The influences of jet precession on large-scale instantaneous turbulent particle clusters

An experimental investigation of the influence of jet precession on the formation of large-scale instantaneous turbulent particle clusters is reported. Instantaneous planar particle distributions in the first seven nozzle diameters downstream from a simulated pulverised fuel burner have been measured using planar nephelometry, a laser-based instantaneous concentration technique. Large-scale instantaneous particle clusters (ITPCs) are identified and quantified from these data. A systematic study is conducted to assess the influence of the ratio of the precessing jet to axial momentum streams on ITPCs. The results show that ITPCs can be modified by this momentum ratio. The average size of ITPCs reaches a maximum for cases with high precessional momentum, although excessive precessional momentum can reduce ITPC size. The particle number density per unit area inside these ITPCs reaches a maximum for an intermediate value of jet precession. The spread of ITPC centroids can be estimated from the mean jet spread of particles and therefore increases with increasing precessing jet momentum once above a certain threshold.     

Scale-up of an unsteady flow field for enhanced spatial and temporal resolution of PIV measurements: application to leaflet wake flow in a mechanical heart valve

A scale-up approach is developed to enhance effective spatial and temporal resolution of PIV measurements. An analysis shows that complete similarity can be maintained for certain unsteady flows and that all types of error in PIV are either reduced or unaffected by scale-up. Implementation and results are described for flow through a mechanical heart valve (MHV), in which high resolution is necessary to advance understanding of the effects of small-scale flow structure on blood cells. With a large-scale model geometry and a low-viscosity model fluid, spatial and temporal resolutions are increased by factors of 5.8 and 118, respectively, yielding the finest resolution to date for MHV flow. Measurements near the downstream tip of a valve leaflet detect eddies as small as 400 μm shed in the leaflet wake. Impulsively started flow exhibits vortex shedding frequencies broadly consistent with the literature on flat-plate and aerofoil wakes, while the physiological unsteady flow waveform promotes 40% higher frequency at peak flow.     

A method to provide statistical measures of large-scale instantaneous particle clusters from planar images

Particle clusters are preferential accumulations of a solid, secondary phase that can be caused by turbulence. It is well known that particle clusters can influence the performance of systems employing suspension flows, such as pulverised fuel combustion systems. However, statistical analysis of clusters is limited by available methods to quantify them. In the current study, a method to identify planar slices of large-scale particle clusters from planar images of instantaneous particle distributions is presented. The method employs smoothing of instantaneous particle scatter images by a length scale, L _S , to produce pseudo-scalar fields of particle distributions. The scalar fields are compared with mean (not smoothed) images to produce cluster masks that are then multiplied by the original instantaneous image to produce a map of the locations of cluster slices. The sensitivity to the smoothing length scale is assessed parametrically for its influence on the statistical measures of the following parameters characterising slices of large-scale clusters in four representative flows: the physical locations of the cluster slice centroids; the area of the cluster slice; and the number of cluster slices per image. While the results are influenced by the selected value of smoothing length scale, L _S , the sensitivity is low in a physically reasonable range and the method performs well in this range for the four different flow cases. The method could be extended to provide volumetric measurements with suitable volumetric imaging systems.     

Deformations of smooth toric surfaces

For a complete, smooth toric variety Y, we describe the graded vector space ${T_Y^1}$ . Furthermore, we show that smooth toric surfaces are unobstructed and that a smooth toric surface is rigid if and only if it is Fano. For a given toric surface we then construct homogeneous deformations by means of Minkowski decompositions of polyhedral subdivisions, compute their images under the Kodaira-Spencer map, and show that they span ${T_Y^1}$ .     

Web servers and services for electrostatics calculations with APBS and PDB2PQR

APBS and PDB2PQR are widely utilized free software packages for biomolecular electrostatics calculations. Using the Opal toolkit, we have developed a Web services framework for these software packages that enables the use of APBS and PDB2PQR by users who do not have local access to the necessary amount of computational capabilities. This not only increases accessibility of the software to a wider range of scientists, educators, and students but also increases the availability of electrostatics calculations on portable computing platforms. Users can access this new functionality in two ways. First, an Opal-enabled version of APBS is provided in current distributions, available freely on the web. Second, we have extended the PDB2PQR web server to provide an interface for the setup, execution, and visualization of electrostatic potentials as calculated by APBS. This web interface also uses the Opal framework which ensures the scalability needed to support the large APBS user community. Both of these resources are available from the APBS/PDB2PQR website: http://www.poissonboltzmann.org/.     

