscript figures, to appear in the Astrophysical Journal, Vol 512, Feb 20 issu

The Tensor Current Divergence Equation in U(1) Gauge Theories is Free of Anomalies

The possible anomaly of the tensor current divergence equation in U(1) gauge theories is calculated by means of perturbative method. It is found that the tensor current divergence equation is free of anomalies.Comment: Revtex4, 7 pages, 2 figure

Relative entropy of entanglement of a kind of two qubit entangled states

We in this paper strictly prove that some block diagonalizable two qubit entangled state with six none zero elements reaches its quantum relative entropy entanglement by the a separable state having the same matrix structure. The entangled state comprises local filtering result state as a special case.Comment: 5 page

Spin and orbital angular momentum in gauge theories (II): QCD and nucleon spin structure

Parallel to the construction of gauge invariant spin and orbital angular momentum for QED in paper (I) of this series, we present here an analogous but non-trivial solution for QCD. Explicitly gauge invariant spin and orbital angular momentum operators of quarks and gluons are obtained. This was previously thought to be an impossible task, and opens a more promising avenue towards the understanding of the nucleon spin structure.Comment: 3 pages, no figure; presented by F. Wang at NSTAR200

Improved lattice QCD with quarks: the 2 dimensional case

QCD in two dimensions is investigated using the improved fermionic lattice Hamiltonian proposed by Luo, Chen, Xu, and Jiang. We show that the improved theory leads to a significant reduction of the finite lattice spacing errors. The quark condensate and the mass of lightest quark and anti-quark bound state in the strong coupling phase (different from t'Hooft phase) are computed. We find agreement between our results and the analytical ones in the continuum.Comment: LaTeX file (including text + 10 figures

On Gauge Theory and Topological String in Nekrasov-Shatashvili Limit

We study the Nekrasov-Shatashvili limit of the N=2 supersymmetric gauge theory and topological string theory on certain local toric Calabi-Yau manifolds. In this limit one of the two deformation parameters \epsilon_{1,2} of the Omega background is set to zero and we study the perturbative expansion of the topological amplitudes around the remaining parameter. We derive differential equations from Seiberg-Witten curves and mirror geometries, which determine the higher genus topological amplitudes up to a constant. We show that the higher genus formulae previously obtained from holomorphic anomaly equations and boundary conditions satisfy these differential equations. We also provide a derivation of the holomorphic anomaly equations in the Nekrasov-Shatashvili limit from these differential equations.Comment: 41 pages, no figure. v2: references adde