A class of Hamilton-Jacobi equations on Banach-Finsler manifolds

The concept of subdifferentiability is studied in the context of $C^1$ Finsler manifolds (modeled on a Banach space with a Lipschitz $C^1$ bump function). A class of Hamilton-Jacobi equations defined on $C^1$ Finsler manifolds is studied and several results related to the existence and uniqueness of viscosity solutions are obtained.Comment: 24 page

Microbial Degradation of Gasoline in Soil: Effect of Season of Sampling

In cases where fire debris contains soil, microorganisms can rapidly and irreversibly alter the chemical composition of any ignitable liquid residue that may be present. In this study, differences in microbial degradation due to the season in which the sample is collected was examined. Soil samples were collected from the same site during Fall, Winter, Spring and Summer and the degradation of gasoline was monitored over 30 days. Predominant viable bacterial populations enumerated using real-time PCR and reverse transcriptase polymerase chain reaction (RT-PCR) enumeration revealed the predominant viable bacterial genera to be Alcaligenes, Bacillus, and Flavobacterium. Overall, the compounds most vulnerable to microbial degradation are the n-alkanes, followed by the mono-substituted alkylbenzenes (e.g., toluene, ethylbenzene, propylbenzene and isopropylbenzene). Benzaldehyde (a degradation product of toluene) was also identified as a marker for the extent of biodegradation. Ultimately, it was determined that soil collected during an unusually hot and dry summer exhibited the least degradation with little to no change in gasoline for up to 4 days, readily detectable n-alkanes for up to 7 days and relatively high levels of resilient compounds such as o-xylene, p-xylene and 1,3,5-trimethylbenzene. These results demonstrate, however, that prompt preservation and/or analysis of soil evidence is required in order to properly classify an ignitable liquid residue

Electrokinetic Behaviour and Interaction with Oxalic Acid of Different Hydrous Chromium(III) Oxides

Three samples of hydrous chromium(III) oxide have been prepared by different procedures, and their electrokinetic mobilities have been measured. In mineral media, isoelectric points were found to be 8.45 ±0.15. This value is shifted from the solution isoelectric point by –0.35 ±0.15, due to the contribution of solvation energy to the energy of ionic adsorption. On the basis of a simple model, it is suggested that the two successive surface acidity constants of hydrous chromium(III) oxide are pKS a1 = 7.17 and pKS a2 = 9.72. The influence of oxalic acidity on mobility may be described in terms of two successive adsorption equilibria, the first one conducive to the neutralization of positive protonic charge, and the second one originating a charge reversal. It is shown that the apparent affinity for this latter mode is lower in one of the samples, suggesting that surface complexation constants may in fact be sensitive to the history of hydrous chromium(III) oxide particles. The three samples show similar dissolution behaviour but the specific rates differ, in one case by two orders of magnitude. This difference is explained in terms of the influence of crosslinking on the reactivity

Electrokinetic Behaviour and Interaction with Oxalic Acid of Different Hydrous Chromium(III) Oxides

Three samples of hydrous chromium(III) oxide have been prepared by different procedures, and their electrokinetic mobilities have been measured. In mineral media, isoelectric points were found to be 8.45 ±0.15. This value is shifted from the solution isoelectric point by –0.35 ±0.15, due to the contribution of solvation energy to the energy of ionic adsorption. On the basis of a simple model, it is suggested that the two successive surface acidity constants of hydrous chromium(III) oxide are pKS a1 = 7.17 and pKS a2 = 9.72. The influence of oxalic acidity on mobility may be described in terms of two successive adsorption equilibria, the first one conducive to the neutralization of positive protonic charge, and the second one originating a charge reversal. It is shown that the apparent affinity for this latter mode is lower in one of the samples, suggesting that surface complexation constants may in fact be sensitive to the history of hydrous chromium(III) oxide particles. The three samples show similar dissolution behaviour but the specific rates differ, in one case by two orders of magnitude. This difference is explained in terms of the influence of crosslinking on the reactivity

Anisotropic lattice changes in femtosecond laser inscribed Nd3+:MgO:LiNbO3 optical waveguides

We report on the fabrication and microspectroscopy imaging of femtosecond laser written double-filament based Nd3+ :MgO:LiNbO3 optical waveguides. The waveguiding high refractive-index regions are identified by blueshifts of the Nd3+ ion fluorescence lines with no deterioration in the fluorescence efficiency, whereas filamentary low-index regions are identified by both a Nd3+ line redshift and a fluorescence efficiency reduction. The lattice structural micromodifications at the origin of both waveguide formation and Nd3+ fluorescence changes have been investigated by means of confocal micro-Raman experiments. We have found that the direct laser written filaments are mainly constituted by a large density of defects, together with a marked axial compression perpendicular to the filaments �along the optical c-axis�. Conversely, the high-index waveguiding regions are characterized by a pronounced anisotropic dilatation of the LiNbO3 lattice xy-planes