Dual condensates at finite isospin chemical potential

The dual observables as order parameters for center symmetry are tested at finite isospin chemical potential $\mu_I$ in a Polyakov-loop enhanced chiral model of QCD with physical quark masses. As a counterpart of the dressed Polyakov-loop, the first Fourier moment of pion condensate is introduced for $\mu_I>{m_\pi}/{2}$ under the temporal twisted boundary conditions for quarks. We demonstrate that this dual condensate exhibits the similar temperature dependence as the conventional Polyakov-loop. We confirm that its rapid increase with $T$ is driven by the evaporating of pion condensation. On the other hand, the dressed Polyakov-loop shows abnormal thermal behavior, which even decreases with $T$ at low temperatures due to the influence of pion condensate. We thus argue that in QCD the critical temperature extracting from a dual observable may have nothing to do with the quark confinement-deconfinement transition if the quark mass is very small.Comment: 8 pages, 6 figure

Securing UAV Communications Via Trajectory Optimization

Unmanned aerial vehicle (UAV) communications has drawn significant interest recently due to many advantages such as low cost, high mobility, and on-demand deployment. This paper addresses the issue of physical-layer security in a UAV communication system, where a UAV sends confidential information to a legitimate receiver in the presence of a potential eavesdropper which are both on the ground. We aim to maximize the secrecy rate of the system by jointly optimizing the UAV's trajectory and transmit power over a finite horizon. In contrast to the existing literature on wireless security with static nodes, we exploit the mobility of the UAV in this paper to enhance the secrecy rate via a new trajectory design. Although the formulated problem is non-convex and challenging to solve, we propose an iterative algorithm to solve the problem efficiently, based on the block coordinate descent and successive convex optimization methods. Specifically, the UAV's transmit power and trajectory are each optimized with the other fixed in an alternating manner until convergence. Numerical results show that the proposed algorithm significantly improves the secrecy rate of the UAV communication system, as compared to benchmark schemes without transmit power control or trajectory optimization.Comment: Accepted by IEEE GLOBECOM 201

Well-posedness in critical spaces for the compressible Navier-Stokes equations with density dependent viscosities

In this paper, we prove the local well-posedness in critical Besov spaces for the compressible Navier-Stokes equations with density dependent viscosities under the assumption that the initial density is bounded away from zero.Comment: 27page

Multiple Timescale Dispatch and Scheduling for Stochastic Reliability in Smart Grids with Wind Generation Integration

Integrating volatile renewable energy resources into the bulk power grid is challenging, due to the reliability requirement that at each instant the load and generation in the system remain balanced. In this study, we tackle this challenge for smart grid with integrated wind generation, by leveraging multi-timescale dispatch and scheduling. Specifically, we consider smart grids with two classes of energy users - traditional energy users and opportunistic energy users (e.g., smart meters or smart appliances), and investigate pricing and dispatch at two timescales, via day-ahead scheduling and realtime scheduling. In day-ahead scheduling, with the statistical information on wind generation and energy demands, we characterize the optimal procurement of the energy supply and the day-ahead retail price for the traditional energy users; in realtime scheduling, with the realization of wind generation and the load of traditional energy users, we optimize real-time prices to manage the opportunistic energy users so as to achieve systemwide reliability. More specifically, when the opportunistic users are non-persistent, i.e., a subset of them leave the power market when the real-time price is not acceptable, we obtain closedform solutions to the two-level scheduling problem. For the persistent case, we treat the scheduling problem as a multitimescale Markov decision process. We show that it can be recast, explicitly, as a classic Markov decision process with continuous state and action spaces, the solution to which can be found via standard techniques. We conclude that the proposed multi-scale dispatch and scheduling with real-time pricing can effectively address the volatility and uncertainty of wind generation and energy demand, and has the potential to improve the penetration of renewable energy into smart grids.Comment: Submitted to IEEE Infocom 2011. Contains 10 pages and 4 figures. Replaces the previous arXiv submission (dated Aug-23-2010) with the same titl