Sound Mode Hydrodynamics from Bulk Scalar Fields

We study the hydrodynamic sound mode using gauge/gravity correspondence by examining a generic black brane background's response to perturbations. We assume that the background is generated by a single scalar field, and then generalize to the case of multiple scalar fields. The relevant differential equations obeyed by the gauge invariant variables are presented in both cases. Finally, we present an analytical solution to these equations in a special case; this solution allows us to determine the speed of sound and bulk viscosity for certain special metrics. These results may be useful in determining sound mode transport coefficients in phenomenologically motivated holographic models of strongly coupled systems.Comment: 17 pages. Corrections made to one of the gauge invariant equations (66). This equation was not used in the other main conclusions of the paper, so the rest of the results are unchange

Numerical simulation of the flow and fuel-air mixing in an axisymmetric piston-cylinder arrangement

The implicit factored method of Beam and Warming was employed to describe the flow and the fuel-air mixing in an axisymmetric piston-cylinder configuration during the intake and compression strokes. The governing equations were established on the basis of laminar flow. The increased mixing due to turbulence was simulated by appropriately chosen effective transport properties. Calculations were performed for single-component gases and for two-component gases and for two-component gas mixtures. The flow field was calculated as functions of time and position for different geometries, piston speeds, intake-charge-to-residual-gas-pressure ratios, and species mass fractions of the intake charge. Results are presented in graphical form which show the formation, growth, and break-up of those vortices which form during the intake stroke and the mixing of fuel and air throughout the intake and compression strokes. It is shown that at bore-to-stroke ratio of less than unity, the vortices may break-up during the intake stroke. It is also shown that vortices which do not break-up during the intake stroke coalesce during the compression stroke. The results generated were compared to existing numerical solutions and to available experimental data

Vortex motion in axisymmetric piston-cylinder configurations

By using the Beam and Warming implicit-factored method of solution of the Navier-Stokes equations, velocities were calculated inside axisymmetric piston cylinder configurations during the intake and compression strokes. Results are presented in graphical form which show the formation, growth and breakup of those vortices which form during the intake stroke by the jet issuing from the valve. It is shown that at bore-to-stroke ratio of less than unity, the vortices may breakup during the intake stroke. It is also shown that vortices which do not breakup during the intake stroke coalesce during the compression stroke

Black holes admitting a Freudenthal dual

The quantised charges x of four dimensional stringy black holes may be assigned to elements of an integral Freudenthal triple system whose automorphism group is the corresponding U-duality and whose U-invariant quartic norm Delta(x) determines the lowest order entropy. Here we introduce a Freudenthal duality x -> \tilde{x}, for which \tilde{\tilde{x}}=-x. Although distinct from U-duality it nevertheless leaves Delta(x) invariant. However, the requirement that \tilde{x} be integer restricts us to the subset of black holes for which Delta(x) is necessarily a perfect square. The issue of higher-order corrections remains open as some, but not all, of the discrete U-duality invariants are Freudenthal invariant. Similarly, the quantised charges A of five dimensional black holes and strings may be assigned to elements of an integral Jordan algebra, whose cubic norm N(A) determines the lowest order entropy. We introduce an analogous Jordan dual A*, with N(A) necessarily a perfect cube, for which A**=A and which leaves N(A) invariant. The two dualities are related by a 4D/5D lift.Comment: 32 pages revtex, 10 tables; minor corrections, references adde

Second order hydrodynamics for a special class of gravity duals

The sound mode hydrodynamic dispersion relation is computed up to order $q^3$ for a class of gravitational duals which includes both Schwarzschild $AdS$ and Dp-Brane metrics. The implications for second order transport coefficients are examined within the context of Israel-Stewart theory. These sound mode results are compared with previously known results for the shear mode. This comparison allows one to determine the third order hydrodynamic contributions to the shear mode for the class of metrics considered here.Comment: 20 page

In vitro gas production as a surrogate measure of the fermentability of cellulosic biomass to ethanol

