Fresnel operator, squeezed state and Wigner function for Caldirola-Kanai Hamiltonian

Based on the technique of integration within an ordered product (IWOP) of operators we introduce the Fresnel operator for converting Caldirola-Kanai Hamiltonian into time-independent harmonic oscillator Hamiltonian. The Fresnel operator with the parameters A,B,C,D corresponds to classical optical Fresnel transformation, these parameters are the solution to a set of partial differential equations set up in the above mentioned converting process. In this way the exact wavefunction solution of the Schr\"odinger equation governed by the Caldirola-Kanai Hamiltonian is obtained, which represents a squeezed number state. The corresponding Wigner function is derived by virtue of the Weyl ordered form of the Wigner operator and the order-invariance of Weyl ordered operators under similar transformations. The method used here can be suitable for solving Schr\"odinger equation of other time-dependent oscillators.Comment: 6 pages, 2 figure

A two component jet model for the X-ray afterglow flat segment in short GRB 051221A

In the double neutron star merger or neutron star-black hole merger model for short GRBs, the outflow launched might be mildly magnetized and neutron rich. The magnetized neutron-rich outflow will be accelerated by the magnetic and thermal pressure and may form a two component jet finally, as suggested by Vlahakis, Peng & K\"{o}nigl (2003). We show in this work that such a two component jet model could well reproduce the multi-wavelength afterglow lightcurves, in particular the X-ray flat segment, of short GRB 051221A. In this model, the central engine need not to be active much longer than the prompt $\gamma-$ray emission.Comment: 11 pages, 2 figure; Accepted for publication by ApJ

Using schema transformation pathways for data lineage tracing

With the increasing amount and diversity of information available on the Internet, there has been a huge growth in information systems that need to integrate data from distributed, heterogeneous data sources. Tracing the lineage of the integrated data is one of the problems being addressed in data warehousing research. This paper presents a data lineage tracing approach based on schema transformation pathways. Our approach is not limited to one specific data model or query language, and would be useful in any data transformation/integration framework based on sequences of primitive schema transformations

Adaptive Optimal Scaling of Metropolis-Hastings Algorithms Using the Robbins-Monro Process

We present an adaptive method for the automatic scaling of Random-Walk Metropolis-Hastings algorithms, which quickly and robustly identifies the scaling factor that yields a specified overall sampler acceptance probability. Our method relies on the use of the Robbins-Monro search process, whose performance is determined by an unknown steplength constant. We give a very simple estimator of this constant for proposal distributions that are univariate or multivariate normal, together with a sampling algorithm for automating the method. The effectiveness of the algorithm is demonstrated with both simulated and real data examples. This approach could be implemented as a useful component in more complex adaptive Markov chain Monte Carlo algorithms, or as part of automated software packages

The Effects of Rotation on the Evolution of Rising Omega-loops in a Stratified Model Convection Zone

We present three-dimensional MHD simulations of buoyant magnetic flux tubes that rise through a stratified model convection zone in the presence of solar rotation. The equations of MHD are solved in the anelastic approximation, and the results are used to determine the effects of solar rotation on the dynamic evolution an Omega-loop. We find that the Coriolis force significantly suppresses the degree of fragmentation at the apex of the loop during its ascent toward the photosphere. If the initial axial field strength of the tube is reduced, then, in the absence of forces due to convective motions, the degree of apex fragmentation is also reduced. We show that the Coriolis force slows the rise of the tube, and induces a retrograde flow in both the magnetized and unmagnetized plasma of an emerging active region. Observationally, we predict that this flow will appear to originate at the leading polarity, and will terminate at the trailing polarity.Comment: 25 pages, 8 figures, ApJ in pres

Neutrino emission from a GRB afterglow shock during an inner supernova shock breakout

The observations of a nearby low-luminosity gamma-ray burst (GRB) 060218 associated with supernova SN 2006aj may imply an interesting astronomical picture where a supernova shock breakout locates behind a relativistic GRB jet. Based on this picture, we study neutrino emission for early afterglows of GRB 060218-like GRBs, where neutrinos are expected to be produced from photopion interactions in a GRB blast wave that propagates into a dense wind. Relativistic protons for the interactions are accelerated by an external shock, while target photons are basically provided by the incoming thermal emission from the shock breakout and its inverse-Compton scattered component. Because of a high estimated event rate of low-luminosity GRBs, we would have more opportunities to detect afterglow neutrinos from a single nearby GRB event of this type by IceCube. Such a possible detection could provide evidence for the picture described above.Comment: 6 pages, 2 figures, accepted for publication in MNRA

GeV-TeV and X-ray flares from gamma-ray bursts

The recent detection of delayed X-ray flares during the afterglow phase of gamma-ray bursts (GRBs) suggests an inner-engine origin, at radii inside the deceleration radius characterizing the beginning of the forward shock afterglow emission. Given the observed temporal overlapping between the flares and afterglows, there must be inverse Compton (IC) emission arising from such flare photons scattered by forward shock afterglow electrons. We find that this IC emission produces GeV-TeV flares, which may be detected by GLAST and ground-based TeV telescopes. We speculate that this kind of emission may already have been detected by EGRET from a very strong burst--GRB940217. The enhanced cooling of the forward shock electrons by the X-ray flare photons may suppress the synchrotron emission of the afterglows during the flare period. The detection of GeV-TeV flares combined with low energy observations may help to constrain the poorly known magnetic field in afterglow shocks. We also consider the self-IC emission in the context of internal-shock and external-shock models for X-ray flares. The emission above GeV from internal shocks is low, while the external shock model can also produce GeV-TeV flares, but with a different temporal behavior from that caused by IC scattering of flare photons by afterglow electrons. This suggests a useful approach for distinguishing whether X-ray flares originate from late central engine activity or from external shocks.Comment: slightly shortened version, accepted for publication in ApJ Letters, 4 emulateapj pages, no figure