Core and repulsion integrals for lowdin orthogonalized atomic orbitals in pi-electron systems

Core and repulsion integrals for Lowdin orthogonalized atomic orbitals in pi-electron system

Constrained Variation Method in Molecular Quantum Mechanics. Comparison of Different Approaches

Constrained variation method in molecular quantum mechanics and results for lithium hydrid

Perturbation theory of constraints - Application to a lithium hydride calculation

Constraint perturbation calculations for ground state of lithium hydride molecul

Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal

We point out that electromagnetic one-way edge modes analogous to quantum Hall edge states, originally predicted by Raghu and Haldane in 2D gyroelectric photonic crystals possessing Dirac point-derived bandgaps, can appear in more general settings. In particular, we show that the TM modes in a gyromagnetic photonic crystal can be formally mapped to electronic wavefunctions in a periodic electromagnetic field, so that the only requirement for the existence of one-way edge modes is that the Chern number for all bands below a gap is non-zero. In a square-lattice gyromagnetic Yttrium-Iron-Garnet photonic crystal operating at microwave frequencies, which lacks Dirac points, time-reversal breaking is strong enough that the effect should be easily observable. For realistic material parameters, the edge modes occupy a 10% band gap. Numerical simulations of a one-way waveguide incorporating this crystal show 100% transmission across strong defects, such as perfect conductors several lattice constants wide, larger than the width of the waveguide.Comment: 4 pages, 3 figures (Figs. 1 and 2 revised.

Submodularity and Optimality of Fusion Rules in Balanced Binary Relay Trees

We study the distributed detection problem in a balanced binary relay tree, where the leaves of the tree are sensors generating binary messages. The root of the tree is a fusion center that makes the overall decision. Every other node in the tree is a fusion node that fuses two binary messages from its child nodes into a new binary message and sends it to the parent node at the next level. We assume that the fusion nodes at the same level use the same fusion rule. We call a string of fusion rules used at different levels a fusion strategy. We consider the problem of finding a fusion strategy that maximizes the reduction in the total error probability between the sensors and the fusion center. We formulate this problem as a deterministic dynamic program and express the solution in terms of Bellman's equations. We introduce the notion of stringsubmodularity and show that the reduction in the total error probability is a stringsubmodular function. Consequentially, we show that the greedy strategy, which only maximizes the level-wise reduction in the total error probability, is within a factor of the optimal strategy in terms of reduction in the total error probability

Detection Performance in Balanced Binary Relay Trees with Node and Link Failures

We study the distributed detection problem in the context of a balanced binary relay tree, where the leaves of the tree correspond to $N$ identical and independent sensors generating binary messages. The root of the tree is a fusion center making an overall decision. Every other node is a relay node that aggregates the messages received from its child nodes into a new message and sends it up toward the fusion center. We derive upper and lower bounds for the total error probability $P_N$ as explicit functions of $N$ in the case where nodes and links fail with certain probabilities. These characterize the asymptotic decay rate of the total error probability as $N$ goes to infinity. Naturally, this decay rate is not larger than that in the non-failure case, which is $\sqrt N$. However, we derive an explicit necessary and sufficient condition on the decay rate of the local failure probabilities $p_k$ (combination of node and link failure probabilities at each level) such that the decay rate of the total error probability in the failure case is the same as that of the non-failure case. More precisely, we show that $\log P_N^{-1}=\Theta(\sqrt N)$ if and only if $\log p_k^{-1}=\Omega(2^{k/2})$

Trailing Edge Noise Reduction by Passive and Active Flow Controls

This paper presents the results on the use of porous metal foams (passive control) and dielectric barrier surface plasma actuations (active control) for the reduction of vortex shedding tonal noises from the nonflat plate type trailing edge serration in a NACA0012 airfoil previously discussed in Chong et al. (AIAA J. Vol. 51, 2013, pp. 2665-2677). The use of porous metal foams to fill the interstices between adjacent members of the sawtooth can almost completely suppress the vortex shedding tonal noise, whilst the serration effect on the broadband noise reduction is retained. This concept will promote the nonflat plate type serrated trailing edge to become a genuine alternative to the conventional flat plate type serrated trailing edge, which is known to have drawbacks in the structural stability, aerodynamic performances and implementation issues. For the plasma actuators, configuration which produces electric wind in a tangential direction is found to be not very effective in suppressing the vortices emanated from the serration blunt root. On the other hand, for the plasma configuration which produces electric wind in a vertical direction, good level of vortex shedding tonal noise reduction has been demonstrated. However, the self noise produced by the plasma actuators negates the noise benefits on the tonal noise reduction. This characteristic illustrates the need to further develop the plasma actuators in a two pronged approach. First is to increase the electric wind speed, thereby allowing the plasma actuators to be used in a higher free jet velocity which naturally produces a larger level of jet noise. Second, the self noise radiated by the plasma actuators should be reduced