Shannon-information entropy sum in the confined hydrogenic atom

The appearance of critical points in the Shannon entropy sum as a function of confinement radius, in ground and excited state confined hydrogenic systems, is discussed. We illustrate that the Coulomb potential in tandem with the hard sphere confinement are responsible for these points. The positions of these points are observed to vary with the intensity of the potential. The effects of the Coulomb potential on the system are further probed, by examining the differences between the densities of the confined atom and those of the particle confined in a spherical box, for the same confinement radius. These differences are quantified by using Kullback-Leibler and cumulative residual Kullback-Leibler distance measures from information theory. These measures detect that the effects of the Coulomb potential are squeezed out of the system as the confinement radius decreases. That is, the confined atom densities resemble the particle in a box ones, for smaller confinement radii. Furthermore, the critical points in the entropy sum lie in the same regions where there are changes in the distance measures, as the atom behaves more particle in a spherical box-like. The analysis is further complemented by examination of the derivative of the entropy sum with respect to confinement radius. This study illustrates the inhomogeneity in the magnitudes of the derivatives of the entropy sum components and their dependence on the Coulomb potential. A link between the derivative and the entropic force is also illustrated and discussed. Similar behaviors are observed when the virial ratio is compared to the entropic power one, as a function of confinement radius.     

An optimal sixth‐order quartic B‐spline collocation method for solving Bratu‐type and Lane‐Emden–type problems

This paper is concerned with the numerical solutions of Bratu‐type and Lane‐Emden–type boundary value problems, which describe various physical phenomena in applied science and technology. We present an optimal collocation method based on quartic B‐spine basis functions to solve such problems. This method is constructed by perturbing the original problem and on a uniform mesh. The method has been tested by four nonlinear examples. In order to show the advantage of the new method, numerical results are compared with those obtained by some of the existing methods, such as normal quartic B‐spline collocation method and the finite difference method (FDM). It has been observed that the order of convergence of the proposed method is six, which is two orders of magnitude larger than the normal quartic B‐spline collocation method. Moreover, our method gives highly accurate results than the FDM.     

Relationship between 18O enrichment in leaf biomass and stomatal conductance

Models that explain the oxygen isotope enrichment in leaf water (and biomass) treat the relationship between the kinetic fractionation that occurs during evapotranspiration and the stomatal conductance in an empirical way. Consequently, the isotopic enrichment is always predicted to decrease with increasing stomatal conductance, regardless of the experimental evidence to the contrary. We explain why and suggest an alternative method to reconcile theory and experiment. We support this with our experimental data on rice and groundnut plants.     

Wax formation in oil pipelines: A critical review

The gelling of waxy crudes and the deposition of wax on the inner walls of subsea crude oil pipelines present a costly problem in the production and transportation of oil. The timely removal of deposited wax is required to address the reduction in flow rate that it causes, as well as to avoid the eventual loss of a pipeline in the event that it becomes completely clogged. In order to understand this problem and address it, significant research has been done on the mechanisms governing wax deposition in pipelines in order to model the process. Furthermore, methods of inhibiting the formation of wax on pipeline walls and of removing accumulated wax have been studied to find the most efficient and cost-effective means of maintaining pipelines prone to wax deposition. This paper seeks to review the current state of research into these areas, highlighting what is so far understood about the mechanisms guiding this wax deposition, and how this knowledge can be applied to modelling and providing solutions to this problem.     

Some theorems on two-temperature generalized thermoelasticity

The aim of the present work is to establish a reciprocal principle of Betti type in the context of linear theory of two-temperature generalized thermoelasticity (Youssef in IMA J Appl Math 71:383–390, 2006; Arch Appl Mech 75:553–565, 2006) for homogeneous and isotropic body. Generalizations of the theorems of Somigliana and Green to two-temperature generalized thermoelasticity are also established on the basis of our reciprocal principle.     

Computational flow and heat transfer of multiple circular jets impinging on a flat surface with effusion

Computational investigations are reported on the local flow and heat transfer characteristics from staggered, multiple circular air jets impinging on a flat surface with effusion holes. The geometrical and flow parameters for the computational study are chosen as per the experimental arrangement of Cho and Rhee J Turbomachinery 123:601–608, (14) so as to explain salient features observed in these experiments. The two peaks in the Nusselt number observed in the case of H/D = 6 and three peaks in the case of H/D = 2 are attributed to the flow characteristics such as primary vortices forming an up-wash region, followed by secondary vortices resulting in a secondary stagnation zone. The magnitude of local peak in heat transfer increases up to 88% with increasing values of D/d from 0.5 to 1.5 at Re = 10,000.     

Enantioselective formal synthesis of palmerolide A

Enantioselective formal synthesis of macrolactone palmerolide A, a polyketide marine natural product, is described. Key strategies in the synthesis include the oxidative furan ring-opening of a chiral furyl carbinol for the installation of the 1,4-dienol core and a Jung nonaldol-aldol reaction for the dienamide core.     

In situ generation of the Coates catalyst: a practical and versatile catalytic system for the carbonylation of meso-epoxides

A highly active catalytic system for the carbonylation of meso- and terminal epoxides to β-lactones is described. The active catalyst, analogous to Coates' catalyst, is generated in situ from commercially available (TPP)CrCl and Co(2)(CO)(8). This practical system circumvents the preparation of air sensitive cobaltate salts, operates at low catalyst loadings, and allows the carbonylation of functionalized, sterically demanding and heterocyclic meso-epoxides.     

Free Convection Boundary Layer Flow Past a Vertical Surface in a Porous Medium with Temperature-Dependent Properties

Numerical solutions for the free convection heat transfer in a viscous fluid at a permeable surface embedded in a saturated porous medium, in the presence of viscous dissipation with temperature-dependent variable fluid properties, are obtained. The governing equations for the problem are derived using the Darcy model and the Boussinesq approximation (with nonlinear density temperature variation in the buoyancy force term). The coupled non-linearities arising from the temperature-dependent density, viscosity, thermal conductivity, and viscous dissipation are included. The partial differential equations of the model are reduced to ordinary differential equations by a similarity transformation and the resulting coupled, nonlinear ordinary differential equations are solved numerically by a second order finite difference scheme for several sets of values of the parameters. Also, asymptotic results are obtained for large values of | f _w|. Moreover, the numerical results for the velocity, the temperature, and the wall-temperature gradient are presented through graphs and tables, and are discussed. It is observed that by increasing the fluid variable viscosity parameter, one could reduce the velocity and thermal boundary layer thickness. However, quite the opposite is true with the non-linear density temperature variation parameter.