Exact Metric for the Exterior of a Global String in the Brans-Dicke Theory

We determine in closed form the general static solution with cylindrical symmetry to the Brans-Dicke equations for an energy-momentum tensor corresponding to that of the straight U(1) global string outside the core radius assuming that the Higgs boson field takes its asymptotic value.     

Solutions of Kramer's Equations for Perfect Fluid Cylinders

Kramer's formulation of Einstein's fieldequations for static perfect fluid cylinders isconsidered. Three approaches are followed in seekingsolutions of Kramer's equations. First, a particularintegral is found which reproduces a previously knownclass of four solutions. Second, a fairly general ansatzis suggested, whereby a class of six new solutions isderived. Finally, the problem for an incompressible perfect fluid, with constant energy density, isreduced to a single second order equation. All solutionsare regular everywhere. Constraints are imposed on thesolutions parameters such that energy conditions are satisfied and hence the solutions arephysically reasonable.     

Surface segregational behaviour studied as an effect of thickness by SIMS and AFM in annealed PS-PMMA blend and block copolymer thin films

The surface behaviour of a two-phase polymer mixture depends on the chemical structure of the polymer components, the interaction between the two polymers and the processing conditions. The microscopic morphology and the surface composition need to be known in order to fully utilize the thin film properties. The technique of static time-of-flight secondary ion mass spectrometry (ToF-SIMS) is used to obtain the molecular surface composition of thin films of blends and block copolymers. The depth profiling tool of Nano-SIMS, a dynamic SIMS technique, helps to provide the chemical mapping of the surface in 2D and 3D. The surface morphology is investigated using AFM. Thin films of PS and PMMA diblock copolymers with molecular weight of 12K-12K and 10K-10K and blends of PS/PMMA (10K/10K) for thicknesses ranging from 5 nm to 50 nm are examined. For the blends, the ToF-SIMS spectra for all the thicknesses show the same behaviour of a high increase of PMMA on the surface after annealing. Nano-SIMS images reveal the formation of nanostructures on the annealed surfaces and AFM studies show these nanostructures to be droplets having distinct phase shift from the surrounding matrix. The droplet dimensions increase with the increase of the thickness of the film but the absolute intensity from the ToF-SIMS spectra for all the annealed films remains almost the same. For the copolymers, the ToF-SIMS spectra show that there is a decrease of PMMA on the surface for the annealed films when compared to the as-cast ones. AFM morphology reveals that, for different thicknesses, annealing induces different topographical features like droplets, holes, spinodal patterns, etc. but with no distinct phase shift between the patterns and the surrounding matrix. The two different copolymers of comparable molecular weight are found to exhibit very different topography even when the thickness of the films remained the same. The surface composition from the ToF-SIMS data, however, was not found to vary even when the topography was completely different.     

Complete space-like submanifolds in locally symmetric semi-definite spaces

The purpose of this paper is to study complete space-like submanifolds with parallel mean curvature vector and flat normal bundle in a locally symmetric semi-defnite space satisfying some curvature conditions. We first give an optimal estimate of the Laplacian of the squared norm of the second fundamental form for such submanifold. Furthermore, the totally umbilical submanifolds are characterized     

Cracking of Homogeneous Self-Gravitating Compact Objects Induced by Fluctuations of Local Anisotropy

We discuss the effect that small fluctuations of local anisotropy (principal stresses unequal) may have on the occurrence of cracking in spherical compact objects. Two families of homogeneous fluid distributions are considered. For both it is shown that departures from equilibrium may lead to the appearance of cracking, only if fluctuations of local anisotropy are allowed. The case of fluctuations in an initially locally isotropic (perfect fluid) configuration deserves particular attention.     

Two Counter-moving Light Beams

The cylindrically symmetric field of two beamsof light shining in opposite directions is studied. Wepresent four static or stationary exact solutions of thecorresponding field equations and compare their properties.