Singularities in cascade models of the Euler equation

The formation of singularities in the three-dimensional Euler equation is investigated. This is done by restricting the number of Fourier modes to a set which allows only for local interactions in wave number space. Starting from an initial large-scale energy distribution, the energy rushes towards smaller scales, forming a universal front independent of initial conditions. The front results in a singularity of the vorticity in finite time, and has scaling form as function of the time difference from the singularity. Using a simplified model, we compute the values of the exponents and the shape of the front analytically. The results are in good agreement with numerical simulations.     

A solution of the DGLAP equation for gluon at low x

We obtain a solution of the DGLAP equation for the gluon at low x first by expanding the gluon in a Taylor series and then using the method of characteristics. We test its validity by comparing it with that of Glück, Reya and Vogt. The convergence criteria of the approximation used are also discussed. We also calculate εF ₂(x,Q)²/ε In Q ² using its approximate relations with the gluon distribution at low x. The predictions are then compared with the HERA data.     

Der Einfluß von Grenzflächenerscheinungen auf den Stoffübergang und die Prozeßführung in Gegenstromkolonnen mit überkritischem CO2

Zusammenfassung Mittels des Einsatzes einer Hochdrucksichtzelle wurden Eigenschaften der Kontaktbereiche in Trennverfahren mit unterschiedlichen wäßrigen Lösungen und CO₂ unter hohen Drücken untersucht. Die Methode des hängenden Tropfens wurde zur Messung der Grenzflächenspannung bis zu Drücken von 280 bar angewandt. Der mit dem Druck abnehmende Verlauf weist nach der Gibbs'schen Theorie auf die Anreicherung von CO₂ in der Phasengrenze. Weiterhin wurde die für Packungskolonnen bedeutsame Feststoffbenetzung in Abhängigkeit von Druck und Oberflächenbeschaffenheit des Feststoffes untersucht. Der die Feststoffbenetzung charakterisierende Kontaktwinkel wurde mittels der Methode der gekippten Platte vermessen und ergab eine schlechtere Benetzung bei höheren Drücken und glatten Stahloberflächen.

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The effect of interfacial phenomena on mass transport and performance of separations in countercurrent columns with supercritical CO₂

Interfacial phenomena affecting countercurrent separation processes have been studied in systems containing aqueous solutions and CO₂ at elevated pressures by means of a high pressure optical cell. The pendant drop method was applied in order to measure the interfacial tension up to 280 bar. The decreasing course as a function of the pressure is due to the adsorption of CO₂ at the interface according to Gibbs' law. Further, wetting characteristics have been investigated as they are of considerable importance to packed columns. Therefore, the contact angle was determined by the method of the tilting plate and came out to increase with pressure and smoothness of the solid surface, indicating the loss of wettability.

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Electrophilic fluorinating reagent mediated synthesis of fluorinated alpha-keto Ethers,benzil, and 6,6'-dialkoxy-2,2'-bipyridines

Interactions of various fluorinated and nonfluorinated alcohols with trans-stilbene in the presence of electrophilic reagents were studied. Under neat conditions, reactions of trans-stilbene (1) with fluorinated alcohols, R(f)OH (R(f) = CF3CH2-, CFH2CH2-, CF3CF2CH2-, CF2H(CF2)3CH2-, (CF3)2CH-, (CF3)3C- (2a-f) in the presence of an electrophilic reagent, 1-(chloromethyl)-4-fluoro-1,4-diazoniabicyclo[2.2.2]octane bis(tetrafluoroborate) (Selectfluor) or N,N-difluoro-2,2'-bipyridinium bis(tetrafluoroborate) (MEC-31), gave alpha-keto ethers (3a-f) and benzil (4) in good to moderate yields. alpha-Keto ether and benzil formation was very much dependent on the reaction time, the degree of fluorination of the alcohols, and whether a solvent such as CH3CN, DMF or DMA was utilized. In solution, alpha-keto ethers and benzil did not form. Interestingly, under neat conditions, nonfluorinated alcohols, ROH (R = CH3-, CH3CH2-, CH3CH2CH2-, CH3CH2CH2CH2-, CH3CH2CH2CH2CH2CH2-) (5g-k) did not react with trans-stilbene in the presence of MEC-31 but gave 6,6'-dialkoxy-2,2'-bipyridines (6g-k), regioselectively, in excellent isolated yields. On the other hand, fluorinated alcohols did not react with MEC-31. Reaction of MEC-31 with an excess of diethylene glycol (7) gave the bipyridine derivative (8) in 88% isolated yield. Reaction of 8 either with diethylaminosulfur trifluoride (DAST) or bis(2-methoxyethyl)aminosulfur trifluoride (Deoxofluor) readily produced the corresponding difluoro derivative (9) in 85% isolated yield. All new compounds have been characterized by spectroscopic and elemental analysis.     

Development and validation of a LC/TOF MS method for the determination of carboplatin and paclitaxel in nanovesicles

Carboplatin and paclitaxel co-loaded nanovesicles (CPT-PTX-CLV), a novel intravenous formulation void of cremophor EL, may have significant advantages over conventional carboplatin and paclitaxel formulations with respect to tumor targeting, sustained drug release, reduced toxicity, and synergistic efficacy profiles. The aim of this study was to develop and validate a rapid, specific, sensitive, and reliable liquid chromatography–time of flight–mass spectrometry (LC/TOF MS)-based bioanalytical method for the simultaneous quantification of CPT and PTX in a fetal bovine serum (FBS) vehicle containing the dispersed nanovesicles. The analytes were extracted from FBS by simple protein precipitation, with subsequent separation of CPT and PTX on a Waters HPLC SunFire C₁₈ column at a flow rate of 0.25 ml/min using gradient elution mode. The total analytical time was only 12 min. Detection and quantitation was performed by electrospray ionization (ESI) in the positive ionization mode with selective ion monitoring (SIM) at m/z 310.0152 for CPT and 876.3224 for PTX. The calibration curves were linear over the concentration range of 10–4,000 ng/ml for CPT and 5–2,000 ng/ml for PTX (r ² ?>?0.99), with the respective lower limit of quantification (LLOQ) at 10 and 5 ng/ml. The intra- and inter-day precision and accuracy of analysis of the quality control samples at low, medium, and high concentration levels were ≤13.6 % relative standard deviation (RSD) and ≤14.6 % relative errors (RE). The rapid, sensitive, and reproducible LC/TOF MS method may be used to support preclinical and clinical pharmacological studies of the CPT-PTX-CLV administered by injection in animal and human cancer models.

Vibration-induced climbing of drops

We report an experimental study of liquid drops moving against gravity, when placed on a vertically vibrating inclined plate, which is partially wetted by the drop. The frequency of vibrations ranges from 30 to 200 Hz, and, above a threshold in vibration acceleration, drops experience an upward motion. We attribute this surprising motion to the deformations of the drop, as a consequence of an up or down symmetry breaking induced by the presence of the substrate. We relate the direction of motion to contact angle measurements. This phenomenon can be used to move a drop along an arbitrary path in a plane, without special surface treatments or localized forcing.