Reprocessed emission from warped accretion discs induced by the Bardeen-Petterson effect

The broad Balmer emission-line profiles resulting from the reprocessing of UV/X-ray radiation from a warped accretion disc induced by the Bardeen-Petterson effect are studied. We adopt a thin warped disc geometry and a central ring-like illuminating source in our model. We compute the steady-state shape of the warped disc numerically, and then use it in the calculation of the line profile. We find that, from the outer radius to the inner radius of the disc, the warp is twisted by an angle of $\sim\pi$ before being flattened efficiently into the equatorial plane. The profiles obtained depend weakly on the illuminating source radius in the range from $3r_{g}$ to $10r_g$, but depend strongly on this radius when it approaches the marginally stable orbit of an extreme Kerr black hole. Double- or triplet-peaked line profiles are present in most cases when the illuminating source radius is low. The triplet-peaked line profiles observed from the Sloan Digital Sky Survey may be a {"}signature" of a warped disc.Comment: 8 pages, 6 figures, typos corrected, matches version to appear in MNRA

On the pinning strategy of complex networks

In pinning control of complex networks, a tacit believing is that the system dynamics will be better controlled by pinning the large-degree nodes than the small-degree ones. Here, by changing the number of pinned nodes, we find that, when a significant fraction of the network nodes are pinned, pinning the small-degree nodes could generally have a higher performance than pinning the large-degree nodes. We demonstrate this interesting phenomenon on a variety of complex networks, and analyze the underlying mechanisms by the model of star networks. By changing the network properties, we also find that, comparing to densely connected homogeneous networks, the advantage of the small-degree pinning strategy is more distinct in sparsely connected heterogenous networks