We consider the effects of velocity shear on the resonance absorption of incompressible magnetohydrodynamic surface waves. We find that there are generally values of the velocity shear for which the surface wave decay rate becomes zero. In some cases, the resonance absorption goes to zero even for very small velocity shears. We also find that the resonance absorption can be strongly enhanced at other values of the velocity shear. The presence of flows may therefore be generally important in determining the effects of resonance absorption, such as might occur in the interaction of p-modes with sunspots, for example. The most interesting result of our work is the fact that there can exist resonances which lead to instability of the global surface mode, and that instability can occur for velocity shears significantly below the Kelvin-Helmholz threshold. These instabilities may play a role in the development of turbulence in regions of strong velocity shear in the solar wind or the Earth's magnetosheath, but an extension of our work to include compressibility is required before we can say anything definitive about those regions.
We study the maximum achievable rate of a two-hop amplified-and-forward (AF) relaying millimeter-wave (mm-wave) system, where two AF relaying schemes, i.e., half-duplex (HD) and full-duplex (FD) are discussed. By considering the two-ray mm-wave channel and the Gaussian-type directional antenna, jointly, the impacts of the beamwidth and the self-interference coefficient on maximum achievable rates are investigated. Results show that, under a sum-power constraint, the rate of FD-AF mm-wave relaying outperforms its HD counterpart only when antennas with narrower beamwidth and smaller self-interference coefficient are applied. However, when the sum-power budget is sufficiently high or the beamwidth of directional antenna is sufficiently small, direct transmission becomes the best strategy, rather than the AF relaying schemes. For both relaying schemes, we show that the rates of both AF relaying schemes scale as O min θ −1 m , θ −2 m with respect to beamwidth θm, and the rate of FD-AF relaying scales as O µ − 1 2 with respect to self-interference coefficient µ. Besides, we show that, ground reflections may significantly affect the performance of mmwave communications, constructively or destructively. Thus, the impact of ground reflections deserves careful considerations for analyzing or designing future mm-wave wireless networks.Index Terms-Millimeter-wave communications, amplify-andforward relaying, Gaussian-type directional antenna, two-ray channel, beamwidth, self-interference.
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