A Numerical Method for a Nonlinear Singularly Perturbed Interior Layer Problem Using an Approximate Layer Location

A class of nonlinear singularly perturbed interior layer problems is examined in this paper. Solutions exhibit an interior layer at an a priori unknown location. A numerical method is presented that uses a piecewise uniform mesh refined around approximations to the first two terms of the asymptotic expansion of the interior layer location. The first term in the expansion is used exactly in the construction of the approximation which restricts the range of problem data considered. The method is shown to converge point-wise to the true solution with a first order convergence rate (overlooking a logarithmic factor) for sufficiently small values of the perturbation parameter. A numerical experiment is presented to demonstrate the convergence rate established

Analysis of Water Footprint of a Photobioreactor Microalgae Biofuel 1 Production System from Blue, Green and Lifecycle Perspectives

Microalgae are currently being investigated as a feedstock for the commercial production of transportation fuels, due to their potential scalability and sustainability advantages over conventional feedstocks. The water consumption of microalgae has been postulated to be a resource barrier for large-scale production. This study presents an assessment of the water footprint (WF) of a closed photobioreactor-based biofuel production system, where microalgae cultivation is simulated with geographical and temporal resolution. The assessment focuses on the WF as modeled for four different fuel conversion pathways, and in 10 continental US locations corresponding to high productivity yields. The WF is comprehensively assessed using a hybrid approach which combines process and economic input-output lifecycle analysis method, using three metrics: blue, green and lifecycle WF. Results show that the blue WF of microalgae biofuels varies between 23 and 85 m3·GJ-1 depending on process and geographic location. The green WF shows that microalgae cultivation may reduce the required local water withdrawals. Water credits from the co-products vary with allocation methods and end uses, from credits of less than 4 m3·GJ-1 up to credits of 334 m3·GJ- 1. Results for the net lifecycle WF with coproduct credits varies between 80 and -291 m3·GJ-1. Discussion focuses on the sensitivity of microalgae biofuels WF and highlights potential local and national strain of water resources relative to other fuels and biofuels

Into the third dimension: stochastic measurements of Stokes parameters within the Poincar\'e sphere

Inspired by recent use of polarimetry to study the Cosmic Microwave Background and extragalatic supernovae, a foray into the statistical properties of Stokes parameters expressed in spherical coordinates is began, allowing circular polarization and linear polarization to be treated in a unified manner. The use of spherical coordinates is quite necessary as it permits a Stokes polarization state to be expressed in terms of the customary polarization angles and degree of polarization usually needed for human interpretation. As shall be demonstrated, circular and linear polarization are not statistically independent quantities but intertwined in a way that is especially important, for instance, at low signal-to-noise. New distributions, classical estimators, and marginalizations are presented for this "three-dimensional" polarization problem including a generalization of the Rice distribution. The paper concludes with discussion regarding the potential pitfalls of a lower dimensional analysis.Comment: 8 pages, 3 figure