W eather and climate on Earth are determined by the amount and distribution of incoming radiation from the sun. For an equilibrium climate, OLR1 necessarily balances the incoming ASR, although there is a great deal of fascinating atmosphere, ocean, and land phenomena that couple the two. Incoming radiant energy may be scattered and reflected by clouds and aerosols or absorbed in the atmosphere....

The Lyapunov stability method is the most popular and applicable stability analysis tool of nonlinear dynamic systems. However, there are some bottlenecks in the Lyapunov method, such as need for negative definiteness of the Lyapunov function derivative in the direction of the system’s solutions. In this paper, we develop a new theorem to dispense the need for negative definite-ness of Lyapunov...

The propagation of light in tissue may be calculated by exact transport theory, or the approximate diffusion theory, provided the optical properties are known at the source wavelength. Optical properties for the exact methods are the absorption coefficient, scattering coefficient, and angular distribution of scattering. Appropriate properties for diffusion theory are the diffusion length and di...

Surface scatter effects from residual optical fabrication errors can severely degrade optical performance. The total integrated scatter (TIS) from a given mirror surface is determined by the ratio of the spatial frequency band-limited " relevant " root-mean-square surface roughness to the wavelength of light. For short-wavelength (extreme-ultraviolet/x-ray) applications, even state-of-the-art o...