Quasi-local energy and the choice of reference

A quasi-local energy for Einstein's general relativity is defined by the value of the preferred boundary term in the covariant Hamiltonian formalism. The boundary term depends upon a choice of reference and a time-like displacement vector field (which can be associated with an observer) on the boundary of the region. Here we analyze the spherical symmetric cases. For the obvious analytic choice of reference based on the metric components, we find that this technique gives the same quasi-local energy values using several standard coordinate systems and yet can give different values in some other coordinate systems. For the homogeneous-isotropic cosmologies, the energy can be non-positive, and one case which is actually flat space has a negative energy. As an alternative, we introduce a way to determine the choice of both the reference and displacement by extremizing the energy. This procedure gives the same value for the energy in different coordinate systems for the Schwarzschild space, and a non-negative value for the cosmological models, with zero energy for the dynamic cosmology which is actually Minkowski space. The timelike displacement vector comes out to be the dual mean curvature vector of the two-boundary.Comment: 21 pages; revised version to appear in CQ

Cross-Correlation-Function-Based Multipath Mitigation Method for Sine-BOC Signals

Global Navigation Satellite Systems (GNSS) positioning accuracy indoor and urban canyons environments are greatly affected by multipath due to distortions in its autocorrelation function. In this paper, a cross-correlation function between the received sine phased Binary Offset Carrier (sine-BOC) modulation signal and the local signal is studied firstly, and a new multipath mitigation method based on cross-correlation function for sine-BOC signal is proposed. This method is implemented to create a cross-correlation function by designing the modulated symbols of the local signal. The theoretical analysis and simulation results indicate that the proposed method exhibits better multipath mitigation performance compared with the traditional Double Delta Correlator (DDC) techniques, especially the medium/long delay multipath signals, and it is also convenient and flexible to implement by using only one correlator, which is the case of low-cost mass-market receivers

Enhanced forward stimulated Brillouin scattering in silicon photonic slot waveguide Bragg grating

We study the forward stimulated Brillouin scattering process in a suspended silicon slot waveguide Bragg grating. Full-vectorial formalism is applied to analyze the interplay of electrostriction and radiation pressure. We show that radiation pressure is the dominant factor in the proposed waveguide. The Brillouin gain strongly depends on the structural parameters and the maximum value in the order of 106 W−1 m−1 is obtained in the slow light regime, which is more than two orders larger than that of the stand-alone strip and slot waveguides