Gamma-Ray Burst Afterglows: Effects of Radiative Corrections and Nonuniformity of the Surrounding Medium

The afterglow of a gamma-ray burst (GRB) is commonly thought to be due to continuous deceleration of a relativistically expanding fireball in the surrounding medium. Assuming that the expansion of the fireball is adiabatic and that the density of the medium is a power-law function of shock radius, viz., $n_{ext}\propto R^{-k}$, we analytically study the effects of the first-order radiative correction and the nonuniformity of the medium on a GRB afterglow. We first derive a new relation among the observed time, the shock radius and the fireball's Lorentz factor: $t_\oplus=R/4(4-k)\gamma^2c$, and also derive a new relation among the comoving time, the shock radius and the fireball's Lorentz factor: $t_{co}=2R/(5-k)\gamma c$. We next study the evolution of the fireball by using the analytic solution of Blandford and McKee (1976). The radiation losses may not significantly influence this evolution. We further derive new scaling laws both between the X-ray flux and observed time and between the optical flux and observed time. We use these scaling laws to discuss the afterglows of GRB 970228 and GRB 970616, and find that if the spectral index of the electron distribution is $p=2.5$, implied from the spectra of GRBs, the X-ray afterglow of GRB970616 is well fitted by assuming $k=2$.Comment: 17 pages, no figures, Latex file, MNRAS in pres

Temporal variability in early afterglows of short gamma-ray bursts

The shock model has successfully explained the observed behaviors of afterglows from long gamma-ray bursts (GRBs). Here we use it to investigate the so-called early afterglows from short GRBs, which arises from blast waves that are not decelerated considerably by their surrounding medium. We consider a nearby medium loaded with $e^{\pm}$ pairs (Beloborodov 2002). The temporal behaviors show first a soft-to-hard spectral evolution, from the optical to hard X-ray, and then a usual hard-to-soft evolution after the blast waves begin to decelerate. The light curves show variability, and consist of two peaks. The first peak, due to the pair effect, can be observed in the X-ray, though too faint and too short in the optical. The second peak will be easily detected by {\it Swift}. We show that detections of the double-peak structure in the light curves of early afterglows are very helpful to determine all the shock parameters of short GRBs, including both the parameters of the relativistic source and the surroundings. Besides, from the requirement that the forward-shock emission in short GRBs should be below the BATSE detection threshold, we give a strong constraint on the shock model parameters. In particular, the initial Lorentz factor of the source is limited to be no more than $\sim 10^3$, and the ambient medium density is inferred to be low, n\la 10^{-1} cm$^{-3}$.Comment: 5 pages, 1 figure, minor changes to match the publish in MNRA

A Generic Dynamical Model of Gamma-ray Burst Remnants

The conventional generic model is deemed to explain the dynamics of $\gamma$-ray burst remnants very well, no matter whether they are adiabatic or highly radiative. However, we find that for adiabatic expansion, the model could not reproduce the Sedov solution in the non-relativistic phase, thus the model needs to be revised. In the present paper, a new differential equation is derived. The generic model based on this equation has been shown to be correct for both radiative and adiabatic fireballs, and in both ultra-relativistic and non-relativistic phase.Comment: 10 pages, LaTeX, 4 postscript figures, accepted for publication in MNRA

Characterisation of real GPRS traffic with analytical tools

With GPRS and UMTS networks lunched, wireless multimedia services are commercially becoming the most attractive applications next to voice. Because of the nature of bursty, packet-switched schemes and multiple data rates, the traditional Erlang approach and Poisson models for characterising voice-centric services traffic are not suitable for studying wireless multimedia services traffic. Therefore, research on the characterisation of wireless multimedia services traffic is very challenging. The typical reference for the study of wireless multimedia services traffic is wired Internet services traffic. However, because of the differences in network protocol, bandwidth, and QoS requirements between wired and wireless services, their traffic characterisations may not be similar. Wired network Internet traffic shows self-similarity, long-range dependence and its file sizes exhibit heavy-tailedness. This paper reports the use of existing tools to analyse real GPRS traffic data to establish whether wireless multimedia services traffic have similar properties as wired Internet services traffic

Superconductivity mediated by the antiferromagnetic spin-wave in chalcogenide iron-base superconductors

The ground state of K$_{0.8+x}$Fe$_{1.6+y}$Se$_2$ and other iron-based selenide superconductors are doped antiferromagnetic semiconductors. There are well defined iron local moments whose energies are separated from those of conduction electrons by a large band gap in these materials. We propose that the low energy physics of this system is governed by a model Hamiltonian of interacting electrons with on-site ferromagnetic exchange interactions and inter-site superexchange interactions. We have derived the effective pairing potential of electrons under the linear spin-wave approximation and shown that the superconductivity can be driven by mediating coherent spin wave excitations in these materials. Our work provides a natural account for the coexistence of superconducting and antiferromagnetic long range orders observed by neutron scattering and other experiments.Comment: 4 pages, 3 figure

A probabilistic model checking approach to analysing reliability, availability, and maintainability of a single satellite system

Satellites now form a core component for space based systems such as GPS and GLONAS which provide location and timing information for a variety of uses. Such satellites are designed to operate in-orbit and have lifetimes of 10 years or more. Reliability, availability and maintainability (RAM) analysis of these systems has been indispensable in the design phase of satellites in order to achieve minimum failures or to increase mean time between failures (MTBF) and thus to plan maintainability strategies, optimise reliability and maximise availability. In this paper, we present formal modelling of a single satellite and logical specification of its reliability, availability and maintainability properties. The probabilistic model checker PRISM has been used to perform automated quantitative analyses of these properties