Gamma-Ray Burst Afterglows with Energy Injection: Homogeneous Versus Wind External Media

Assuming an adiabatic evolution of a gamma-ray burst (GRB) fireball interacting with an external medium, we calculate the hydrodynamics of the fireball with energy injection from a strongly magnetic millisecond pulsar through magnetic dipole radiation, and obtain the light curve of the optical afterglow from the fireball by synchrotron radiation. Results are given both for a homogeneous external medium and for a wind ejected by GRB progenitor. Our calculations are also available in both ultra-relativistic and non-relativistic phases. Furthermore, the observed R-band light curve of GRB{000301C} can be well fitted in our model, which might provide a probe of the properties of GRB progenitors.Comment: revised version for publication in Chin. Phys. Let

Computation over multi-access channels : multi-hop implementation and resource allocation

For future wireless networks, enormous numbers of interconnections are required, creating a multi-hop topology and leading to a great challenge on data aggregation. Instead of collecting data individually, a more efficient technique, computation over multi-access channels (CoMAC), has emerged to compute functions by exploiting the signal-superposition property of wireless channels. However, it is still an open problem on the implementation of CoMAC in multi-hop wireless networks considering fading channel and resource allocation. In this paper, we propose multi-layer CoMAC (ML-CoMAC) by combining CoMAC and orthogonal communication to compute functions in the multi-hop network. Firstly, to make the multi-hop network more tractable, we reorganize it into a hierarchical network with multiple layers that consists of subgroups and groups. Then, in the hierarchical network, the implementation of ML-CoMAC is given by computing and communicating subgroup and group functions over layers, where CoMAC is applied to compute each subgroup function and orthogonal communication is adopted for each group to obtain the group function. The general computation rate is derived and the performance is further improved through time allocation and power control. The closed-form solutions to optimization problems are obtained, which suggests that orthogonal communication and existing CoMAC schemes are generalized

The Evolution of Universe with th B-I Type Phantom Scalar Field

We considered the phantom cosmology with a lagrangian $\displaystyle L=\frac{1}{\eta}[1-\sqrt{1+\eta g^{\mu\nu}\phi_{, \mu}\phi_{, \nu}}]-u(\phi)$, which is original from the nonlinear Born-Infeld type scalar field with the lagrangian $\displaystyle L=\frac{1}{\eta}[1-\sqrt{1-\eta g^{\mu\nu}\phi_{, \mu}\phi_{, \nu}}]-u(\phi)$. This cosmological model can explain the accelerated expansion of the universe with the equation of state parameter $w\leq-1$. We get a sufficient condition for a arbitrary potential to admit a late time attractor solution: the value of potential $u(X_c)$ at the critical point $(X_c,0)$ should be maximum and large than zero. We study a specific potential with the form of $u(\phi)=V_0(1+\frac{\phi}{\phi_0})e^{(-\frac{\phi}{\phi_0})}$ via phase plane analysis and compute the cosmological evolution by numerical analysis in detail. The result shows that the phantom field survive till today (to account for the observed late time accelerated expansion) without interfering with the nucleosynthesis of the standard model(the density parameter $\Omega_{\phi}\simeq10^{-12}$ at the equipartition epoch), and also avoid the future collapse of the universe.Comment: 17 pages, 10 figures,typos corrected, references added,figures added and enriched, title changed, main result remaine

Determinants of immediate price impacts at the trade level in an emerging order-driven market

The common wisdom argues that, in general, large trades cause large price changes, while small trades cause small price changes. However, for extremely large price changes, the trade size and news play a minor role, while the liquidity (especially price gaps on the limit order book) is a more influencing factor. Hence, there might be other influencing factors of immediate price impacts of trades. In this paper, through mechanical analysis of price variations before and after a trade of arbitrary size, we identify that the trade size, the bid-ask spread, the price gaps and the outstanding volumes at the bid and ask sides of the limit order book have impacts on the changes of prices. We propose two regression models to investigate the influences of these microscopic factors on the price impact of buyer-initiated partially filled trades, seller-initiated partially filled trades, buyer-initiated filled trades, and seller-initiated filled trades. We find that they have quantitatively similar explanation powers and these factors can account for up to 44% of the price impacts. Large trade sizes, wide bid-ask spreads, high liquidity at the same side and low liquidity at the opposite side will cause a large price impact. We also find that the liquidity at the opposite side has a more influencing impact than the liquidity at the same side. Our results shed new lights on the determinants of immediate price impacts.Comment: 21 IOP tex pages including 5 figures and 5 tables. Accepted for publication in New Journal of Physic

