Fate of the resonating valence bond in graphene

We apply a variational wave function capable of describing qualitatively and quantitatively the so-called "resonating valence bond" (RVB) in realistic materials, by improving standard ab initio calculations by means of quantum Monte Carlo methods. In this framework we clearly identify the Kekulé and Dewar contributions to the chemical bond of the benzene molecule and establish the corresponding RVB energy of these structures (?0.01 eV/atom). We apply this method to unveil the nature of the chemical bond in undoped graphene, providing an estimate of the RVB energy gain, and show that this picture remains only within a small "resonance length" of a few atomic units.     

11B and constraints on neutrino oscillations and spectra from neutrino nucleosynthesis

We study the sensitivity to variations in the triple-alpha and 12C(α,γ)16O reaction rates, of the yield of the neutrino-process isotopes 7Li, 11B, 19F, 138La, and 180Ta in core-collapse supernovae. Compared to solar abundances, less than 15% of 7Li, about 25%-80% of 19F, and about half of 138La is produced in these stars. Over a range of ±2σ for each helium-burning rate, 11B is overproduced and the yield varies by an amount larger than the variation caused by the effects of neutrino oscillations. The total 11B yield, however, may eventually provide constraints on supernova neutrino spectra.     

Best Fourier Approximation and Application in Efficient Blurred Signal Reconstruction

We expand upon the known results on sharp linear Fourier methods of approximation where the approximation is the best in terms of both rate and constant among all polynomial procedures of approximation. So far these results have been studied due to their mathematical beauty rather than their practical importance. In this paper we show that they are the core mathematics underlying best statistical methods of solving noisy ill-posed problems. In particular, we suggest a procedure for recovery of noisy blurred signals based on samples of small sizes where a traditional statistics concludes that the complexity of such a setting makes the problem not worthy of a further study. Thus, we present a problem where a combination of the classical approximation theory and statistics leads to interesting practical results.     

Integrating across Pascal's triangle

Sums across the rows of Pascal's triangle yield n² while certain diagonal sums yield the Fibonacci numbers which are asymptotic to ?n where ? is the golden ratio. Sums across other diagonals yield quantities asymptotic to cn where c depends on the directions of the diagonals. We generalize this to the continuous case. Using the gamma function, we generalize the binomial coefficients to real variables and thus form a generalization of Pascal's triangle. Integration over various families of lines and curves yields quantities asymptotic to cx where c is determined by the family and x is a parameter. Finally, we revisit the discrete case to get results on sums along curves.     

Acoustic metamaterial with negative density

We fabricated a one-dimensional acoustic metamaterial with negative effective density using an array of very thin elastic membranes. We observed acoustic equivalence of the plasma oscillation at ωc=735 Hz. The metamaterial was opaque in the frequency range from 0 to 735 Hz, and was transparent above 735 Hz. We report direct observation of negative acceleration in this acoustic medium below 735 Hz. The frequency characteristics of the metamaterial have the same form as that of metals with negative permittivity. We also provide a simple theory to explain the experimental results.     

Effect of annealing treatment on luminescence property of MgO nanowires

Magnesium oxide nanowires (NWs) were synthesized by a current heating process. The effect of annealing treatment in air on their structural and optical characteristics was investigated. As-grown NWs in diameter ranging from 30 to 70 nm and length up to several 10 μm were obtained. Carbon-coating layers were observed in the as-grown NWs which were oxidized during the annealing treatment at high temperature. Ionoluminescence spectra of the as-grown and annealed NWs have showed two emission peaks centered at 360 nm (UV emission) and 492 nm (green emission). The intensities of green emission were maximum at the annealing temperature of 650 °C for 2 h, whereas those of UV emission were decreased with increasing the annealing temperature. It is anticipated that maximum green emission correlates to the sufficient density of oxygen vacancies which was occurred by the optimum annealing parameters of both temperature and time.