Path integrals and wavepacket evolution for damped mechanical systems

Damped mechanical systems with various forms of damping are quantized using the path integral formalism. In particular, we obtain the path integral kernel for the linearly damped harmonic oscillator and a particle in a uniform gravitational field with linearly or quadratically damped motion. In each case, we study the evolution of Gaussian wavepackets and discuss the characteristic features that help us distinguish between different types of damping. For quadratic damping, we show that the action and equation of motion of such a system has a connection with the zero dimensional version of a currently popular scalar field theory. Furthermore we demonstrate that the equation of motion (for quadratic damping) can be identified as a geodesic equation in a fictitious two-dimensional space.Comment: 15 pages, 6 figure

On Property (FA) for wreath products

We characterize permutational wreath products with Property (FA). For instance, the standard wreath product A wr B of two nontrivial countable groups A,B, has Property (FA) if and only if B has Property (FA) and A is a finitely generated group with finite abelianisation. We also prove an analogous result for hereditary Property (FA). On the other hand, we prove that many wreath products with hereditary Property (FA) are not quotients of finitely presented groups with the same property.Comment: 12 pages, 0 figur

Niemann-Pick disease, type B with TRAP-positive storage cells and secondary sea blue histiocytosis

We present 2 cases of Niemann Pick disease, type B with secondary sea-blue histiocytosis. Strikingly, in both cases the Pick cells were positive for tartrate resistant acid phosphatase, a finding hitherto described only in Gaucher cells. This report highlights the importance of this finding as a potential cytochemical diagnostic pitfall in the diagnosis of Niemann Pick disease

Geometry of deformations of branes in warped backgrounds

The `braneworld' (described by the usual worldvolume action) is a D dimensional timelike surface embedded in a N dimensional ($N>D$) warped, nonfactorisable spacetime. We first address the conditions on the warp factor required to have an extremal flat brane in a five dimensional background. Subsequently, we deal with normal deformations of such extremal branes. The ensuing Jacobi equations are analysed to obtain the stability condition. It turns out that to have a stable brane, the warp factor should have a minimum at the location of the brane in the given background spacetime. To illustrate our results we explicitly check the extremality and stability criteria for a few known co-dimension one braneworld models. Generalisations of the above formalism for the cases of (i) curved branes (ii) asymmetrical warping and (iii) higher co-dimension braneworlds are then presented alongwith some typical examples for each. Finally, we summarize our results and provide perspectives for future work along these lines.Comment: 21 pages. Version matching final version. Accepted for publication in Class. Quant. Gra

A New process for the enrichment of nickel in Sukinda chromite overburden ore

Chrontite Over Burden (COB) ore from .Sukinda taller, Orissa is too lean in nickel concentration to he exploited for the extraction of nickel. The average nickel concentration in the COB ore lies in the range of 0.4-0.6%. An acid leaching route at atmospheric prsssure has been developed for screening out silica as insoluble. Metal values in the leach liquor are retrieved as hydroxides by appropriate manoeuvring of pH. The metal hydroxides are converted to corresponding oxides by calcining at 900°C. The resultant nickel content in the mixed oxide has been consistent1 ' .found to he 1.6% and above. This product star he directly used as a starting material for the preparation of ferro-nickel

A New process for the Enrichment of Nickel in Sukinda Chromite Overburden ore

Chromite Over Burden (COB) ore from Sukinda valley, Orissa is too lean in nickel concentration to be exploited for the extraction of nickel.The average nickel concentration in the COB are lies in the range of 0.4-0.6%. An acid leaching route at atmospheric prsssure has been developed for screening out silica as insoluble. Metal values in the leach liquor are retrieved as hydroxides by appropriate nia manoeuvring of pH. The metal hydroxides are converted to corresponding oxides by calcining at 900°C. The resu-ltant nickel content in the mixed oxide has been consist-ently found to be 1.6% and above. This product may be directly used as a starting material for the preparation of ferro- nickel

Kinematics of flows on curved, deformable media

In this article, we first investigate the kinematics of specific geodesic flows on two dimensional media with constant curvature, by explicitly solving the evolution (Raychaudhuri) equations for the expansion, shear and rotation along the flows. We point out the existence of singular (within a finite value of the time parameter) and non-singular solutions and illustrate our results through a `phase' diagram. This diagram demonstrates under which initial conditions (or combinations thereof) we end up with a singularity in the congruence and when, if at all, we encounter non--singular solutions for the kinematic variables. Our analysis illustrates the differences which arise due to a positive or negative value of the curvature. Subsequently, we move on to geodesic flows on two dimensional spaces with varying curvature. As an example, we discuss flows on a torus, where interesting oscillatory features of the expansion, shear and rotation emerge, which are found to depend on the ratio of the radii of the torus. The singular (within a finite time)/non--singular nature of the solutions are also discussed. Finally, we arrive at some general statements and point out similarities or dissimilarities that arise in comparison to our earlier work on media in flat space.Comment: Corrections in some equations and in one figure