Approximate analytical solutions of a class of boundary layer equations over nonlinear stretching surface

Third order nonlinear ordinary differential equations, subject to appropriate boundary conditions arising in fluid dynamics, are solved using three different methods viz., the Dirichlet series, method of stretching of variables, and asymptotic function method. Similarity transformations are used to convert the governing partial differential equations into nonlinear ordinary differential equations. The numerical results obtained from the above methods for various problems are given in terms of skin friction. Our study revealed that the results obtained from these methods agree well with those of direct numerical simulation of ordinary differential equations. Also, these methods have advantages over pure numerical methods in obtaining derived quantities such as velocity profile accurately for various values of the parameters at a stretch.     

Imaging nonequilibrium atomic vibrations with x-ray diffuse scattering

We use picosecond x-ray diffuse scattering to image the nonequilibrium vibrations in the lattice following ultrafast laser excitation. We present images of nonequilibrium phonons in InP and InSb throughout the Brillouin zone which remain out of equilibrium up to nanoseconds. The results are analyzed using a Born model that helps identify the phonon branches contributing to the observed features in the time-resolved diffuse scattering. In InP this analysis shows a delayed increase in the transverse-acoustic (TA) phonon population along high-symmetry directions accompanied by a decrease in the longitudinal-acoustic phonons. In InSb the increase in TA phonon population is less directional.     

Simple pulse-acquire NMR methods for the quantitative analysis of calcium, magnesium and sodium in human serum

Simple pulse-acquire NMR methods are presented for accurate quantitation of calcium (Ca(2+)), magnesium (Mg(2+)) and sodium (Na(+)) in human serum. Ca(2+) and Mg(2+) can be determined simultaneously by (1)H NMR via their EDTA (ethylenediaminetetraacetic acid) complexes. Spectra are acquired before and after addition of EDTA, and the difference spectrum is used for integration of the signals from the complexes relative to an internal reference. Serum sodium can also be determined through pulse-acquire (23)Na NMR by integration of the free sodium signal relative to a reference signal (Na(+)+EDTA in a coaxial capillary tube). The method shows excellent accuracy and precision for all three metal ions. Slow chemical exchange between complexed and free EDTA at the natural pH of serum does not limit the accuracy of the determination of Ca(2+) and Mg(2+), and the large errors associated with spin-echo spectral editing methods are avoided.     

Theory of the helical spin crystal: a candidate for the partially ordered state of MnSi

MnSi is an itinerant magnet which at low temperatures develops a helical spin-density wave. Under pressure it undergoes a transition into an unusual partially ordered state whose nature is debated. Here we propose that the helical spin crystal (the magnetic analog of a solid) is a useful starting point to understand partial order in MnSi. We consider different helical spin crystals and determine conditions under which they may be energetically favored. The most promising candidate has bcc structure and is reminiscent of the blue phase of liquid crystals in that it has line nodes of magnetization protected by symmetry. We introduce a Landau theory to study the properties of these states, in particular, the effect of crystal anisotropy, magnetic field, and disorder. These results compare favorably with existing data on MnSi from neutron scattering and magnetic field studies. Future experiments to test this scenario are also proposed.     

Spin-charge separated solitons in a topological band insulator

In this Letter we construct a simple, controllable, two-dimensional model based on a topological band insulator. It has many attractive properties. (1) We obtain spin-charge separated solitons that are associated with dynamic pi fluxes. (2) These solitons obey Bose statistics and their condensation triggers a phase transition from a spin Hall insulator to an easy-plane ferromagnet. (3) It suggests an alternative way to classify the Z2 topological band insulator without resorting to the sample boundary.     

Ultrasound assisted synthesis of isopropyl esters from palm fatty acid distillate

Esterification is one of the most preferred synthesis routes for organic esters which are most frequently used as plasticizers, solvents and perfumery and flavour chemicals. The present work deals with acid catalyzed synthesis of isopropyl esters from palm fatty acid distillate (PFAD) in the presence of ultrasonic irradiations operating at 25kHz frequency and 1kW of supplied power. Effect of different operating parameters such as molar ratio of reactants, catalyst quantity and operating temperature has been studied with an aim of optimization. It has been observed that ultrasound enhances the rate of reaction and the extent of equilibrium conversion. The optimum parameters for this process have been found to be 1:5 molar ratio of PFAD to isopropanol, catalyst concentration of 5% of PFAD and 60 degrees C reaction temperature. Maximum conversion levels of about 80% have been obtained in 6h of reaction time under these optimized conditions. Analysis of the kinetic data indicates that the reaction follows first order reversible path.     

Inertia effects in circular squeeze film bearing using Herschel–Bulkley lubricants

Recent engineering trends in lubrication emphasize that in order to analyze the performance of bearings adequately, it is necessary to take into account the combined effects of fluid inertia forces and non-Newtonian characteristics of lubricants. In the present work, the effects of fluid inertia forces in the circular squeeze film bearing lubricated with Herschel–Bulkley fluids with constant squeeze motion have been investigated. Herschel–Bulkley fluids are characterized by an yield value which leads to the formation of a rigid core in the flow region. The shape and extent of the core formation along the radial direction is determined numerically for various values of Herschel–Bulkley number and power-law index. The bearing performances such as pressure distribution and load capacity for different values of Herschel–Bulkley number, Reynolds number, power-law index have been computed. The effects of fluid inertia and non-Newtonian characteristics on the bearing performances have been discussed.     

Ultracold atoms in a tunable optical kagome lattice

We realize a two-dimensional kagome lattice for ultracold atoms by overlaying two commensurate triangular optical lattices generated by light at the wavelengths of 532 and 1064 nm. Stabilizing and tuning the relative position of the two lattices, we explore different lattice geometries including a kagome, a one-dimensional stripe, and a decorated triangular lattice. We characterize these geometries using Kapitza-Dirac diffraction and by analyzing the Bloch-state composition of a superfluid released suddenly from the lattice. The Bloch-state analysis also allows us to determine the ground-state distribution within the superlattice unit cell. The lattices implemented in this work offer a near-ideal realization of a paradigmatic model of many-body quantum physics, which can serve as a platform for future studies of geometric frustration.     

Dibutyltin oxide catalyzed aminolysis of oxalate to carbamate,oxamate and derivatives of imidazolidine trione

Catalytic aminolysis of oxalates by simple and substituted ureas has been shown to give carbamates, oxamates and derivatives of imidazolidine trione. Various substituted ureas and oxalates were screened to verify the applicability of the protocol. The role of dibutyltin oxide as catalyst, effect of solvent and reaction conditions on product distribution pattern has been discussed. Copyright © 2010 John Wiley & Sons, Ltd.