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

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

Time Delay Interferometry for LISA with one arm dysfunctional

In order to attain the requisite sensitivity for LISA - a joint space mission of the ESA and NASA- the laser frequency noise must be suppressed below the secondary noises such as the optical path noise, acceleration noise etc. By combining six appropriately time-delayed data streams containing fractional Doppler shifts - a technique called time delay interferometry (TDI) - the laser frequency noise may be adequately suppressed. We consider the general model of LISA where the armlengths vary with time, so that second generation TDI are relevant. However, we must envisage the possibility, that not all the optical links of LISA will be operating at all times, and therefore, we here consider the case of LISA operating with two arms only. As shown earlier in the literature, obtaining even approximate solutions of TDI to the general problem is very difficult. Since here only four optical links are relevant, the algebraic problem simplifies considerably. We are then able to exhibit a large number of solutions (from mathematical point of view an infinite number) and further present an algorithm to generate these solutions

Effect of dietary supplementation of Bacillus subtilis on haematological and immunological parameters of Catla catla (Hamilton)

Effect of dietary supplementation of a Gram-positive, aerobic, probiotic bacterium Bacillus subtilis on the immunohaematological indices during pre- and post-challenge in Indian major carp, catla (Catla catla), was studied. The B. subtilis was administered orally at four different doses 1.0 × 106 (T1), 1.0 × 107 (T2), 1.0 × 108 (T3), and 1.0 × 109 (T4) cfu g−1 feed to C. catla for 90 days. The positive control (Cp) and negative control (Cn) were fed with feed without B. subtilis for the same period. On the 60th day, blood and serum were sampled to determine various haematological and serum parameters. Fish were challenged intraperitoneally with Aeromonas hydrophila after 60 days in all the treatment groups and Cp, while the Cn was challenged with phosphate-buffered saline (PBS, pH 7.2) only. Dietary supplementation of B. subtilis leads to the rise of various immunological and haematological parameters in catla during the pre- and post-challenge. During pre-challenge, the highest TEC (1.30 ± 0.02 × 106 cells mm−3), haemoglobin (7.43 ± 0.25 g %), total serum protein (3.89 ± 0.08 g dL−1), and serum lysozyme activity (8.39 ± 0.01 µg ml−1) were recorded in fishes fed feed containing B. subtilis at 1 × 109 cfu/g feed (T4). The highest survival percentage (86.33 %) was also observed in T4 group. The significantly increased survival percentage (P < 0.05) of B. subtilis-treated groups in comparison with control group (Cp) suggests that dietary supplementation of this probiotic bacterium can protect catla from A. hydrophila infection by enhancing innate immunity