Energy-Dependent GRB Pulse Width due to the Curvature Effect and Intrinsic Band Spectrum

Previous studies have found that the width of gamma-ray burst (GRB) pulse is energy dependent and that it decreases as a power-law function with increasing photon energy. In this work we have investigated the relation between the energy dependence of pulse and the so-called Band spectrum by using a sample including 51 well-separated fast rise and exponential decay long-duration GRB pulses observed by BATSE (Burst and Transient Source Experiment on the Compton Gamma Ray Observatory). We first decompose these pulses into rise, and decay phases and find the rise widths, and the decay widths also behavior as a power-law function with photon energy. Then we investigate statistically the relations between the three power-law indices of the rise, decay and total width of pulse (denoted as $\delta_r$, $\delta_d$ and $\delta_w$, respectively) and the three Band spectral parameters, high-energy index ($\alpha$), low-energy index ($\beta$) and peak energy ($E_p$). It is found that (1)$\alpha$ is strongly correlated with $\delta_w$ and $\delta_d$ but seems uncorrelated with $\delta_r$; (2)$\beta$ is weakly correlated with the three power-law indices and (3)$E_p$ does not show evident correlations with the three power-law indices. We further investigate the origin of $\delta_d-\alpha$ and $\delta_w-\alpha$. We show that the curvature effect and the intrinsic Band spectrum could naturally lead to the energy dependence of GRB pulse width and also the $\delta_d-\alpha$ and $\delta_w-\alpha$ correlations. Our results would hold so long as the shell emitting gamma rays has a curve surface and the intrinsic spectrum is a Band spectrum or broken power law. The strong $\delta_d-\alpha$ correlation and inapparent correlations between $\delta_r$ and three Band spectral parameters also suggest that the rise and decay phases of GRB pulses have different origins.Comment: 29 pages, 9 figures, 4 tables. Accepted for publication in The Astrophysical Journa

The Mechanism of Kuznetsov-Ma Breather

We discuss how to understand the dynamical process of Kuznetsov-Ma breather, based on some basic physical mechanisms. It is shown that dynamical process of Kuznetsov-Ma breather involves at least two distinctive mechanisms: modulational instability, and the interference effects between a bright soliton and a plane wave background. Our analysis indicates that modulational instability plays dominant roles in mechanism of Kuznetsov-Ma breather admitting weak perturbations, and the interference effect plays dominant role for the Kuznetsov-Ma breather admitting strong perturbations. For intermediate cases, the two mechanisms are both involved greatly. These characters provide a possible way to understand the evolution of strong perturbations on a plane wave background.Comment: 5 pages, 4 figure

Blow up solutions to a viscoelastic fluid system and a coupled Navier-Stokes/Phase-Field system in R^2

We find explicit solutions to both the Oldroyd-B model with infinite Weissenberg number and the coupled Navier-Stokes/Phase-Field system. The solutions blow up in finite time.Comment: 5 page

Lattice dynamical wavelet neural networks implemented using particle swarm optimization for spatio-temporal system identification

In this brief, by combining an efficient wavelet representation with a coupled map lattice model, a new family of adaptive wavelet neural networks, called lattice dynamical wavelet neural networks (LDWNNs), is introduced for spatio-temporal system identification. A new orthogonal projection pursuit (OPP) method, coupled with a particle swarm optimization (PSO) algorithm, is proposed for augmenting the proposed network. A novel two-stage hybrid training scheme is developed for constructing a parsimonious network model. In the first stage, by applying the OPP algorithm, significant wavelet neurons are adaptively and successively recruited into the network, where adjustable parameters of the associated wavelet neurons are optimized using a particle swarm optimizer. The resultant network model, obtained in the first stage, however, may be redundant. In the second stage, an orthogonal least squares algorithm is then applied to refine and improve the initially trained network by removing redundant wavelet neurons from the network. An example for a real spatio-temporal system identification problem is presented to demonstrate the performance of the proposed new modeling framework