A numerical study on flow through the spiral casing of a hydraulic turbine

Flow through the spiral casing of a hydraulic turbine was analyzed. Reynolds averaged Navier–Stokes equations were solved using a finite element method. The physical domain was divided into a number of hexahedral elements which are isoparametrically mapped onto standard cubic elements. Numerical integration for the unsteady momentum equation is performed over such hexahedral elements to obtain a provisional velocity field. Compliance with the mass conservation equation and determination of the pressure correction are accomplished through an iterative procedure. The velocity distribution inside the spiral casing corroborates the results available in literature. The static pressure at the midplane generally decreases from the outside wall towards the exit of the spiral casing. © 1998 John Wiley & Sons, Ltd.     

A combined computational and experimental study of methane activation during oxidative coupling of methane (OCM) by surface metal oxide catalysts

The experimentally validated computational models developed herein, for the first time, show that Mn-promotion does not enhance the activity of the surface Na₂WO₄ catalytic active sites for CH₄ heterolytic dissociation during OCM. Contrary to previous understanding, it is demonstrated that Mn-promotion poisons the surface WO₄ catalytic active sites resulting in surface WO₅ sites with retarded kinetics for C–H scission. On the other hand, dimeric Mn₂O₅ surface sites, identified and studied via ab initio molecular dynamics and thermodynamics, were found to be more efficient in activating CH₄ than the poisoned surface WO₅ sites or the original WO₄ sites. However, the surface reaction intermediates formed from CH₄ activation over the Mn₂O₅ surface sites are more stable than those formed over the Na₂WO₄ surface sites. The higher stability of the surface intermediates makes their desorption unfavorable, increasing the likelihood of over-oxidation to CO_x, in agreement with the experimental findings in the literature on Mn-promoted catalysts. Consequently, the Mn-promoter does not appear to have an essential positive role in synergistically tuning the structure of the Na₂WO₄ surface sites towards CH₄ activation but can yield MnO_x surface sites that activate CH₄ faster than Na₂WO₄ surface sites, but unselectively.

The experimentally validated computational models developed herein, for the first time, show that Mn-promotion does not necessarily enhance the activity of the surface Na₂WO₄ catalytic active sites for CH₄ heterolytic dissociation during OCM.     

Vibration of an infinite inhomogeneous transversely isotropic viscoelastic medium with cylindrical hole

This paper investigates the influences of higher order viscoelasticity and the inhomogeneities of the transversely isotropic elastic parameters on the disturbances in an infinite medium, caused by the presence of a transient radial force or twist on the surface of a cylindrical hole with circular cross section. Following Voigt＇s model for higher order viscoelasticity, the nonvanishing stress components valid for a transversely isotropic and higher order viscoelastic solid medium have been deduced in terms of radial displacement component. Considering the power law variation of elastic and viscoelastic parameters, the stress equation of motion has been developed. Solving this equation under suitable boundary conditions, due to transient forces and twists, radial displacement and relevant stress components have been determined in terms of modified Bessel functions. The problem for the presence of transient radial force has been numerically analysed. Modulations of displacement and stresses due to different order of viscoelasticity and inhomogeneity have been graphically depicted. The numerical study of the disturbance caused by the presence of twist on the surface may be similarly done but is not pursued in this paper.     

Study of the Mo-Ba partition in 252Cf spontaneous fission

Measurements of fission fragment yields and neutron multiplicities have been carried out for the Mo-Ba fragment pairs in the spontaneous fission of ²⁵²Cf, using the γ-ray spectroscopy technique to analyze γ-γ-γ coincidence data. Prompt γ -ray multiplicities were also measured as a function of the number of neutrons emitted in the fission process leading to the Mo-Ba partition. We do not observe the enhancement in the yields of events with high neutron emission multiplicity (ν_n > 7) that has been associated to a second fission mode leading to the production of hyperdeformed Ba fragments, as reported in some earlier studies. The average γ-ray multiplicity is found to be rather weakly dependent on the number of neutrons emitted in the fission process. Received: 21 July 1999 / Revised version: 19 November 1999     

Highly stereoselective and enantiodivergent synthesis of cyclopropylphosphonates with engineered carbene transferases

Organophosphonate compounds have represented a rich source of biologically active compounds, including enzyme inhibitors, antibiotics, and antimalarial agents. Here, we report the development of a highly stereoselective strategy for olefin cyclopropanation in the presence of a phosphonyl diazo reagent as carbene precursor. In combination with a ‘substrate walking’ protein engineering strategy, two sets of efficient and enantiodivergent myoglobin-based biocatalysts were developed for the synthesis of both (1R,2S) and (1S,2R) enantiomeric forms of the desired cyclopropylphosphonate ester products. This methodology enables the efficient transformation of a broad range of vinylarene substrates at a preparative scale (i.e. gram scale) with up to 99% de and ee. Mechanistic studies provide insights into factors that contribute to make this reaction inherently more challenging than hemoprotein-catalyzed olefin cyclopropanation with ethyl diazoacetate investigated previously. This work expands the range of synthetically useful, enzyme-catalyzed transformations and paves the way to the development of metalloprotein catalysts for abiological carbene transfer reactions involving non-canonical carbene donor reagents.

Two enantiocomplementary myoglobin-based carbene transfer biocatalysts were developed for the synthesis of cyclopropylphosphonate esters with high diastereo- and enantioselectivity and in high yields.     

On the maximal space analyticity radius for the 3D Navier–Stokes equations and energy cascades

In this paper, we study the maximal space analyticity radius associated with a regular solution of the Navier–Stokes equations and its connection to turbulence. In order to do this, we introduce a new auxiliary ODE for the evolution of the analyticity radius involving the Gevrey class norms. We further show that jumps in the maximal space analyticity radius are an intermittent event and are connected to inverse energy cascade. Our approach also leads to a new type of global regularity test for the Navier–Stokes equation.     

A harmonic-type maximal principle in the three chains completion problem

In this note, we prove a harmonic-type maximal principle for the Schur parametrization of all contractive interpolants in the three chains completion problem (see [4]), which is analogous to the maximal principle proven in [2] in case of the Schur parametrization of all contractive intertwining liftings in the commutant lifting theorem.     

On the generalized $$text {SO}(2n,{{mathbb {C}}})$$ SO ( 2 n,C ) -opers

Annals of Global Analysis and Geometry - Since their introduction by Beilinson–Drinfeld (Opers, 1993. arXiv math/0501398; Quantization of Hitchin’s integrable system and Hecke...