A simple formula for local burnup based on constant relative reaction rate per nuclei

A simple and analytical formula is suggested to solve the problems of the local burnup and the isotope distributions. The present method considers two extreme conditions of neutrons penetrating the fuel rod. Based on these considerations, the formula is obtained to calculate the reaction rates of $^{235}$U, $^{238}$U, and $^{239}$Pu and straightforward the local burnup and the isotope distributions. Starting from an initial burnup level, the parameters of the formula are fitted to the reaction rates given by a Monte Carlo (MC) calculation. Then the present formula independently gives very similar results as the MC calculation from the starting to high burnup level, but takes just a few minutes. The relative reaction rates are found to be almost independent on the radius (except $(n,\gamma)$ of $^{238}$U) and the burnup, providing a solid background for the present formula. A more realistic examination is also performed when the fuel rods locate in an assembly. A combination of the present formula and the MC calculation is expected to have a nice balance on the accuracy and the cost on time

Extremely low scattering cross section of a perforated silver film

With a perforated silver film, we demonstrate that an extremely low scattering cross section with an efficiency of less than 1% can be achieved at tunable wavelengths with tunable widths. The resonance wavelength, width, and intensity are influenced by the size, shape, and arrangement pattern of the holes, as well as the distance separating the holes along the polarization direction. The discovered phenomenon holds promise for the development of photovoltaic devices with improved energy conversion efficiency