Unified Homogenization Theory for Magnetoinductive and Electromagnetic Waves in Split Ring Metamaterials

A unified homogenization procedure for split ring metamaterials taking into account time and spatial dispersion is introduced. The procedure is based on two coupled systems of equations. The first one comes from an approximation of the metamaterial as a cubic arrangement of coupled LC circuits, giving the relation between currents and local magnetic field. The second equation comes from macroscopic Maxwell equations, and gives the relation between the macroscopic magnetic field and the average magnetization of the metamaterial. It is shown that electromagnetic and magnetoinductive waves propagating in the metamaterial are obtained from this analysis. Therefore, the proposed time and spatially dispersive permeability accounts for the characterization of the complete spectrum of waves of the metamaterial. Finally, it is shown that the proposed theory is in good quantitative and qualitative agreement with full wave simulations.Comment: 4 pages, 3 figure

Is a night better than a day: Empirical evidence

In this study, we analyze the portfolio allocation based on time asymmetry of stock characteristics. In particular, we analyzed the empirical data of changes in financial stock prices during the day period and during the night period and have found that characteristics such as mean and variance are different for changes during the day and changes during the night. Also, the portfolio characteristics, such as covariance between stocks, differ on whether we take into account day changes or night changes in prices. That greatly affects the allocation of fund to the portfolio for an investor who trades frequently. The portfolio should be re-balanced every day in order to achieve optimality and much higher return. At the same level of risk the returns on this new portfolio may by several times larger than the returns on a portfolio without everyday re-balancing. We computed numerically the allocation of funds for the stocks from the finance industry and showed that the increase in returns is substantial