Expected Reflection Distance in G(r, 1, n) after a Fixed Number of Reflections

Extending to r > 1 a formula of the authors, we compute the expected reflection distance of a product of t random reflections in the complex reflection group G(r, 1, n). The result relies on an explicit decomposition of the reflection distance function into irreducible G(r, 1, n)-characters and on the eigenvalues of certain adjacency matrices.Received December 8, 2003     

Whirling frequencies and amplitudes due to deviations of generator shape

Earlier measurements in large synchronous generators indicate the existence of backward whirling motion, and also relatively large deviations of shape in both the rotor and the stator. These non-symmetric geometries produce an attraction force between the rotor and the stator, called unbalanced magnetic pull (UMP). The target of this paper is to analyse the whirling frequencies and amplitude of the response for large synchronous generators with a high number of poles, due to deviations of shape in the rotor and stator. A mathematical model is developed to describe the shapes of the rotor and stator, and the corresponding UMP is obtained by using the law of energy conservation. The UMP is analysed due to different deviations of shape. The result gives the average angular frequency and the magnitude of the UMP for certain deviations of shape. From this result, the whirling frequency and the amplitude of the corresponding response can be approximated. Simulations of the response of a Jeffcott rotor model show good agreement with the theoretical results of the UMP for some generator geometries. The conclusion is that different whirling frequencies, both backward and forward whirling, can occur in these machines due to deviations in shape of the generator. Therefore, the shape of the generator can excite resonance vibrations on several other frequencies than the rotation frequency. During maintenance of hydropower generators the shapes of the rotor and stator are frequently measured. The results from this paper can be used to evaluate such measurements and to explain the existence of complicated whirling motion.     

Optimisation and robustness analysis of a hydrophobic interaction chromatography step

Process development, optimisation and robustness analysis for chromatography separations are often entirely based on experimental work and generic knowledge. The present study proposes a method of gaining process knowledge and assisting in the robustness analysis and optimisation of a hydrophobic interaction chromatography step using a model-based approach. Factorial experimental design is common practice in industry today for robustness analysis. The method presented in this study can be used to find the critical parameter variations and serve as a basis for reducing the experimental work. In addition, the calibrated model obtained with this approach is used to find the optimal operating conditions for the chromatography column. The methodology consists of three consecutive steps. Firstly, screening experiments are performed using a factorial design. Secondly, a kinetic-dispersive model is calibrated using gradient elution and column load experiments. Finally, the model is used to find optimal operating conditions and a robustness analysis is conducted at the optimal point. The process studied in this work is the separation of polyclonal IgG from BSA using hydrophobic interaction chromatography.     

Crystalline Morphology and Polymorphic Phase Transitions in Electrospun Nylon 6 Nanofibers

Uniform nylon 6 nanofibers with diameters around 200 nm were prepared by electrospinning. Polymorphic phase transitions and crystal orientation of nylon 6 in unconfined (i.e., as-electrospun) and a high T(g) (340 degrees C) polyimide confined nanofibers were studied. Similar to melt-spun nylon 6 fibers, electrospun nylon 6 nanofibers also exhibited predominant, meta-stable gamma crystalline form, and the gamma-crystal (chain) axes preferentially oriented parallel to the fiber axis. Upon annealing above 150 degrees C, gamma-form crystals gradually melted and recrystallized into the thermodynamically stable alpha-form crystals, which ultimately melted at 220 degrees C. Release of surface tension accompanied this melt-recrystallization process, as revealed by differential scanning calorimetry. For confined nanofibers, both the melt-recrystallization and surface tension release processes were substantially depressed; gamma-form crystals did not melt and recrystallize into alpha-form crystals until 210 degrees C, only 10 degrees C below the T(m) at 220 degrees C. After complete melting of nano-confined crystals at 240 degrees C and recrystallization at 100 degrees C, only alpha-form crystals oriented perpendicular to the nanofiber axis were obtained. In the polyimide-confined nanofibers, the Brill transition (from the monoclinic alpha-form to a high temperature monoclinic form) was observed at 180-190 degrees C, which was at least 20 degrees C higher than that in unconfined nylon 6 at approximately 160 degrees C. This, again, was attributed to the confinement effect.     

Synthesis of Optically Active endo,endo Bicyclo[2.2.2]octane-2,5-diol, Bicyclo[2.2.2]octane-2,5-dione, and Related Compounds

Optically active C(2)-symmetric (1S,2S,4S,5S)-bicyclo[2.2.2]octane-2,5-diol ((+)-12; 98% ee) and several selectively protected optically active intermediates useful for synthetic transformations were synthesized via a 1,2-carbonyl transposition route starting from the easily available optically active (1R,4S,6S)-6-hydroxybicyclo[2.2.2]octan-2-one ((-)-2). The synthetic route also allowed the preparation of optically active (1S,4S)-bicyclo[2.2.2]octane-2,5-dione ((+)-14; 98% ee).     

Synthesis of 2,3′-biindolyls and indolo[3,2-a]carbazoles

Several highly activated 2,3′-biindolyls were prepared from methyl 5,6-dimethoxyindole-2-carboxylate and oxindoles. The 2,3′-biindolyls were further transformed into a hydroxy indolo[3,2-a]carbazole and a bisindole amide.     

Charge recombination fluorescence in photosystem I reaction centers from Chlamydomonas reinhardtii

The fluorescence kinetics of photosystem I core particles from Chlamydomonas reinhardtii have been measured with picosecond resolution in order to test a previous hypothesis suggesting a charge recombination mechanism for the early electron-transfer steps and the fluorescence kinetics (Müller et al. Biophys. J. 2003, 85, 3899-3922). Performing global target analyses for various kinetic models on the original fluorescence data confirms the "charge recombination" model as the only acceptable one of the models tested while all of the other models can be excluded. The analysis allowed a precise determination of (i) the effective charge separation rate constant from the equilibrated reaction center excited state (438 ns(-1)) confirming our previous assignment based on transient absorption data (Müller et al. Biophys. J. 2003, 85, 3899-3922), (ii) the effective charge recombination rate constant back to the excited state (52 ns(-1)), and (iii) the intrinsic secondary electron-transfer rate constant (80 ns(-1)). The average energy equilibration lifetime core antenna/RC is about 1 ps in the "charge recombination" model, in agreement with previous transient absorption data, vs the 18-20 ps energy transfer lifetime from antenna to RC within "transfer-to-the-trap-limited" models. The apparent charge separation lifetime in the recombination model is about three times faster than in the "transfer-to-the-trap-limited" model. We conclude that the charge separation kinetics is trap-limited in PS I cores devoid of red antenna states such as in C. reinhardtii.