Perturbative manifolds and the Noether generators of nth-order Poisson equations

A manifold that contains small perturbations will induce a perturbed partial differential equation. The partial differential equation that we select is the Poisson equation – in order to explore the interplay between the geometry of the manifold and the perturbations. Specifically, we show how the problem of symmetry determination, for higher-order perturbations, can be elegantly expressed via geometric conditions.     

Invertible point transformations,Painlevé test,and the second Painlevé transcendent

The techniques of invertible point transformations and the Painlevé analysis can be used to construct integrable ordinary differential equations. We compare both techniques for the second Painlevé transcendent.     

Unforeseen formation of 2-bromo-3-hydroxybenzaldehyde by bromination of 3-hydroxybenzaldehyde

Contrary to literature reports, bromination of 3-hydroxybenzaldehyde can afford both 2-bromo-5-hydroxybenzaldehyde and 2-bromo-3-hydroxybenzaldehyde, but 4-bromo-3-hydroxybenzaldehyde was not detected. 2-Bromo-3-hydroxybenzaldehyde was converted into 2-(benzyloxy)-1-bromo-5-methoxy-7-methylnaphthalene. X-ray crystallographic analysis supports the identity of 2-bromo-3-hydroxybenzaldehyde.     

Alpha decay rate enhancement in metals: An unlikely scenario

It has been recently suggested that one might drastically shorten the alpha lifetime of nuclear waste products, if these are embedded in metals at low temperatures. Using quantum mechanical tunneling arguments, we show that such an effect is likely to be very small, if present at all.     

Symmetry study of the coupled Burgers system

The inverse of the recursion operator of a coupled Burgers equation is given explicitly. Three sets of infinitely many symmetries of the considered model are obtained by acting the recursion operator and it’s inverse on the trivial symmetries, space translation, identity transformation and the scaling transformation respectively. These symmetries constitute an infinite dimensional Lie algebra.     

Thickness induced transversal percolation in Pt-Al2O3 nano-composites

Investigations of thickness induced percolation process in Pt_ξ-Al₂O₃ nano-composites were carried out using grazing angle X-ray scattering. It is shown that the morphological characteristics of the nano-scaled Pt particles change significantly within the growth transversal direction. The initially non percolated two phases Pt_ξ-Al₂O₃ nano-composites show a noteworthy tendency to a percolated morphology with a gradual transversal increase of Pt nano-particles' average diameter in addition to the increase of the Pt nano-particles' poly-dispersity. This transversal morphological evolution is followed by a percolation phenomenon of the Pt nano-particles for a thickness of about ∼119.5 nm. This transversal morphological evolution seems to corroborate far too much with a columnar growth process.     

Scalar curvature of spheres

Financial support from the FRD is gratefully acknowledged     

Oblique reflection of shock waves from rigid porous materials

A study to determine the general gas dynamic behaviour associated with the impact of a shock wave on a porous wedge has been undertaken. A number of interesting features are noted. The pattern of wave reflection is shown to be significantly affected by the inflow of gas into the wedge. This has the effect of reducing the triple point trajectory angle for cases of Mach reflection and for strongly reducing the reflection angle in regular reflection. The permeability of the wedge has a significant effect on the strength of the reflected wave and in some cases this wave can be attenuated to the extent that it is almost eradicated. Pressure measurements taken under the wedge are characterized by oscillations which are of similar shape, for a given wedge, over a range of shock wave Mach numbers. It is shown that the wave transmitted into the wedge is attenuated to varying degrees depending on the material properties, and that for weak incident waves the mean propagation velocity can be less than the sound speed in the pore fluid. Photographs taken using a specially constructed wedge which allows the transmitted wave to be visualised, show that the transmitted wave is nearly plane.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.