Synthesis of unsymmetrical 3,4-diaryl-3-pyrrolin-2-ones utilizing pyrrole Weinreb amides

A regiocontrolled synthesis of unsymmetrical 3,4-diaryl-3-pyrrolin-2-ones has been achieved in three steps from 1,2-diaryl-1-nitroethenes with pyrrole-2-carboxamides (pyrrole Weinreb amides) serving as the key linchpin intermediates. Two different methods for the preparation of the requisite nitroalkenes were investigated: (1) modified Henry reaction between arylnitromethanes and arylimines; and (2) Suzuki-Miyaura cross-coupling reaction of 2-aryl-1-bromo-1-nitroethenes with arylboronic acids. Some difficulty was encountered in the preparation of arylnitromethanes, thus leading to the exploration of a cross-coupling strategy that proved more useful. A Barton-Zard pyrrole cyclocondensation reaction between 1,2-diaryl-1-nitroethenes and N-methoxy-N-methyl-2-isocyanoacetamide gave the corresponding pyrrole Weinreb amides, which were then converted into the desired 3-pyrrolin-2-ones in two steps. Overall, this method allowed for the construction of 3,4-diaryl-3-pyrrolin-2-ones with complete regiocontrol of the substituents with respect to the lactam carbonyl. The utility of this synthetic methodology was demonstrated by the preparation of eight unsymmetrical and symmetrical 3,4-diaryl-3-pyrrolin-2-ones including the N-H lactam analogue of the selective COX-II inhibitor, rofecoxib.     

A systematic investigation of quaternary ammonium ions as asymmetric phase-transfer catalysts. Synthesis of catalyst libraries and evaluation of catalyst activity

Despite over three decades of research into asymmetric phase-transfer catalysis (APTC), a fundamental understanding of the factors that affect the rate and stereoselectivity of this important process are still obscure. This paper describes the initial stages of a long-term program aimed at elucidating the physical organic foundations of APTC employing a chemoinformatic analysis of the alkylation of a protected glycine imine with libraries of enantiomerically enriched quaternary ammonium ions. The synthesis of the quaternary ammonium ions follows a diversity-oriented approach wherein the tandem inter[4 + 2]/intra[3 + 2] cycloaddition of nitroalkenes serves as the key transformation. A two-part synthetic strategy comprised of (1) preparation of enantioenriched scaffolds and (2) development of parallel synthesis procedures is described. The strategy allows for the facile introduction of four variable groups in the vicinity of a stereogenic quaternary ammonium ion. The quaternary ammonium ions exhibited a wide range of activity and to a lesser degree enantioselectivity. Catalyst activity and selectivity are rationalized in a qualitative way on the basis of the effective positive potential of the ammonium ion.     

Multi-domain Fourier-continuation/WENO hybrid solver for conservation laws

We introduce a multi-domain Fourier-continuation/WENO hybrid method (FC–WENO) that enables high-order and non-oscillatory solution of systems of nonlinear conservation laws, and which enjoys essentially dispersionless, spectral character away from discontinuities, as well as mild CFL constraints (comparable to those of finite difference methods). The hybrid scheme employs the expensive, shock-capturing WENO method in small regions containing discontinuities and the efficient FC method in the rest of the computational domain, yielding a highly effective overall scheme for applications with a mix of discontinuities and complex smooth structures. The smooth and discontinuous solution regions are distinguished using the multi-resolution procedure of Harten [J. Comput. Phys. 115 (1994) 319–338]. We consider WENO schemes of formal orders five and nine and a FC method of order five. The accuracy, stability and efficiency of the new hybrid method for conservation laws is investigated for problems with both smooth and non-smooth solutions. In the latter case, we solve the Euler equations for gas dynamics for the standard test case of a Mach three shock wave interacting with an entropy wave, as well as a shock wave (with Mach 1.25, three or six) interacting with a very small entropy wave and evaluate the efficiency of the hybrid FC–WENO method as compared to a purely WENO-based approach as well as alternative hybrid based techniques. We demonstrate considerable computational advantages of the new FC-based method, suggesting a potential of an order of magnitude acceleration over alternatives when extended to fully three-dimensional problems.     

Pressure broadening and collisional shift of the Rb D2 absorption line by CH4, C2H6, C3H8, n-C4H10, and He

The pressure broadening and shift rates of the rubidium D2 absorption line 5²S_1/2→5²P_3/2 (780.24 nm) with CH₄, C₂H₆, C₃H₈, n-C₄H₁₀, and He were measured for pressures ≤80 Torr using high-resolution laser spectroscopy. The broadening rates γ_B for CH₄, C₂H₆, C₃H₈, n-C₄H₁₀, and He are 28.0, 28.1, 30.5, 31.3, and 20.3 (MHz/Torr), respectively. The corresponding shift rates γ_S are −8.4, −8.8, −9.7, −10.0, and 0.39 (MHz/Torr), respectively. The measured rates of Rb for the hydrocarbon buffer gas series of this study are also compared to the theoretically calculated rates of a purely attractive van der Waals difference potential. Good agreement is found to exist between measured and theoretical rates.