A Reverse-Shock Model for the Early Afterglow of GRB 050525A

The prompt localization of gamma-ray burst (GRB) 050525A by {\em Swift} allowed the rapid follow-up of the afterglow. The observations revealed that the optical afterglow had a major rebrightening starting at $\sim 0.01$ days and ending at $\sim 0.03$ days, which was followed by an initial power-law decay. Here we show that this early emission feature can be interpreted as the reverse shock emission superposed by the forward shock emission in an interstellar medium environment. By fitting the observed data, we further constrain some parameters of the standard fireball-shock model: the initial Lorentz factor of the ejecta $\gamma_0>120$, the magnetic energy fraction $\epsilon_B>4\times10^{-6}$, and the medium density $n<2 {\rm cm^{-3}}$. These limits are consistent with those from the other very-early optical afterglows observed so far. In principle, a wind environment for GRB 050525A is disfavored.Comment: 11 pages, 1 figure, accepted for publication in Ap

Stability of simple periodic solutions of neutral functional differential equations

We study the stability property of a simple periodic solution of an autonomous neutral functional differential equation (NFDE) of the form $${d\over dt} D(x_t) = f (x_t).$$ A new proof based on local integral manifold theory and the implicit function theorem is given for the classical result that a simple periodic orbit of the equation above is asymptotically orbitally stable with asymptotic phase. The technique used overcomes the difficulty that the solution operator of a NFDE does not smooth as $t$ increases

Behavior of X-Ray Dust Scattering and Implications for X-Ray Afterglows of Gamma-Ray Bursts

The afterglows of gamma-ray bursts (GRBs) have commonly been assumed to be due to shocks sweeping up the circum-stellar medium. However, most GRBs have been found in dense star-forming regions where a significant fraction of the prompt X-ray emission can be scattered by dust grains. Here we revisit the behavior of dust scattering of X-rays in GRBs. We find that the features of some X-ray afterglows from minutes to days after the gamma-ray triggers are consistent with the scattering of prompt X-ray emission from GRBs off host dust grains. This implies that some of the observed X-ray afterglows (especially those without sharp rising and decaying flares) could be understood with a dust-scattering--driven emission model.Comment: ApJ, in pres

Grey Fuzzy Sliding Mode Control with Grey Estimator for Brushless Doubly Fed Motor

In this paper, a grey fuzzy sliding mode controller (GFSMC) for brushless doubly fed motor (BDFM) adjustable speed system is presented. A grey model estimator and adaptive fuzzy control technology are incorporated into the sliding mode control (SMC) to adaptively regulate the adaptive law of SMC. The proposed adaptive fuzzy equivalent controller, adaptive fuzzy switching controller, and grey model compensation controller for BDFM can eliminate the average chattering encountered by most SMC schemes, improve the robustness, and obtain excellent static and dynamic performances of SMC. Simulation results show that the proposed control strategy is feasible, correct and effective