A test of the power law relationship between gamma-ray burst pulse width ratio and energy expected in fireballs or uniform jets

Recently, under the assumption that the Doppler effect of the relativistically expanding fireball surface is important, Qin et al. showed that in most cases the power law relationship between the pulse width and energy of gamma-ray bursts (GRBs)would exist in a certain energy range. We check this prediction with two GRB samples which contain well identified pulses. A power law anti-correlation between the full pulse width and energy and a power law correlation between the pulse width ratio and energy are seen in the light curves of the majority (around 65%) of bursts of the two samples within the energy range of BATSE, suggesting that these bursts are likely to arise from the emission associated with the shocks occurred on a relativistically expanding fireball surface. For the rest of the bursts, the relationships between these quantities were not predicted previously. We propose to consider other spectral evolutionary patterns or other radiation mechanisms such as a varying synchrotron or Comptonized spectrum to check if the observed relationships for these rest bursts can also be accounted for by the Doppler model. In addition, we find that the upper limits of the width ratio for the two samples do not exceed 0.9, in agrement with what predicted previously by the Doppler model. The plateau/power law/plateau and the peaked features predicted and detected previously by Qin et al. are generally observed, with the exceptions being noticed only in a few cases. According to the distinct values of two power law indices of FWHM and ratio and energy, we divide the bursts into three subsets which are located in different areas of the two indices plane. We suspect that different locations of the two indices might correspond to different mechanisms.Comment: 16 pages, 7 figures, MNRAS accepte

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

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

Two-dimensional structures of ferroelectric domain inversion in LiNbO3 by direct electron beam lithography

We report on the fabrication of domain-reversed structures in LiNbO3 by means of direct electron beam lithography at room temperature without any static bias. The LiNbO3 crystals were chemically etched after the exposure of electron beam and then, the patterns of domain inversion were characterized by atomic force microscopy (AFM). In our experiment, an interesting phenomenon occurred when the electron beam wrote a one-dimensional (1-D) grating on the negative c-face: a two-dimensional (2-D) dotted array was observed on the positive c- face, which is significant for its potential to produce 2-D and three-dimensional photonic crystals. Furthermore, we also obtained 2-D ferroelectric domain inversion in the whole LiNbO3 crystal by writing the 2-D square pattern on the negative c-face. Such a structure may be utilized to fabricate 2-D nonlinear photonic crystal. AFM demonstrates that a 2-D domain-reversed structure has been achieved not only on the negative c-face of the crystal, but also across the whole thickness of the crystal.Comment: 17 pages, 4 figure

Plaquette order and deconfined quantum critical point in the spin-1 bilinear-biquadratic Heisenberg model on the honeycomb lattice

We have precisely determined the ground state phase diagram of the quantum spin-1 bilinear-biquadratic Heisenberg model on the honeycomb lattice using the tensor renormalization group method. We find that the ferromagnetic, ferroquadrupolar, and a large part of the antiferromagnetic phases are stable against quantum fluctuations. However, around the phase where the ground state is antiferroquadrupolar ordered in the classical limit, quantum fluctuations suppress completely all magnetic orders, leading to a plaquette order phase which breaks the lattice symmetry but preserves the spin SU(2) symmetry. On the evidence of our numerical results, the quantum phase transition between the antiferromagnetic phase and the plaquette phase is found to be either a direct second order or a very weak first order transition.Comment: 6 pages, 9 figures, published versio