Ricci flow of unwarped and warped product manifolds

We analyse Ricci flow (normalised/un-normalised) of product manifolds --unwarped as well as warped, through a study of generic examples. First, we investigate such flows for the unwarped scenario with manifolds of the type $\mathbb S^n\times \mathbb S^m$, $\mathbb S^n\times \mathbb H^m$, $\mathbb H^m\times \mathbb H^n$ and also, similar multiple products. We are able to single out generic features such as singularity formation, isotropisation at particular values of the flow parameter and evolution characteristics. Subsequently, motivated by warped braneworlds and extra dimensions, we look at Ricci flows of warped spacetimes. Here, we are able to find analytic solutions for a special case by variable separation. For others we numerically solve the equations (for both the forward and backward flow) and draw certain useful inferences about the evolution of the warp factor, the scalar curvature as well the occurence of singularities at finite values of the flow parameter. We also investigate the dependence of the singularities of the flow on the inital conditions. We expect our results to be useful in any physical/mathematical context where such product manifolds may arise.Comment: 25 pages, 25 figures, some figures replace

Enhanced Structural Support of Metal Sites as Nodes in Metal-Organic Frameworks Compared to Metal Complexes

Metal-organic frameworks are a new class of crystalline, porous solid-state materials with metal ions periodically linked by organic linkers. This gives rise to one-, two- or three-dimensional structures. Here, we compare the stability of similar metal sites toward external ligand (solvent) induced disruption of the coordination environment in metal complexes and in metal-organic frameworks. Our experimental results show that a metal site as node of a metal-organic framework retains much higher stability compared to a similar metal site in a metal complex

Statistical isotropy violation in WMAP CMB maps resulting from non-circular beams

Statistical isotropy (SI) of Cosmic Microwave Background (CMB) fluctuations is a key observational test to validate the cosmological principle underlying the standard model of cosmology. While a detection of SI violation would have immense cosmological ramification, it is important to recognise their possible origin in systematic effects of observations. WMAP seven year (WMAP-7) release claimed significant deviation from SI in the bipolar spherical harmonic (BipoSH) coefficients $A_{ll}^{20}$ and $A_{l-2l}^{20}$. Here we present the first explicit reproduction of the measurements reported in WMAP-7, confirming that beam systematics alone can completely account for the measured SI violation. The possibility of such a systematic origin was alluded to in WMAP-7 paper itself and other authors but not as explicitly so as to account for it accurately. We simulate CMB maps using the actual WMAP non-circular beams and scanning strategy. Our estimated BipoSH spectra from these maps match the WMAP-7 results very well. It is also evident that only a very careful and adequately detailed modelling, as carried out here, can conclusively establish that the entire signal arises from non-circular beam effect. This is important since cosmic SI violation signals are expected to be subtle and dismissing a large SI violation signal as observational artefact based on simplistic plausibility arguments run the serious risk of "throwing the baby out with the bathwater".Comment: 4 pages, 3 figures. Published version. Includes major revision in the text and one important figure. No change in the result

A Mathematical Model Of Blood Flow Of A Stenosed Artery In Variable Shape

In this theoretical study, a mathematical model is developed to carry out a systematic analysis of flow behaviour in a two-dimensional vessel (modeled as artery) with a locally variable shaped constriction. An artificial artery, which containing a viscous incompressible fluid that representing the flowing blood can be treated as inflexible vessel. The shape of the stenosis in the arterial lumen is chosen to be symmetric as well as asymmetric about the middle cross section is perpendicular to the axis of the vessel. The constricted vessel is resolved into a straight vessel and the entire resulting equations are solved by a numerical method with Reynolds number and ‘n’, a number giving the shape of the constriction as parameters. The impacts of these parameters on wall shear stress, pressure gradient and velocity have been analysed. It is found that the flow resistance decreases as the shape of a smooth stenosis changes and extreme resistance is attained for the symmetric stenosis. But the length of separation increases for the asymmetric constrictions and the oscillation in the shear layer appears earlier for asymmetric constriction than that in the case of symmetric constriction. The extreme resistance is attained for inflexible stenosed vessel rather than the flexible one