A system of parabolic equations in nonequilibrium thermodynamics including thermal and electrical effects

The time-dependent equations for a charged gas or fluid consisting of several components, exposed to an electric field, are considered. These equations form a system of strongly coupled, quasilinear parabolic equations which in some situations can be derived from the Boltzmann equation. The model uses the duality between the thermodynamic fluxes and the thermodynamic forces. Physically motivated mixed Dirichlet-Neumann boundary conditions and initial conditions are prescribed.The existence of weak solutions is proven. The key of the proof is (i) a transformation of the problem by using the entropic variables, or electro-chemical potentials, which symmetrizes the equations, and (ii) a priori estimates obtained by using the entropy function. Finally, the entropy inequality is employed to show the convergence of the solutions to the thermal equilibrium state as the time tends to infinity.     

A Nonlinear Drift - Diffusion System with Electric Convection Arising in Electrophoretic and Semiconductor Modeling

A multi-dimensional transient drift-diffusion model for (at most) three charged particles, consisting of the continuity equations for the concentrations of the species and the Poisson equation for the electric potential, is considered. The diffusion terms depend on the concentrations. Such a system arises in electrophoretic modeling of three species (neutrally, positively and negatively charged) and in semiconductor theory for two species (positively charged holes and negatively charged electrons). Diffusion terms of degenerate type are also possible in semiconductor modeling. For the initial boundary value problem with mixed Dirichlet - Neumann boundary conditions and general reaction rates, a global existence result is proved. Uniqueness of solutions follows in the Dirichlet boundary case if the diffusion terms are uniformly parabolic or if the initial and boundary densities are strictly positive. Finally, we prove that solutions exist which are positive uniformly in time and globally bounded if the reaction rates satisfy appropriate growth conditions.     

Solid-phase synthesis of dihydrovirginiamycin S1, a streptogramin B antibiotic

We describe the first solid-phase synthesis of dihydrovirginiamycin S(1), a member of the streptogramin B family of antibiotics, which are nonribosomal-peptide natural products produced by Streptomyces. These compounds, along with the synergistic group A components, are "last line of defense" antimicrobial agents for the treatment of life-threatening infections such as vancomycin-resistant enterococci. The synthesis features an on-resin cyclization and is designed to allow production of streptogramin B analogues with diversification at positions 1', 1, 2, 3, 4, and 6. Several synthetic challenges known to hinder the synthesis of this class of compounds were solved, including sensitivity to acids and bases, and epimerization and rearrangements, through the judicious choice of deprotection conditions, coupling conditions, and synthetic strategy. This work should enable a better understanding of structure-activity relationships in the streptogramin B compounds, possible identification of analogues that bypass known resistance mechanisms, and perhaps the identification of analogues with novel biological activities.     

Application of non-thermal atmospheric pressure ac plasmas to the carbon dioxide reforming of methane

Methane conversions of 11.9%, yields of hydrogen as high as 23.3% and energy yields of 1.0 mol H₂/kWh have been achieved from CO₂ reforming of CH₄ in non-thermal, atmospheric pressure plasma reactors with Pt coated electrodes. Two reactors have been studied. A novel fan type reactor consisting of a movable rotor and immobile stator produced the highest yields in contrast to a tube type (silent discharge) reactor with a glass dielectric barrier. Conversions, yields of hydrogen and energy yields (expressed as mol H₂/kWh) were studied for CO₂/CH₄ concentrations of 1.1% and 5.0% in He as a function of flow rate and input voltage. Hydrogen yields are observed to increase as the input voltage is increased from 411 V to 911 V and the flow rate is decreased from 100 cc/min to 30 cc/min. Energy yields vary only slightly with input voltage and flow rate. Hydrogen yields show little dependence on CO₂/CH₄ concentrations, but energy yields are approximately five times greater for the 5.0% mixture than the 1.1% mixture. Selectivities to H₂, CO, coke, and low molecular weight hydrocarbons were also evaluated and compared to data obtained without CO₂ in the feed. Hydrogen selectivities of nearly 100% were obtained, with small amounts of ethane and propane as the only observed side products and the selectivites were approximately the same whether CO₂ was present or absent in the mixture. However, the reaction proceeds much more cleanly when CO₂ is present, producing CO. The syngas product has an H₂ : CO ratio of 1.5 with the fan type reactor and 0.67 with the tubular reactor. In the absence of CO₂, coke is the main carbonaceous product. Under all conditions studied the fan type reactor demonstrated higher methane conversions (up to 11.9%) and selectivities to hydrogen.