49,975 research outputs found

    Inversion formula and Parsval theorem for complex continuous wavelet transforms studied by entangled state representation

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    In a preceding Letter (Opt. Lett. 32, 554 (2007)) we have proposed complex continuous wavelet transforms (CCWTs) and found Laguerre--Gaussian mother wavelets family. In this work we present the inversion formula and Parsval theorem for CCWT by virtue of the entangled state representation, which makes the CCWT theory complete. A new orthogonal property of mother wavelet in parameter space is revealed.Comment: 4 pages no figur

    Entangled Husimi distribution and Complex Wavelet transformation

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    Based on the proceding Letter [Int. J. Theor. Phys. 48, 1539 (2009)], we expand the relation between wavelet transformation and Husimi distribution function to the entangled case. We find that the optical complex wavelet transformation can be used to study the entangled Husimi distribution function in phase space theory of quantum optics. We prove that the entangled Husimi distribution function of a two-mode quantum state |phi> is just the modulus square of the complex wavelet transform of exp{-(|eta|^2)/2} with phi(eta)being the mother wavelet up to a Gaussian function.Comment: 7 page

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

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    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 γ−\gamma-ray emission.Comment: 11 pages, 2 figure; Accepted for publication by ApJ

    Early photon-shock interaction in stellar wind: sub-GeV photon flash and high energy neutrino emission from long GRBs

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    For gamma-ray bursts (GRBs) born in a stellar wind, as the reverse shock crosses the ejecta, usually the shocked regions are still precipitated by the prompt MeV \gamma-ray emission. Because of the tight overlapping of the MeV photon flow with the shocked regions, the optical depth for the GeV photons produced in the shocks is very large. These high energy photons are absorbed by the MeV photon flow and generate relativistic e^\pm pairs. These pairs re-scatter the soft X-ray photons from the forward shock as well as the prompt \gamma-ray photons and power detectable high energy emission, significant part of which is in the sub-GeV energy range. Since the total energy contained in the forward shock region and the reverse shock region are comparable, the predicted sub-GeV emission is independent on whether the GRB ejecta are magnetized (in which case the reverse shock IC and synchrotron self-Compton emission is suppressed). As a result, a sub-GeV flash is a generic signature for the GRB wind model, and it should be typically detectable by the future {\em Gamma-Ray Large Area Telescope} (GLAST). Overlapping also influence neutrino emission. Besides the 10^{15} \sim 10^{17} eV neutrino emission powered by the interaction of the shock accelerated protons with the synchrotron photons in both the forward and reverse shock regions, there comes another 101410^{14}eV neutrino emission component powered by protons interacting with the MeV photon flow. This last component has a similar spectrum to the one generated in the internal shock phase, but the typical energy is slightly lower.Comment: 7 pages, accepted for publication in Ap

    Microstructure control during twin roll casting of an AZ31 magnesium alloy

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    The existing twin roll casting technique for magnesium alloys suffers heterogeneity in both microstructure and chemistry and downstream processing is required to improve the strip quality, resulting in cost rise. In the present work, twin roll casting was carried out using an AZ31 magnesium alloy, with the application of intensive shearing melt conditioning prior to casting. The effect of process parameters such as pouring temperature and casting speed on microstructure control during casting and subsequent downstream processing was studied. Experimental results showed that the melt conditioning treatment allowed the production of AZ31 strips with uniform and refined microstructure free of centreline segregations. It was also shown that an optimized combination of pouring temperature and casting speed, in conjunction with a strip thickness control operation, resulted in uniformly distributed stored energies due to enhanced plastic deformation, which promoted recrystallization during casting and subsequent heat treatment. Strips prepared by twin roll casting and homogenization developed similar microstructural features to those prepared by twin roll casting followed by lengthy downstream processing by homogenization, hot rolling and annealing and displayed a weaker basal texture, exhibiting a potentially better formability.The EPSRC (UK

    Energy average formula of photon gas rederived by using the generalized Hermann-Feynman theorem

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    By virtue of the generalized Hermann-Feynmam theorem and the method of characteristics we rederive energy average formula of photon gas, this is another useful application of the theorem.Comment: 2 page
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