Local well-posedness and low Mach number limit of the compressible magnetohydrodynamic equations in critical spaces

The local well-posedness and low Mach number limit are considered for the multi-dimensional isentropic compressible viscous magnetohydrodynamic equations in critical spaces. First the local well-posedness of solution to the viscous magnetohydrodynamic equations with large initial data is established. Then the low Mach number limit is studied for general large data and it is proved that the solution of the compressible magnetohydrodynamic equations converges to that of the incompressible magnetohydrodynamic equations as the Mach number tends to zero. Moreover, the convergence rates are obtained.Comment: 37page

Cooperative Communications in Smart Grid Networks

The conventional grid system is facing great challenges due to the fast growing electricity demand throughout the world. The smart grid has emerged as the next generation of grid power systems, aimed at providing secure, reliable and low cost power generation, distribution and consumption intelligently. The smart grid communication system within the smart grid network is of fundamental importance to support data transfer and information exchange within the smart grid system. The National Institute of Standards and Technology has identified wireless communications as an important networking technology to be employed in power systems. The reliability of the data transmission is essential for the smart grid system to achieve high accuracy for the power generation, distribution and consumption. In this thesis, we investigate cooperative communications to improve transmission reliability in smart grid networks. Although many issues within cooperative communication have already been addressed, there is a lack of research efforts on cooperative communication for the wireless smart grid communication system which has its own network features and different transmission requirements. In our research, the smart grid communication networks were studied, and cooperative communications in smart grid networks were analysed. The research work mainly focuses on three problems: the application of cooperative relay communications to modern smart grid communication networks, the cooperative relay-based network development strategy, and the optimization of cooperative relay communication for smart grids. For the first problem, the application of cooperative relay communication to a home area network (HAN) of smart grid system is presented. The wireless transmission reliability is identified as the issue of most concern in wireless smart grid networks. We model the smart grid HAN as a wireless mesh network that deploys cooperative relay communication to enhance the transmission reliability. We apply cooperative relay communication to provide a user equipment selection scheme to effectively improve the transmission quality between the electricity equipment and the smart meter. For the second problem, we address the network design and planning problem in the smart grid HAN. The outage performance of direct transmission and cooperative transmission was analysed. Based on the reliability performance metric that we have defined, we propose a HAN deployment strategy to improve the reliability of the transmission links. The proposed HAN deployment strategy is tested in a home environment. The smart meter location optimization problem has also been identified and solved. The simulation results show that our proposed network deployment strategy can guarantee high reliability for smart grid communications in home area networks. For the third problem, the research focuses on the optimization of the cooperative relay transmission regarding the power allocation and relay selection in the neighbourhood area network (NAN) of the smart grid system. Owing to the complexity of the joint optimization problem, reduced-complexity algorithms have been proposed to minimize the transmission power, at the same time, guarantee the link reliability of the cooperative communications. The optimization problem of power allocation and relay selection is formulated and treated as a combinatorial optimization problem. Two sub-optimal solutions that simplify the optimization process are devised. Based on the solutions, two different algorithms are proposed to solve the optimization problem with reduced complexity. The simulation results demonstrate that both two algorithms have good performance on minimizing the total transmission power while guaranteeing the transmission reliability for the wireless smart grid communication system. In this thesis, we consider cooperative communications in a smart grid scenario. We minimize the outage probability and thus improve the reliability of the communications taking place in the smart grid by considering the optimization problem of power control, relay selection and the network deployment problem. Although similar problems might have been well investigated in conventional wireless networks, such as the cellular network, little research has been conducted in smart grid communications. We apply new optimization techniques and propose solutions for these optimization problems specifically tailored for smart grid communications. We demonstrate that, compared to naively applying the algorithms suitable for conventional communications to the smart gird scenario, our proposed algorithm significantly improves the performance of smart grid communications. Finally, we note that, in future work, it will be possible to consider more complex smart grid communications system models. For example, it is worthwhile considering hetregeneous smart communications by combining HAN and wide area networks (WAN). In addition, instead of assuming that all communications have the equal priority, as in this thesis, more comprehensive analysis of the priority of the smart grid communication can be applied to the research

Spectral Lags Obtained by CCF of Smoothed Lightcurves

We present a new technique to calculate the spectral lags of gamma-ray bursts (GRBs). Unlike previous processing methods, we first smooth the light curves of gamma-ray bursts in high and low energy bands using the "Loess" filter, then, we directly define the spectral lags as such to maximize the cross-correlation function (CCF) between two smoothed light curves. This method is suitable for various shapes of CCF; it effectively avoids the errors caused by manual selections for the fitting function and fitting interval. Using the method, we have carefully measured the spectral lags of individual pulses contained in BAT/Swift gamma-ray bursts with known redshifts, and confirmed the anti-correlation between the spectral lag and the isotropy luminosity. The distribution of spectral lags can be well fitted by four Gaussian components, with the centroids at 0.03 s, 0.09 s, 0.15 s, and 0.21 s, respectively. We find that some spectral lags of the multi-peak GRBs seem to evolve with time

The accretion rate independence of horizontal branch oscillation in XTE J1701-462

We study the temporal and energy spectral properties of the unique neutron star low-mass X-ray binary XTE J1701-462. After assuming the HB/NB vertex as a reference position of accretion rate, the horizontal branch oscillation (HBO) of the HB/NB vertex is roughly 50 Hz. It indicates that the HBO is independent with the accretion rate or the source intensity. The spectral analysis shows $R_{\rm{in}}\propto\dot{M}_{\rm{Disk}}^{2.9\pm0.09}$ in the HB/NB vertex and $R_{\rm{in}}\propto\dot{M}_{\rm{Disk}}^{1.7\pm0.06}$ in the NB/FB vertex, which implies that different accretion rate may be produced in the HB/NB vertex and the NB/FB vertex. The Comptonization component could be fitted by constrained broken power law (CBPL) or nthComp. Different with GX 17+2, the frequencies of HBO positively correlate with the inner disk radius, which contradict with the prediction of Lense-Thirring precession model. XTE J1701-462, both in the Cyg-like phase and in the Sco-like phase, follows a positive correlation between the break frequency of broad band noise and the characteristic frequency of HBO, which is called the W-K relation. An anticorrelation between the frequency of HBO and photon energy is observed. Moreover, the rms of HBO increases with photon energy till ~10 keV. We discuss the possible origin of HBO from corona in XTE J1701-462.Comment: 45 pages, 18 figures, accepted by Ap