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The aim of this paper is to present a new kind of numerical processing for hyperbolic systems of conservation laws with source terms. This is achieved by means of a non-conservative reformulation of the zero-order terms of the right-hand side of the equations. In this context, we decided to use the results of Dal Maso, Le Floch and Murat about non-conservative products, and the generalized Roe matrices introduced by Toumi to derive a first-order linearized well-balanced scheme in the sense of Greenberg and Le Roux. As a main feature, this approach is able to preserve the right asymptotic behavior of the original inhomogeneous system, which is not an obvious property. Numerical results for the Euler equations are shown to handle correctly these equilibria in various situations.

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Two systems of hyperbolic equations, arising in the multiphase semiclassical limit of the linear Schrödinger equations, are investigated. One stems from a Wigner measure analysis and uses a closure by the Delta functions, whereas the other relies on the classical WKB expansion and uses the Heaviside functions for closure. The two resulting moment systems are weakly and non-strictly hyperbolic respectively. They provide two different Eulerian methods able to reproduce superimposed signals with a finite number of phases. Analytical properties of these moment systems are investigated and compared. Efficient numerical discretizations and test-cases with increasing difficulty are presented.

Intact cells are the most stable form of nature's photosynthetic machinery. Coating-immobilized microbes have the potential to revolutionize the design of photoabsorbers for conversion of sunlight into fuels. Multi-layer adhesive polymer coatings could spatially combine photoreactive bacteria and algae (complementary biological irradiance spectra) creating high surface area, thin, flexible structures optimized for light trapping, and production of hydrogen (H(2)) from water, lignin, pollutants, or waste organics. We report a model coating system which produced 2.08 +/- 0.01 mmol H(2) m(-2) h(-1) for 4,000 h with nongrowing Rhodopseudomonas palustris, a purple nonsulfur photosynthetic bacterium. This adhesive, flexible, nanoporous Rps. palustris latex coating produced 8.24 +/- 0.03 mol H(2) m(-2) in an argon atmosphere when supplied with acetate and light. A simple low-pressure hydrogen production and trapping system was tested using a 100 cm(2) coating. Rps. palustris CGA009 was combined in a bilayer coating with a carotenoid-less mutant of Rps. palustris (CrtI(-)) deficient in peripheral light harvesting (LH2) function. Cryogenic field emission gun scanning electron microscopy (cryo-FEG-SEM) and high-pressure freezing were used to visualize the microstructure of hydrated coatings. A light interaction and reactivity model was evaluated to predict optimal coating thickness for light absorption using the Kubelka-Munk theory (KMT) of reflectance and absorptance. A two-flux model predicted light saturation thickness with good agreement to observed H(2) evolution rate. A combined materials and modeling approach could be used for guiding cellular engineering of light trapping and reactivity to enhance overall photosynthetic efficiency per meter square of sunlight incident on photocatalysts.

Nonuniform light distribution is a fundamental limitation to biological hydrogen production by phototrophic bacteria. Numerous light distribution designs and culture conditions have been developed to reduce self-shading and nonuniform reactivity within bioreactors. In this study, highly concentrated (2.0 x 108 CFU/muL formulation) nongrowing Rhodopseudomonas palustris CGA009 were immobilized in thin, nanoporous, latex coatings. The coatings were used to study hydrogen production in an argon atmosphere as a function of coating composition, thickness, and light intensity. These coatings can be generated aerobically or anaerobically and are more reactive than an equivalent number of suspended or settled cells. Rhodopseudomonas palustris latex coatings remained active after hydrated storage for greater than 3 months in the dark and over 1 year when stored at -80 degrees C. The initial hydrogen production rate of the microphotobioreactors containing 6.25 cm2, 58.4 mum thick Rps. palustris latex coatings illuminated by 34.1 PAR mumol photons m-2 s-1 was 6.3 mmol H2 m-2 h-1 and had a final yield of 0.55 mol H2 m-2 in 120 h. A dispersible latex blend has been developed for direct comparison of the specific activity of settled, suspended, and immobilized Rps. palustris.