Current methods for measuring ethanol yields from lignocellulosic biomass are relatively slow and are not well geared for analyzing large numbers of samples generated by feedstock management and breeding research. The objective of this study was to determine if an in vitro ruminal fermentation assay used in forage quality research was predictive of results obtained using a conventional biomass-to-ethanol conversion assay. In the conventional assay, herbaceous biomass samples were converted to ethanol by Saccharomyces cerevisiae cultures in the presence of cellulase enzymes. Cultures were grown in sealed serum bottles and gas production monitored by measuring increasing head space pressure. Gas accumulation as calculated from the pressure measurements was highly correlated (r2\u3e0.9) with ethanol production measured by gas chromatography at 24 h or 7 days. The same feedstocks were also analyzed by in vitro ruminal digestion, as also measured by gas accumulation. Good correlations (r2∼0.63–0.82) were observed between ethanol production during simultaneous saccharification and fermentation and gas accumulation in parallel in vitro ruminal fermentations. Because the in vitro ruminal fermentation assay can be performed without sterilization of the medium and does not require aseptic conditions, this assay may be useful for biomass feedstock agronomic and breeding research

The ultraviolet limit and sum rule for the shear correlator in hot Yang-Mills theory

We determine a next-to-leading order result for the correlator of the shear stress operator in high-temperature Yang-Mills theory. The computation is performed via an ultraviolet expansion, valid in the limit of small distances or large momenta, and the result is used for writing operator product expansions for the Euclidean momentum and coordinate space correlators as well as for the Minkowskian spectral density. In addition, our results enable us to confirm and refine a shear sum rule originally derived by Romatschke, Son and Meyer.Comment: 16 pages, 2 figures. v2: small clarifications, one reference added, published versio

Generalized Robba rings

We prove that any projective coadmissible module over the locally analytic distribution algebra of a compact $p$-adic Lie group is finitely generated. In particular, the category of coadmissible modules does not have enough projectives. In the Appendix a "generalized Robba ring" for uniform pro-$p$ groups is constructed which naturally contains the locally analytic distribution algebra as a subring. The construction uses the theory of generalized microlocalization of quasi-abelian normed algebras that is also developed there. We equip this generalized Robba ring with a self-dual locally convex topology extending the topology on the distribution algebra. This is used to show some results on coadmissible modules.Comment: with an appendix by Peter Schneider; revised; new titl

Influence of Nitrogen Fertilization on the Quality and Quantity of Streamflow from a Forested Watershed

This project was designed to determine the effects of nitrogen fertilization on the quality and quantity of streamflow eminating from an eastern hardwood forest watershed. A 40.67 ha watershed, located in mountainous eastern Kentucky, was aerially fertilized in late April 1975. The forest stand was principally oak, hickory, and yellow poplar, 50 - 55 years of age and in a relatively undisturbed condition. A helicopter applied anunonium nitrate at a rate of 504 kg/ha. Because a large part of applied nitrogen fertilizer ends up in the highly mobile nitrate nitrogen.form, this is the principal ion monitored in this study. No effort was made to avoid live streams during application and, consequently, very high levels of nitrate nitrogen were detected (640 mg/1) in streamfiow within the watershed. Levels potentially toxic to humans and animals persisted in the streamflow for several days following application. Although elevated concentrations of nitrate nitrogen persisted in streamflow leaving the watershed over a two year period no algal blooms or excessive growth of aquatic plants were noted. Rather high concentrations of nitrate nitrogen were found in the soils of the watershed, with greatest concentrations in the surface layer (0 - 5 cm), intermediate amounts at 15 - 20 cm, and the lowest concentrations at the 41 - 46 cm depth. The effects of the fertilizer application on soils persisted less than one year in the 0 - 46 cm depth sampled. Analysis of streamf1ow records indicated a reduction in water yield the first and second growing seasons after treatment. Gross budgeting of nitrate nitrogen inputs vs. outputs suggests this anion accumulates on these relatively undisturbed watersheds at an annual rate of 3 to 5 kg/ha