Wave Propagation in 1-D Spiral geometry

In this article, we investigate the wave equation in spiral geometry and study the modes of vibrations of a one-dimensional (1-D) string in spiral shape. Here we show that the problem of wave propagation along a spiral can be reduced to Bessel differential equation and hence, very closely related to the problem of radial waves of two-dimensional (2-D) vibrating membrane in circular geometry

General relativistic treatment of LISA optical links

LISA is a joint space mission of the NASA and the ESA for detecting low frequency gravitational waves in the band $10^{-5} - 1$ Hz. In order to attain the requisite sensitivity for LISA, the laser frequency noise must be suppressed below the other secondary noises such as the optical path noise, acceleration noise etc. This is achieved by combining time-delayed data for which precise knowledge of time-delays is required. The gravitational field, mainly that of the Sun and the motion of LISA affect the time-delays and the optical links. Further, the effect of the gravitational field of the Earth on the orbits of spacecraft is included. This leads to additional flexing over and above that of the Sun. We have written a numerical code which computes the optical links, that is, the time-delays with great accuracy $\sim 10^{-2}$ metres - more than what is required for time delay interferometry (TDI) - for most of the orbit and with sufficient accuracy within $\sim 10$ metres for an integrated time window of about six days, when one of the arms tends to be tangent to the orbit. Our analysis of the optical links is fully general relativistic and the numerical code takes into account effects such as the Sagnac, Shapiro delay, etc.. We show that with the deemed parameters in the design of LISA, there are symmetries inherent in the configuration of LISA and in the physics, which may be used effectively to suppress the residual laser noise in the modified first generation TDI. We demonstrate our results for some important TDI variables

Swarm-intelligent search for gravitational waves from eccentric binary mergers

We implement an eccentric search for compact binary mergers based on particle swarm optimization. The orbital eccentricity is an invaluable input for understanding the formation scenarios of the binary mergers and can play a pivotal role in finding their electromagnetic counterparts. Current modelled searches rely on pre-computed template banks that are computationally expensive and resistant towards expanding the search parameter space dimensionality. On the other hand, particle swarm optimization offers a straightforward algorithm that dynamically selects template points while exploring an arbitrary dimensional parameter space. Through extensive evaluation using simulated signals from spin-aligned eccentric binary mergers, we discovered that the search exhibits a remarkable autonomy in capturing the effects of both eccentricity and spin. We describe our search pipeline and revisit some of the merger candidates from the gravitational wave transient catalogs

Standard Coupling Unification in SO(10), Hybrid Seesaw Neutrino Mass and Leptogenesis, Dark Matter, and Proton Lifetime Predictions

We discuss gauge coupling unification of the SM descending directly from SO(10) while providing solutions to the three outstanding problems: neutrino masses, dark matter, and the baryon asymmetry of the universe. Conservation of matter parity as gauged discrete symmetry in the model calls for high-scale spontaneous symmetry breaking through ${126}_H$ Higgs representation. This naturally leads to the hybrid seesaw formula for neutrino masses mediated by heavy scalar triplet and right-handed neutrinos. The seesaw formula predicts two distinct patterns of RH$\nu$ masses, one hierarchical and another not so hierarchical (or compact) when fitted with the neutrino oscillation data. Predictions of the baryon asymmetry via leptogenesis are investigated through the decays of both the patterns of RH$\nu$ masses. A complete flavor analysis has been carried out to compute CP-asymmetries and solutions to Boltzmann equations have been utilized to predict the baryon asymmetry. The additional contribution to vertex correction mediated by the heavy left-handed triplet scalar is noted to contribute as dominantly as other Feynman diagrams. We have found successful predictions of the baryon asymmetry for both the patterns of RH$\nu$ masses. The triplet fermionic dark matter at the TeV scale carrying even matter parity is naturally embedded into the non-standard fermionic representation ${45}_F$ of SO(10). In addition to the triplet scalar and the triplet fermion, the model needs a nonstandard color octet fermion of mass $\sim 10^7$ GeV to achieve precision gauge coupling unification. Threshold corrections due to superheavy components of ${126}_H$ and other representations are estimated and found to be substantial. It is noted that the proton life time predicted by the model is accessible to the ongoing and planned experiments over a wide range of parameter space.Comment: 58 pages PDFLATEX, 19 Figures, Revised as suggested by JHEP Revie

