Prompt Optical Emission from Gamma-ray Bursts with Non-single Timescale Variability of Central Engine Activities

The complete high-resolution lightcurves of Swift GRB 080319B present an opportunity for detailed temporal analysis of the prompt optical emission. With a two-component distribution of initial Lorentz factors, we simulate the dynamical process of the ejected shells from the central engine in the framework of the internal shock model. The emitted radiation are decomposed into different frequency ranges for a temporal correlation analysis between the lightcurves in different energy bands. The resulting prompt optical and gamma-ray emission show similar temporal profiles, both as a superposition of a slow variability component and a fast variability component, except that the gamma-ray lightcurve is much more variable than its optical counterpart. The variability features in the simulated lightcurves and the strong correlation with a time lag between the optical and gamma-ray emission are in good agreement with the observations of GRB 080319B. Our simulations suggest that the variations seen in the lightcurves stem from the temporal structure of the shells injected from the central engine of gamma-ray bursts. The future high temporal resolution observations of prompt optical emission from GRBs, e.g., by UFFO-Pathfinder and SVOM-GWAC, provide a useful tool to investigate the central engine activity.Comment: 12 pages, 6 figures, RAA accepte

On Regular Courant Algebroids

For any regular Courant algebroid, we construct a characteristic class a la Chern-Weil. This intrinsic invariant of the Courant algebroid is a degree-3 class in its naive cohomology. When the Courant algebroid is exact, it reduces to the Severa class (in H^3_{DR}(M)). On the other hand, when the Courant algebroid is a quadratic Lie algebra g, it coincides with the class of the Cartan 3-form (in H^3(g)). We also give a complete classification of regular Courant algebroids and discuss its relation to the characteristic class.Comment: Section 3.3 and references added; An error about classification is correcte

A Hopf algebra associated to a Lie pair

The quotient $L/A[-1]$ of a pair $A\hookrightarrow L$ of Lie algebroids is a Lie algebra object in the derived category $D^b(\mathscr{A})$ of the category $\mathscr{A}$ of left $\mathcal{U}(A)$-modules, the Atiyah class $\alpha_{L/A}$ being its Lie bracket. In this note, we describe the universal enveloping algebra of the Lie algebra object $L/A[-1]$ and we prove that it is a Hopf algebra object in $D^b(\mathscr{A})$.Comment: 6 page

Weak Lie 2-bialgebra

We introduce the notion of weak Lie 2-bialgebra. Roughly, a weak Lie 2-bialgebra is a pair of compatible 2-term $L_\infty$-algebra structures on a vector space and its dual. The compatibility condition is described in terms of the big bracket. We prove that (strict) Lie 2-bialgebras are in one-one correspondence with crossed modules of Lie bialgebras.Comment: 14 pages, LaTeX; typoes removed; references modifie

Charged States and Band-Gap Narrowing in Codoped ZnO Nanowires for Enhanced Photoelectrochemical Responses

By means of first-principles calculations within the density functional theory, we study the structural and optical properties of codoped ZnO nanowires and compare them with those of the bulk and film. It is disclosed that the low negatively charged ground states of nitrogen related defects play a key role in the optical absorption spectrum tail that narrows the band-gap and enhances the photoelectrochemical response significantly. A strategy of uncompensated N, P and Ga codoping in ZnO nanowires is proposed to produce a red-shift of the optical absorption spectra further than the exclusive N doping and to get a proper formation energy with a high defect concentration and a suppressed recombination rate. In this way, the absorption of the visible light can be improved and the photocurrent can be raised. These observations are consistent with the existing experiments, which will be helpful to improve the photoelectrochemical responses for the wide-band-gap semiconductors especially in water splitting applications.Comment: 10 pages, 7 figure