Symmetries and exact solutions of KP equation with an arbitrary nonlinear term

The generalized KP (GKP) equations with an arbitrary nonlinear term model and characterize many nonlinear physical phenomena. The symmetries of GKP equation with an arbitrary nonlinear term are obtained. The condition that must satisfy for existence the symmetries group of GKP is derived and also the obtained symmetries are classified according to different forms of the nonlinear term. The resulting similarity reductions are studied by performing the bifurcation and the phase portrait of GKP and also the corresponding solitary wave solutions of GKP
equation are constructed.

A developed stage of Alfven wave phase mixing

Alfven wave phase mixing is an extensively studied mechanism for dissipating wave energy in an inhomogeneous medium. It is common in the vast majority of phase mixing papers to assume that even though short scale lengths and steep gradients develop as a result of phase mixing, nonlinear wave coupling does not occur. However, weakly nonlinear studies have shown that phase mixing generates magnetoacoustic modes. Numerical results are presented which show the nonlinear generation of magnetosonic waves by Alfven wave phase mixing. The efficiency of the effect is determined by the wave amplitude, the frequency of the Alfven waves and the gradient in the background Alfven speed. Weakly nonlinear theory has shown that the amplitude of the fast magnetosonic wave grows linearly in time. The simulations presented in this paper extend this result to later times and show saturation of the fast magnetosonic component at amplitudes much lower than that of the Alfven wave. For the case when Alfven waves are driven at the boundary, simulating photospheric footpoint motion, a clear modulation of the saturated amplitude is observed. All the results in this paper are for a low amplitude (less than or equal to 0.1), single frequency Alfven wave and a uniform background magnetic field in a two dimensional domain. For this simplified geometry, and with a monochromatic driver, we concluded that the nonlinear generation of fast modes has little effect on classical phase mixing.

Observation of stable phase jump lines in convection of a twisted nematic liquid crystal

We report observations of stable, localized, linelike structures in the spatially periodic pattern formed by nematic electroconvection, along which the phase of the pattern jumps by pi. With increasing electric voltage, these lines form a gridlike structure that goes over into a structure indistinguishable from the well-known grid pattern. We present theoretical arguments that suggest that the twisted cell geometry we are using is indirectly stabilizing the phase jump lines, and that the phase jump lines lattice is caused by an interaction of phase jump lines and a zig-zag instability of the surrounding pattern.

Two-phase flow regimes in microchannels

Capillary hydrodynamics has three considerable distinctions from macrosystems: first, there is an increase in the ratio of the surface area of the phases to the volume that they occupy; second, a flow is characterized by small Reynolds numbers at which viscous forces predominate over inertial forces; and third, the microroughness and wettability of the wall of the channel exert a considerable influence on the flow pattern. In view of these differences, the correlations used for tubes with a larger diameter cannot be used to calculate the boundaries of the transitions between different flow regimes in microchannels. In the present review, an analysis of published data on a gas-liquid two-phase flow in capillaries of various shapes is given, which makes it possible to systematize the collected body of information. The specific features of the geometry of a mixer and an inlet section, the hydraulic diameter of a capillary, and the surface tension of a liquid exert the strongest influence on the position of the boundaries of two-phase flow regimes. Under conditions of the constant geometry of the mixer, the best agreement in the position of the boundaries of the transitions between different hydrodynamic regimes in capillaries is observed during the construction of maps of the regimes with the use of the Weber numbers for a gas and a liquid as coordinate axes.

Palladium-catalyzed liquid-phase hydrogenation/hydrogenolysis of disulfides

For the first time, the hydrogenation/hydrogenolysis of a range of disulfides has been achieved over a supported palladium catalyst using hydrogen under relatively benign conditions. These unexpected results demonstrate that it is possible to avoid the poisoning of the catalyst by either the nitrogen-containing groups or the sulfur species, allowing both efficient reaction and recycling of the catalyst under the proper conditions (e.g., at low temperatures). A slight loss in activity was found on recycling; however, the catalyst activity can be recovered using hydrogen pretreatment. The reaction mechanism for the hydrogenolysis and hydrogenation of ortho-, meta-, and para-dinitrodiphenyldisulfide to the corresponding aminothiophenol has been elucidated. Density functional theory calculations were used to investigate the adsorption mode of the dinitrodiphenyldisulfides; a clear dependence on adsorption geometry was found regarding whether the molecule is cleaved at the S-S bond before the reduction of the nitro group or vice versa. This study demonstrates the versatility of these catalysts for the hydrogenation/hydrogenolysis of sulfur-containing molecules, which normally are considered poisons, and will extend their use to a new family of substrates. (C) 2007 Elsevier Inc. All rights reserved.

Use of Short Time-on-Stream Attenuated Total Internal Reflection Infrared Spectroscopy To Probe Changes in Adsorption Geometry for Determination of Selectivity in the Hydrogenation of Citral

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A new experimental procedure based on attenuated total reflection infrared spectroscopy has been developed to investigate surface species under liquid phase reaction conditions. The technique has been tested by investigating the enhanced selectivity in the hydrogenation of α,β-unsaturated aldehyde citral over a 5% Pt/SiO2 catalyst toward unsaturated alcohols geraniol/nerol, which occurs when citronellal is added to the reaction. The change in selectivity is proposed to be the result of a change in the citral adsorption mode in the presence of citronellal. Short time on stream attenuated total internal reflection infrared spectroscopy has allowed identification of the adsorption modes of citral. With no citronellal, citral adsorbs through both the C═C and C═O groups; however, in the presence of citronellal, citral adsorption occurs through the C═O group only, which is proposed to be the cause of the altered reaction selectivity.

Extent and mechanism of phase separation during the extrusion of calcium phosphate pastes

The aim of this study was to increase understanding of the mechanism and dominant drivers influencing phase separation during ram extrusion of calcium phosphate (CaP) paste for orthopaedic applications. The liquid content of extrudate was determined, and the flow of liquid and powder phases within the syringe barrel during extrusion were observed, subject to various extrusion parameters. Increasing the initial liquid-to-powder mass ratio, LPR, (0.4-0.45), plunger rate (5-20 mm/min), and tapering the barrel exit (45°-90°) significantly reduced the extent of phase separation. Phase separation values ranged from (6.22 ± 0.69 to 18.94 ± 0.69 %). However altering needle geometry had no significant effect on phase separation. From powder tracing and liquid content determination, static zones of powder and a non-uniform liquid distribution was observed within the barrel. Measurements of extrudate and paste LPR within the barrel indicated that extrudate LPR remained constant during extrusion, while LPR of paste within the barrel decreased steadily. These observations indicate the mechanism of phase separation was located within the syringe barrel. Therefore phase separation can be attributed to either; (1) the liquid being forced downstream by an increase in pore pressure as a result of powder consolidation due to the pressure exerted by the plunger or (2) the liquid being drawn from paste within the barrel, due to suction, driven by dilation of the solids matrix at the barrel exit. Differentiating between these two mechanisms is difficult; however results obtained suggest that suction is the dominant phase separation mechanism occurring during extrusion of CaP paste.