On the singular values and eigenvalues of the Fox–Li and related operators

The Fox–Li operator is a convolution operator over a finite interval with a special highly oscillatory kernel. It plays an important role in laser engineering. However, the mathematical analysis of its spectrum is still rather incomplete. In this expository paper we survey part of the state of the art, and our emphasis is on showing how standard Wiener–Hopf theory can be used to obtain insight into the behaviour of the singular values of the Fox–Li operator. In addition, several approximations to the spectrum of the Fox–Li operator are discussed and results on the singular values and eigenvalues of certain related operators are derived

Crystal structure of Schmallenberg orthobunyavirus nucleoprotein-RNA complex reveals a novel RNA sequestration mechanism

Schmallenberg virus (SBV) is a newly emerged orthobunyavirus (family Bunyaviridae) that has caused severe disease in the offspring of farm animals across Europe. Like all orthobunyaviruses, SBV contains a tripartite negative-sense RNA genome that is encapsidated by the viral nucleocapsid (N) protein in the form of a ribonucleoprotein complex (RNP). We recently reported the three-dimensional structure of SBV N that revealed a novel fold. Here we report the crystal structure of the SBV N protein in complex with a 42-nt-long RNA to 2.16 Å resolution. The complex comprises a tetramer of N that encapsidates the RNA as a cross-shape inside the protein ring structure, with each protomer bound to 11 ribonucleotides. Eight bases are bound in the positively charged cleft between the N- and C-terminal domains of N, and three bases are shielded by the extended N-terminal arm. SBV N appears to sequester RNA using a different mechanism compared with the nucleoproteins of other negative-sense RNA viruses. Furthermore, the structure suggests that RNA binding results in conformational changes of some residues in the RNA-binding cleft and the N- and C-terminal arms. Our results provide new insights into the novel mechanism of RNA encapsidation by orthobunyaviruses

Comptonization signatures in the rapid aperiodic variability of Galactic black-hole candidates

We investigate the effect of inverse-Compton scattering of flares of soft radiation in different geometries of a hot, Comptonizing region and a colder accretion disk around a solar-mass black hole. The photon-energy dependent light curves, their Fourier transforms, power spectra and Fourier-period dependent time lags of hard photons with respect to softer photons are discussed. On the basis of a comparison with existing data we find arguments against Comptonization of external soft radiation as well as Comptonization in a homogeneous medium as dominant mechanisms for the rapid aperiodic variability in Galactic black-hole candidates. Possible further observational tests for the influence of Comptonization on the rapid aperiodic variability of Galactic black-hole candidates are suggested.Comment: 32 pages, including 10 figures and 2 tables; uses epsf.sty, rotate.sty; submitted to Ap

Field-induced structure transformation in electrorheological solids

We have computed the local electric field in a body-centered tetragonal (BCT) lattice of point dipoles via the Ewald-Kornfeld formulation, in an attempt to examine the effects of a structure transformation on the local field strength. For the ground state of an electrorheological solid of hard spheres, we identified a novel structure transformation from the BCT to the face-centered cubic (FCC) lattices by changing the uniaxial lattice constant c under the hard sphere constraint. In contrast to the previous results, the local field exhibits a non-monotonic transition from BCT to FCC. As c increases from the BCT ground state, the local field initially decreases rapidly towards the isotropic value at the body-centered cubic lattice, decreases further, reaching a minimum value and increases, passing through the isotropic value again at an intermediate lattice, reaches a maximum value and finally decreases to the FCC value. An experimental realization of the structure transformation is suggested. Moreover, the change in the local field can lead to a generalized Clausius-Mossotti equation for the BCT lattices.Comment: Submitted to Phys. Rev.

The Energy Dependence of the Aperiodic Variability for Cygnus X-1, GX 339-4, GRS 1758-258, & 1E 1740.7-2942

Using the data from the Rossi X-ray Timing Explorer (RXTE), we report the different energy dependence of the variability of the four persistent hard X-ray sources in the low-hard state: Cygnus X-1, GX 339-4, GRS 1758-258 and 1E 1740.7-2942. Cygnus X-1 is found to have a flatter power density spectrum (PDS) shape at higher energies. The other three sources have energy independent PDS shapes. The energy dependence of the overall variability (the integrated rms amplitude) varies from source to source and from observation to observation. 1E~1740.7-2942, for example, has a variability generally increasing with energy while GX 339-4 has a decreasing variability. A general trend is found in the four sources that the integrated rms amplitude anti-correlates with the X-ray flux. We compare these distinct energy dependent behaviors with several emission models. None of the models can fully explain all the features that we have found.Comment: 18 pages, 6 figures. Accepted for publication in Ap

Effects of geometric anisotropy on local field distribution: Ewald-Kornfeld formulation

We have applied the Ewald-Kornfeld formulation to a tetragonal lattice of point dipoles, in an attempt to examine the effects of geometric anisotropy on the local field distribution. The various problems encountered in the computation of the conditionally convergent summation of the near field are addressed and the methods of overcoming them are discussed. The results show that the geometric anisotropy has a significant impact on the local field distribution. The change in the local field can lead to a generalized Clausius-Mossotti equation for the anisotropic case.Comment: Accepted for publications, Journal of Physics: Condensed Matte

Monte-Carlo simulations of thermal/nonthermal radiation from a neutron-star magnetospheric accretion shell

We discuss the space-and-time-dependent Monte Carlo code we have developed to simulate the relativistic radiation output from compact astrophysical objects, coupled to a Fokker-Planck code to determine the self-consistent lepton populations. We have applied this code to model the emission from a magnetized neutron star accretion shell near the Alfven radius, reprocessing the radiation from the neutron sar surface. We explore the parameter space defined by the accretion rate, stellar surface field and the level of wave turbulence in the shell. Our results are relevant to the emission from atoll sources, soft-X-ray transient X-ray binaries containing weakly magnetized neutron stars, and to recently suggested models of accretion-powered emission from anomalous X-ray pulsars.Comment: 24 pages, including 7 figures; uses epsf.sty. final version, accepted for publication in ApJ. Extended introduction and discussio

Multiwavelength Observations of GX 339-4 in 1996. II. Rapid X-ray Variability

As part of our multiwavelength campaign of GX 339-4 observations in 1996 we present the rapid X-ray variability observed July 26 using the RXTE when the source was in a hard state (= soft X-ray low state). We found that the source was extremely variable, with many bright flares. The flares have relatively symmetric time profiles. There are a few time intervals where the flux rises steadily and then drops suddenly, sometimes to a level lower than the average before the increase. Hardness ratios showed that the source was slightly softer when the flux was brighter. The power density spectra (PDS) were also complicated and we found that broken power laws do not provide adequate fits to any of them. Instead a pair of zero-centered Lorentzians gives a good general description of the shape of the PDS. We found several quasi-periodic oscillations (QPO), including some that are harmonically spaced with the most stable frequency at 0.35 Hz. While the overall rms variability of the source was close to being constant throughout the observation (29% integrating between 0.01 and 50 Hz), there is a small but significant change in the PDS shape with time. More importantly, we show that the soft 2-5 keV band is more variable than the harder 5-10 and 10-40 keV bands, which is unusual for this source and for other black hole candidates. Cross correlation functions (CCF) between these bands show that the light curve for the 10-40 keV band lags that of the 2-5 keV band by 5 msec.Comment: Submitted to Astrophysical Journal. 20 pages. 8 figure