Optimising the directional sensitivity of LISA

It was shown in a previous work that the data combinations canceling laser frequency noise constitute a module - the module of syzygies. The cancellation of laser frequency noise is crucial for obtaining the requisite sensitivity for LISA. In this work we show how the sensitivity of LISA can be optimised for a monochromatic source - a compact binary - whose direction is known, by using appropriate data combinations in the module. A stationary source in the barycentric frame appears to move in the LISA frame and our strategy consists of "coherently tracking" the source by appropriately "switching" the data combinations so that they remain optimal at all times. Assuming that the polarisation of the source is not known, we average the signal over the polarisations. We find that the best statistic is the `network' statistic, in which case LISA can be construed of as two independent detectors. We compare our results with the Michelson combination, which has been used for obtaining the standard sensitivity curve for LISA, and with the observable obtained by optimally switching the three Michelson combinations. We find that for sources lying in the ecliptic plane the improvement in SNR increases from 34% at low frequencies to nearly 90% at around 20 mHz. Finally we present the signal-to-noise ratios for some known binaries in our galaxy. We also show that, if at low frequencies SNRs of both polarisations can be measured, the inclination angle of the plane of the orbit of the binary can be estimated.Comment: 16 pages, 8 figures, submitted to Phys Rev

A User’s Perspective on the Database of Services Sector in Indian Economy

Measuring the contribution of services to the Indian economy is a challenging task because it presents problems not encountered in the primary and secondary sectors. The authors discuss problems found particularly in quantifying the contribution of the banking and software sectors and suggest ways of overcoming these problems.database; services sector; banking; software sector; India

Ca2+ Efflux from Temperature Sensitive Liposomes and In Situ Formation of Metal Cholate Liposome Gels: Basic Studies and Potentials for Sustained Site-Specific Drug Delivery

Liposomes or vesicles are biomimetic close containers for the delivery of drugs at the local site for an extended period of time. On the other hand hydrogels which are three-dimensional hydrophilic matrices are another class of popular materials for sustained release. Such hybrids combine the features of liposomes and polymer to ensure a sustained local drug delivery. In the present work a novel liposome/hydrogel soft assembly is explored which may be potentially useful for drug delivery applications. We report thermally triggered release of Ca+2 from temperature sensitive liposomal  compartments constituted as 90 mol% DPPC and 10 mol% DMPC to induce rapid gelation of a solution of calcium cholate and AgNO3 (extravesicular precursor fluid). Calcium chloride loaded liposomes were prepared using the lipid film rehydration method. The formation of unilamellar bilayer were supported by the fluorometric studies using a compatible and labeled fluoropore (NBD-PS). Hydrogels were obtained by mixing Ca+2 loaded liposome with extravesicular precursor fluid and incubating the content at 37oC. The concentration of the cholate during gelation was sublytic in order to avoid vesicle solubilization. The integrity of liposomes within the hydrogels were preserved during gelation as confirmed by transmission electron microscopy (TEM). The presence of low concentration of cholate (for example 0.05 mM) also permitted spectrophotometric monitoring of Ca+2 efflux for Ca-vesicles employing calcium sensitive dye, Arsenazo III.  We expect that this simple experiment may also be useful for developing implantable as well as rapidly gelling injectable biomaterials for site-specific drug delivery. The present work is also significant as the antimicrobial properties of hydrogels containing silver has been widely recognized for its therapeutic profile.   Keywords: Liposome, triggered release, metal cholate liposome gel, site-specific delivery

Gyroscopic Precession and Inertial Forces in Axially Symmetric Stationary Spacetimes

We study the phenomenon of gyroscopic precession and the analogues of inertial forces within the framework of general relativity. Covariant connections between the two are established for circular orbits in stationary spacetimes with axial symmetry. Specializing to static spacetimes, we prove that gyroscopic precession and centrifugal force both reverse at the photon orbits. Simultaneous non-reversal of these in the case of stationary spacetimes is discussed. Further insight is gained in the case of static spacetime by considering the phenomena in a spacetime conformal to the original one. Gravi-electric and gravi-magnetic fields are studied and their relation to inertial forces is established.Comment: 21 pages, latex, no figures, http://202.41.67.76/~nayak/gpifass.te