The Ultraviolet flash accompanying GRBs from neutron-rich internal shocks

In the neutron-rich internal shocks model for Gamma-ray Burts (GRBs), the Lorentz factors (LFs) of ions shells are variable, so are the LFs of accompanying neutron shells. For slow neutron shells with a typical LF tens, the typical beta-decay radius reads R_{\beta,s} several 10^{14} cm, which is much larger than the typical internal shocks radius 10^{13} cm, so their impact on the internal shocks may be unimportant. However, as GRBs last long enough (T_{90}>20(1+z) s), one earlier but slower ejected neutron shell will be swept successively by later ejected ion shells in the range 10^{13}-10^{15} cm, where slow neutrons have decayed significantly. We show in this work that ion shells interacting with the beta-decay products of slow neutron shells can power a ultraviolet (UV) flash bright to 12th magnitude during the prompt gamma-ray emission phase or slightly delayed, which can be detected by the upcoming Satellite SWIFT in the near future.Comment: 6 pages (2 eps figures), accepted for publication in ApJ

Counting integral points in certain homogeneous spaces

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Diverse Temporal Properties of GRB Afterglow

The detection of delayed X-ray, optical and radio emission, "afterglow", associated with $\gamma$-ray bursts (GRBs) is consistent with fireball models, where the emission are produced by relativistic expanding blast wave, driven by expanding fireball at cosmogical distances. The emission mechanisms of GRB afterglow have been discussed by many authors and synchrotron radiation is believed to be the main mechanism. The observations show that the optical light curves of two observed gamma-ray bursts, GRB970228 and GRB GRB970508, can be described by a simple power law, which seems to support the synchrotron radiation explanation. However, here we shall show that under some circumstances, the inverse Compton scattering (ICS) may play an important role in emission spectrum and this may influence the temporal properties of GRB afterglow. We expect that the light curves of GRB afterglow may consist of multi-components, which depends on the fireball parameters.Comment: Latex, no figures, minor correctio

Laplacian flow for closed G_2 structures: Shi-type estimates, uniqueness and compactness

We develop foundational theory for the Laplacian flow for closed G_2 structures which will be essential for future study. (1). We prove Shi-type derivative estimates for the Riemann curvature tensor Rm and torsion tensor T along the flow, i.e. that a bound on $\Lambda(x,t)=\left(|\nabla T(x,t)|_{g(t)}^2+|Rm(x,t)|_{g(t)}^2\right)^{\frac 12}$ will imply bounds on all covariant derivatives of Rm and T. (2). We show that $\Lambda(x,t)$ will blow up at a finite-time singularity, so the flow will exist as long as $\Lambda(x,t)$ remains bounded. (3). We give a new proof of forward uniqueness and prove backward uniqueness of the flow, and give some applications. (4). We prove a compactness theorem for the flow and use it to strengthen our long time existence result from (2). (5). Finally, we study compact soliton solutions of the Laplacian flow.Comment: 59 pages, v2: minor corrections and additions, accepted version for GAF