Large-time Behavior of Solutions to the Inflow Problem of Full Compressible Navier-Stokes Equations

Large-time behavior of solutions to the inflow problem of full compressible Navier-Stokes equations is investigated on the half line $R^+ =(0,+\infty)$. The wave structure which contains four waves: the transonic(or degenerate) boundary layer solution, 1-rarefaction wave, viscous 2-contact wave and 3-rarefaction wave to the inflow problem is described and the asymptotic stability of the superposition of the above four wave patterns to the inflow problem of full compressible Navier-Stokes equations is proven under some smallness conditions. The proof is given by the elementary energy analysis based on the underlying wave structure. The main points in the proof are the degeneracies of the transonic boundary layer solution and the wave interactions in the superposition wave.Comment: 27 page

Two types of softening detected in X-ray afterglows of Swift bursts: internal and external shock origins?

The softening process observed in the steep decay phase of early X-ray afterglows of Swift bursts has remained a puzzle since its discovery. The softening process can also be observed in the later phase of the bursts and its cause has also been unknown. Recently, it was suggested that, influenced by the curvature effect, emission from high latitudes would shift the Band function spectrum from higher energy band to lower band, and this would give rise to the observed softening process accompanied by a steep decay of the flux density. The curvature effect scenario predicts that the terminating time of the softening process would be correlated with the duration of the process. In this paper, based on the data from the UNLV GRB group web-site, we found an obvious correlation between the two quantities. In addition, we found that the softening process can be divided into two classes: the early type softening ($t_{s,max}\leq "4000"s$) and the late type softening ($t_{s,max} > "4000"s$). The two types of softening show different behaviors in the duration vs. terminating time plot. In the relation between the variation rates of the flux density and spectral index during the softening process, a discrepancy between the two types of softening is also observed. According to their time scales and the discrepancy between them, we propose that the two types are of different origins: the early type is of internal shock origin and the late type is of external shock origin. The early softening is referred to the steep decay just following the prompt emission, whereas the late decay typically conceives the transition from flat decay to late afterglow decay. We suspect that there might be a great difference of the Lorentz factor in two classes which is responsible for the observed discrepancy.Comment: 20 pages, 5 figures, 2 tables, Accepted for Publication to Journal of Cosmology and Astroparticle Physics (JCAP

Effect of disorder with long-range correlation on transport in graphene nanoribbon

Transport in disordered armchair graphene nanoribbons (AGR) with long-range correlation between quantum wire contact is investigated by transfer matrix combined with Landauer's formula. Metal-insulator transition is induced by disorder in neutral AGR. Thereinto, the conductance is one conductance quantum for metallic phase and exponentially decays otherwise when the length of AGR is infinity and far longer than its width. Similar to the case of long-range disorder, the conductance of neutral AGR first increases and then decreases while the conductance of doped AGR monotonically decreases, as the disorder strength increases. In the presence of strong disorder, the conductivity depends monotonically and non-monotonically on the aspect ratio for heavily doped and slightly doped AGR respectively.Comment: 6 pages, 8 figures; J. Phys: Condensed Matter (May 2012