A New Spin-Orbit Induced Universality Class in the Quantum Hall Regime ?

Using heuristic arguments and numerical simulations it is argued that the critical exponent $\nu$ describing the localization length divergence at the quantum Hall transition is modified in the presence of spin-orbit scattering with short range correlations. The exponent is very close to $\nu=4/3$, the percolation correlation length exponent, the prediction of a semi-classical argument. In addition, a region of weakly localized regime, where the localization length is exponentially large, is conjectured.Comment: 4 two-column pages including 4 eps figure

A Comprehensive Analysis of Swift/XRT Data: III. Jet Break Candidates in X-ray and Optical Afterglow Lightcurves

The Swift/XRT data of 179 GRBs (from 050124 to 070129) and the optical afterglow data of 57 pre- and post-Swift GRBs are analyzed, in order to systematically investigate the jet-like breaks in the X-ray and optical afterglow lightcurves. We find that not a single burst can be included in the ``Platinum'' sample, in which the data satisfy all the criteria of a jet break. By releasing one or more requirements to define a jet break, some candidates of various degrees could be identified. In the X-ray band, 42 out of the 103 well-sampled X-ray lightcurves have a decay slope of the post-break segment >1.5 (``Bronze'' sample), and 27 of them also satisfy the closure relations of the forward models (``Silver'' sample). The numbers of the ``Bronze'' and ``Silver'' candidates in the optical lightcurves are 27 and 23, respectively. Thirteen bursts have well-sampled optical and X-ray lightcurves, but only seven cases are consistent with an achromatic break, but even in these cases only one band satisfies the closure relations (``Gold'' sample). The observed break time in the XRT lightcurves is systematically earlier than that in the optical bands. All these raise great concerns in interpreting the jet-like breaks as jet breaks and further inferring GRB energetics from these breaks. By assuming that these breaks are jet breaks, we perform a similar analysis as previous work to calculate the jet opening angle (theta_j) and energetics (E_k) with the ``Silver'' and ``Gold'' jet break candidates. The derived E_K distribution reveals a much larger scatter than the pre-Swift sample. A tentative anti-correlation between theta_j and E_{K,iso} is found for both the pre-Swift and Swift GRBs, indicating that the E_K could still be quasi-universal, if the breaks in discussion are indeed jet breaks(abridge).Comment: 48 pages, including 5 tables and 8 figures. Accepted for publication in ApJ. This is the third paper of a series. Paper I and II see astro-ph/0612246 (ApJ, 2007, 666,1002) and arXiv:0705.1373 (ApJ, 2007, 669, n2,in press

Emergence of long memory in stock volatility from a modified Mike-Farmer model

The Mike-Farmer (MF) model was constructed empirically based on the continuous double auction mechanism in an order-driven market, which can successfully reproduce the cubic law of returns and the diffusive behavior of stock prices at the transaction level. However, the volatility (defined by absolute return) in the MF model does not show sound long memory. We propose a modified version of the MF model by including a new ingredient, that is, long memory in the aggressiveness (quantified by the relative prices) of incoming orders, which is an important stylized fact identified by analyzing the order flows of 23 liquid Chinese stocks. Long memory emerges in the volatility synthesized from the modified MF model with the DFA scaling exponent close to 0.76, and the cubic law of returns and the diffusive behavior of prices are also produced at the same time. We also find that the long memory of order signs has no impact on the long memory property of volatility, and the memory effect of order aggressiveness has little impact on the diffusiveness of stock prices.Comment: 6 pages, 6 figures and 1 tabl