The hydrodynamics of liquid–liquid upflow through a venturimeter

The present work reports the influence of a venturimeter on liquid–liquid phase distribution during upflow through a vertical pipe. The optical probe technique has been adopted for the characterization of flow. The probability density function and the wavelet multi-resolution analysis of the random probe signals have provided an insight into the details of the flow patterns and the intrinsic differences at the upstream, throat and the downstream sections. The experiments have indicated the flow pattern transitions to occur at lower velocities at the downstream region of the venturi. The pressure drop readings across the venturi have been used to estimate the mass flow rate of the mixture by using suitable models for the different patterns.     

Three-dimensional numerical study of jet-in-crossflow characteristics at low Reynolds number

A numerical study of a square jet in a cross flow is carried out at a Reynolds number of 100. The flow field and heat transfer characteristic downstream of the jet have been explored by solving three-dimensional unsteady Navier–Stokes equations and energy equation using higher order spatial and temporal discretization. The projection of vortical structure on a plane is seen to give the component of vortex normal to the plane. Four combinations of velocity profile namely (1) uniform crossflow and uniform jet, (2) laminar boundary layer crossflow and uniform jet, (3) uniform crossflow and parabolic jet profile, and (4) laminar boundary layer crossflow and parabolic jet are compared at same phase to see their effect on the flow field and heat transfer characteristic. All the four cases are seen to exhibit unsteadiness but the jet with parabolic profile is seen to show stronger unsteadiness. The instantaneous vortical structures of all the cases at the same phase show that the structures are more complex for the jet with parabolic velocity profile. The temperature field is seen to be correlated with the vortical structures. Comparison of the time averaged flow field reveals that the jet penetration is the highest for the jet having parabolic profile and boundary layer crossflow. The adiabatic effectiveness is observed to be more for the jet with uniform velocity profile and uniform crossflow and was least for the jet with parabolic velocity profile and boundary layer crossflow.     

Renormalized energy-momentum tensor of λ Φ<Superscript>4</Superscript> theory in curved space-time

Divergenceless expression for the energy-momentum tensor of scalar field is obtained using the momentum cut-off regularization technique. We consider a scalar field with quartic self-coupling in a spatially flat (3+1)-dimensional Robertson-Walker space-time, having arbitrary mass and coupled to gravity. As special cases, energy-momentum tensor for conformal and minimal coupling are also obtained. The energy-momentum tensor is observed to exhibit trace anomaly in curved space-time     

Asymmetric multi-component reactions: convenient access to acyclic stereocenters and functionalized cyclopentenoids

Asymmetric multi-component reactions of optically active phenyl dihydrofuran, keto ester or N-tosyl imino ester, and allylsilane provided functionalized phenyl tetrahydrofurans with multiple stereogenic centers diastereoselectively. Cleavage of the resulting substituted tetrahydrofurans readily provided acyclic derivatives with three contiguous asymmetric centers via an acyloxycarbenium ion intermediate. Ring closing olefin metathesis, using Grubbs catalyst, afforded functionalized cyclopentene derivatives in optically active form. A one pot tandem tetrahydrofuran ring cleavage followed by ring closing olefin metathesis also provided functionalized cyclopentenes in good yield.     

Conformal curvature flows: From phase transitions to active vision

In this paper, we analyze geometric active contour models from a curve evolution point of view and propose some modifications based on gradient flows relative to certain new feature-based Riemannian metrics. This leads to a novel edge-detection paradigm in which the feature of interest may be considered to lie at the bottom of a potential well. Thus an edge-seeking curve is attracted very naturally and efficiently to the desired feature. Comparison with the Allen-Cahn model clarifies some of the choices made in these models, and suggests inhomogeneous models which may in return be useful in phase transitions. We also consider some 3-dimensional active surface models based on these ideas. The justification of this model rests on the careful study of the viscosity solutions of evolution equations derived from a level-set approach.     

Nanosized rare earth cobaltite LaCoO<Subscript>3</Subscript> synthesized by urea combustion method

The structural, magnetic, and electrical properties of nano- and bulk samples of LaCoO₃, prepared by a urea combustion method, are investigated in this paper. The structures of phases, calcined at different temperatures, were refined in two different space groups rhombohedral R-3c and monoclinic I2/a, and a good agreement was obtained between the observed and calculated XRD patterns. Magnetic measurements reveal that the magnetic susceptibility increases with reduction in particle size. It is observed that there are two types of mechanisms which govern the conduction in different temperature ranges of these samples, and no single law of conduction fits the entire range of temperature. In high temperature range (200–300 K), Arrhenius law fits well, while in the low temperature region (100–200 K), the conduction is governed by Efros-Shklovskii’s (ES) hopping.