Hartogs Phenomena and Antisyzygies for Systems of Differential Equations

We introduce the notion of antisyzygies, which studies the inverse problem of finding a system of PDEs, given compatibility conditions. The system obtained possesses the property of removability of compact singularities. We write explicit computations in the cases of the Cauchy-Fueter system and Maxwell’s system for electromagnetism, and we conclude with a study of systems of non-maximal rank.      

Measurement and analysis of the dextran partition coefficient in sucrose crystallization

The effect of crystallization conditions on the dextran partition coefficient between impure syrup and sugar crystal has been investigated in a batch crystallizer. The crystallizer is operated isothermally at temperatures of 30, 40, and 50 °C, at constant relative supersaturations of 0.05, 0.07, and 0.09, and with mother liquor dextran concentrations of 1000 and 2000 ppm/Brix. The dextran content has been determined by the CSR method. A 1:1 mass ratio of high-fraction dextran (approximately 250,000 Da) and low-fraction dextran (60,000-90,000 Da) is used to represent a wide range of dextran contamination. It is seen that the dextran partition coefficient in sucrose crystallization increases with both increasing supersaturation and increasing crystallization temperature. However it appears that these are secondary effects, with the partition coefficient strongly correlating with crystal growth rate alone, despite the regressed data having large variations in temperature, mother liquor dextran content, and supersaturation. Dextran incorporation into the sugar crystal results from both dextran adsorption onto the crystal surface and mother liquor inclusions. The explanation for the variation in the dextran content in sugar crystal with respect to the growth rate is due to increased adsorption due to the higher surface roughness of crystals grown at high growth rates. Although the dextran concentration in the solution affects the dextran content in the crystal, it does not strongly affect the dextran partition coefficient.     

Novel light-fluorous TEMPO reagents and their application in oxidation reactions

The synthesis of two light-fluorous TEMPO derivatives is reported, along with their application in oxidation reactions.     

The enhancement of oxygen flux on Ba0.5Sr0.5Co0.8Fe0.2O3−δ (BSCF) hollow fibers using silver surface modification

Ba_0.5Sr_0.5Co_0.8Fe_0.2O_3−δ (BSCF) hollow fibers were fabricated using a phase inversion/sintering method. As oxygen permeation of BSCF hollow fibers is controlled by the rate surface exchange kinetics, catalytic Ag particles were coated on both inner and outer surfaces using chemical deposition method, as verified by SEM and EDX. The Ag coated BSCF membranes showed up to 100% increase in oxygen permeation at 700 °C, and improvements lower than 10% were measured at 950 °C as compared with unmodified membranes. It was found that Ag catalyst surface loading was non-homogenous and concentrated on the perovskite grain boundaries. As a result, lighter Ag surface loading delivered improved oxygen flux while oxygen flux reached a maximum even though in the presence of excess catalyst loading. The catalytic activity of Ag was beneficial in enhancing surface reaction kinetics up to 850 °C attributed to the spillover effect. Above this temperature, the increase in oxygen permeation rate was marginally diminished due to the reduction of the spillover effect.     

Synthesis and Characterization of Dinuclear Ruthenium(II) Complexes Based on 4,4′‐Bipyridyl Type Bridging Ligands

The synthesis, spectroscopic, electrochemical and photophysical characterization of a series of dinuclear ruthenium(II) complexes of the type [(bpy)₂Ru(NnN)₂RuCl(bpy)₂](PF₆)₃, where NnN = 4,4′‐bipyridyl (N0N), 1,2‐bis(4‐pyridyl)ethylene (NEN), 1,2‐bis(4‐pyridyl)ethane (N2N), and 4,4′‐trimethylenedipyridine (N3N) are reported. The photophysical and electrochemical properties are discussed with particular emphasis on the ability of the bridging ligands to support intercomponent interaction.     

High resolution measurement of turbulent structure in a channel with particle image velocimetry

High resolution particle image velocimetry is used to measure the turbulent velocity field for fully developed flow (Re = 2,872) in an enclosed channel. Photographs of particle displacement are obtained in a plane that is parallel to the flow and perpendicular to the walls. These are analyzed to give simultaneous measurements of two components of the velocity at more than 10,000 points. Maps of velocity vectors, spanwise vorticity and Reynolds stress reveal structural aspects of the turbulence. In particular, internal shear layers are observed, in agreement with predictions of direct numerical simulation. Ensemble-averaging of a number of photographs yields statistical properties of the velocity in good agreement with laser-Doppler velocimeter measurements, and with direct numerical simulations.