The Generalised Raychaudhuri Equations : Examples

Specific examples of the generalized Raychaudhuri Equations for the evolution of deformations along families of $D$ dimensional surfaces embedded in a background $N$ dimensional spacetime are discussed. These include string worldsheets embedded in four dimensional spacetimes and two dimensional timelike hypersurfaces in a three dimensional curved background. The issue of focussing of families of surfaces is introduced and analysed in some detail.Comment: 8 pages (Revtex, Twocolumn format). Corrected(see section on string worldsheets), reorganised and shortened slightl

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

Decoupling of silicon carbide optical sensor response for temperature and pressure measurements (Erratum)

Single crystal silicon carbide is a chemically inert transparent material with superior oxidation-resistant properties at elevated temperatures compared to black polycrystalline silicon carbide substrates. These improved properties make crystalline silicon carbide a good optical sensor material for harsh environments such as combustion chambers and turbine systems. Interferometric optical sensors are orders of magnitude more sensitive than electrical sensors and are proposed for these applications. Silicon carbide itself behaves as a Fabry-Perot etalon eliminating the need for an external interferometer for any measurement using this silicon carbide as a sensor. The principle of the optical sensor in this study is the temperature- and pressure-dependent refractive index of silicon carbide, which can be used to determine the temperatures and pressures of gases that are in contact with silicon carbide. Interference patterns produced by a silicon carbide (4H-SiC) wafer due to multiple reflections of a helium-neon laser beam of wavelength of 632.8 nm have been obtained at temperatures up to 500 degrees C and pressures up to 600 psi. The pattern changes for the same gas at different temperatures and pressures and for different gases at the same temperature and pressure. The refractive index at the wafer-gas interface is calculated from the interference pattern and the refractive index gradients with respect to temperature and pressure, respectively, are also determined. Decoupling temperature and pressure using these gradients and the measured reflectivity data are discussed in this paper

On a Raychaudhuri equation for hot gravitating fluids

We generalize the Raychaudhuri equation for the evolution of a self gravitating fluid to include an Abelian and non-Abelian hybrid magneto fluid at a finite temperature. The aim is to utilize this equation for investigating the dynamics of astrophysical high temperature Abelian and non-Abelian plasmas.Comment: 13 pages, Invited contribution to Pramana special issue dedicated to A.K. Raychaudhuri, "The Raychaudhuri equation and its role in Modern Cosmology". Pramana style files include

Focusing of timelike worldsheets in a theory of strings

An analysis of the generalised Raychaudhuri equations for string world sheets is shown to lead to the notion of focusing of timelike worldsheets in the classical Nambu-Goto theory of strings. The conditions under which such effects can occur are obtained . Explicit solutions as well as the Cauchy initial value problem are discussed. The results closely resemble their counterparts in the theory of point particles which were obtained in the context of the analysis of spacetime singularities in General Relativity many years ago.Comment: 14 pages, RevTex, no figures, extended, to appear in Phys Rev

Orbifold resolutions with general profile

A very general class of resolved versions of the C/Z_N, T^2/Z_N and S^1/Z_2 orbifolds is considered and the free theory of 6D chiral fermions studied on it. As the orbifold limit is taken, localized 4D chiral massless fermions are seen to arise at the fixed points. Their number, location and chirality is found to be independent on the detailed profile of the resolving space and to agree with the result of hep-th/0409229, in which a particular resolution was employed. As a consistency check of the resolution procedure, the massive equation is numerically studied. In particular, for S^1/Z_2, the "resolved" mass--spectrum and wave functions in the internal space are seen to correctly reproduce the usual orbifold ones, as the orbifold limit is taken.Comment: 28 pages, 3 figures, typos corrected, references adde