Multi-layer Unmanned Aerial Vehicle Networks: Modeling and Performance Analysis

Since various types of unmanned aerial vehicles (UAVs) with different hardware capabilities are introduced, we establish a foundation for the multi-layer aerial network (MAN). First, the MAN is modeled as K layer ANs, and each layer has UAVs with different densities, floating altitudes, and transmission power. To make the framework applicable for various scenarios in MAN, we consider the transmitter- and the receiver-oriented node association rules as well as the air-to-ground and air-to-air channel models, which form line of sight links with a location-dependent probability. We then newly analyze the association probability, the main link distance distribution, successful transmission probability (STP), and area spectral efficiency (ASE) of MAN. The upper bounds of the optimal densities that maximize STP and ASE are also provided. Finally, in the numerical results, we show the optimal UAV densities of an AN that maximize the ASE and the STP decrease with the altitude of the network. We also show that when the total UAV density is fixed for two layer AN, the use of single layer in higher(lower) altitude only for all UAVs can achieve better performance for low(high) total density case, otherwise, distributing UAVs in two layers, i.e., MAN, achieves better performance

Do Small-mass Neutrinos participate in Gauge Transformations?

Neutrino oscillation experiments presently suggest that neutrinos have a small but finite mass. If neutrinos are to have mass, there should be a Lorentz frame in which they can be brought to rest. This paper discusses how Wigner's little groups can be used to distinguish between massive and massless particles. We derive a representation of the SL(2,c) group which separates out the two sets of spinors contained therein. One set is gauge dependent. The other set is gauge-invariant and represents polarized neutrinos. We show that a similar calculation can be done for the Dirac equation. In the large-momentum/zero-mass limit, the Dirac spinors can be separated into large and small components. The large components are gauge invariant, while the small components are not. These small components represent spin-$\frac{1}{2}$ non-zero mass particles. If we renormalize the large components, these gauge invariant spinors again represent the polarization of neutrinos. Massive neutrinos cannot be invariant under gauge transformations.Comment: 15 page

Hawking Radiation from Non-Extremal D1-D5 Black Hole via Anomalies

We take the method of anomaly cancellation for the derivation of Hawking radiation initiated by Robinson and Wilczek, and apply it to the non-extremal five-dimensional D1-D5 black hole in string theory. The fluxes of the electric charge flow and the energy-momentum tensor from the black hole are obtained. They are shown to match exactly with those of the two-dimensional black body radiation at the Hawking temperature.Comment: 14 page

Stability Of contact discontinuity for steady Euler System in infinite duct

In this paper, we prove structural stability of contact discontinuities for full Euler system

Determination of Intrinsic Ferroelectric Polarization in Orthorhombic Manganites with E-type Spin Order

By directly measuring electrical hysteresis loops using the Positive-Up Negative-Down (PUND) method, we accurately determined the remanent ferroelectric polarization Pr of orthorhombic RMnO3 (R = Ho, Tm, Yb, and Lu) compounds below their E-type spin ordering temperatures. We found that LuMnO3 has the largest Pr of 0.17 uC/cm^2 at 6 K in the series, indicating that its single-crystal form can produce a Pr of at least 0.6 \muuC/cm^2 at 0 K. Furthermore, at a fixed temperature, Pr decreases systematically with increasing rare earth ion radius from R = Lu to Ho, exhibiting a strong correlation with the variations in the in-plane Mn-O-Mn bond angle and Mn-O distances. Our experimental results suggest that the contribution of the Mn t2g orbitals dominates the ferroelectric polarization.Comment: 16 pages, 4 figure

Hawking radiation, W-infinity algebra and trace anomalies

We apply the "trace anomaly method" to the calculation of moments of the Hawking radiation of a Schwarzschild black hole. We show that they can be explained as the fluxes of chiral currents forming a W-infinity algebra. Then we construct the covariant version of these currents and verify that up to order 6 they are not affected by any trace anomaly. Using cohomological methods we show that actually, for the fourth order current, no trace anomalies can exist. The results reported here are strictly valid in two dimensions.Comment: 22 pages, typos correcte

Fano resonances in a three-terminal nanodevice

The electron transport through a quantum sphere with three one-dimensional wires attached to it is investigated. An explicit form for the transmission coefficient as a function of the electron energy is found from the first principles. The asymmetric Fano resonances are detected in transmission of the system. The collapse of the resonances is shown to appear under certain conditions. A two-terminal nanodevice with an additional gate lead is studied using the developed approach. Additional resonances and minima of transmission are indicated in the device.Comment: 11 pages, 5 figures, 2 equations are added, misprints in 5 equations are removed, published in Journal of Physics: Condensed Matte