Singularity: Raychaudhuri Equation once again

I first recount Raychaudhuri's deep involvement with the singularity problem in general relativity. I then argue that precisely the same situation has arisen today in loop quantum cosmology as obtained when Raychaudhuri discovered his celebrated equation. We thus need a new analogue of the Raychaudhuri equation in quantum gravity.Comment: 11 pages, Contribution to Special issue of Pramana on Raychaudhuri Equation at Cross-roads, edited by Naresh Dadhich, Pankaj Joshi and Probir Ro

Non-linear electrical conduction and broadband noise in charge-ordered rare earth manganate Nd_0.5Ca_0.5MnO_3

Measurements of the dc transport properties and the low-frequency conductivity noise in films of charge ordered Nd_0.5Ca_0.5MnO_3 grown on Si subtrate reveal the existence of a threshold field in the charge ordered regime beyond which strong non linear conduction sets in along with a large broad band conductivity noise. Threshold-dependent conduction disappears as T -> T_{CO}, the charge ordering temperature. This observation suggests that the charge ordered state gets depinned at the onset of the non-linear conduction.Comment: 3 pages of two-column text and 4 eps figure

Magnetoresistance of metallic perovskite oxide LaNiO3−δ_{3-\delta}

We report a study of the magnetoresistance (MR) of the metallic perovskite oxide LaNiO$_{3-\delta}$ as a function of the oxygen stoichiometry $\delta$ ($\delta \leq$ 0.14), magnetic field (H $\leq 6T$) and temperature (1.5K $\leq$ T $\leq$ 25K). We find a strong dependence of the nature of MR on the oxygen stoichiometry. The MR at low temperatures change from positive to negative as the sample becomes more oxygen deficient (i.e, $\delta$ increases). Some of the samples which are more resistive, show a resistivity minima at $T_{min}$ $\approx$ 20K. We find that in these samples the MR is positive at T > $T_{min}$ and negative for T < $T_{min}$. We conclude that in the absence of strong magnetic interaction, the negative MR in these oxides can arise from weak localisation effects.Comment: 10 pages in REVTeX format, 4 eps fig

Standardization of setting temperature and time for fish meat

Meat to water ratio used for washing was 1:3 for oil sardine and mackerel; but for pink perch and croaker, it was 1:2. Again the washing process was repeated three times for oil sardine and mackerel; but two times for pink perch and croaker. The washed meat was mixed with 2.5% NaC1 and set at +5°C and +40°C for 1, 2 and 3hrs. The gel strength and expressible water content was measured. Basing on this study, setting temperature at +40°C was selected and with respect to time 1hr for sardine and mackerel and 3hrs for pink perch and croaker was selected

GUTs with dim-5 interactions: Gauge Unification and Intermediate Scales

Dimension-5 corrections to the gauge kinetic term of Grand Unified Theories (GUTs) may capture effects of quantum gravity or string compactification. Such operators modify the usual gauge coupling unification prediction in a calculable manner. Here we examine SU(5), SO(10), and E(6) GUTs in the light of all such permitted operators and calculate the impact on the intermediate scales and the unification programme. We show that in many cases at least one intermediate scale can be lowered to even 1-10 TeV, where a neutral Z' and possibly other states are expected.Comment: 23 pages, 8 figures, 10 tables, Treatment of U(1) mixing effects corrected. Published version

Colossal electroresistance in ferromagnetic insulating state of single crystal Nd0.7_0.7Pb0.3_0.3MnO3_3

Colossal electroresistance (CER) has been observed in the ferromagnetic insulating (FMI) state of a manganite. Notably, the CER in the FMI state occurs in the absence of magnetoresistance (MR). Measurements of electroresistance (ER) and current induced resistivity switching have been performed in the ferromagnetic insulating state of a single crystal manganite of composition Nd$_0.7$Pb$_0.3$MnO$_3$ (NPMO30). The sample has a paramagnetic to ferromagnetic (Curie) transition temperature, Tc = 150 K and the ferromagnetic insulating state is realized for temperatures, T <~ 130 K. The colossal electroresistance, arising from a strongly nonlinear dependence of resistivity ($\rho$) on current density (j), attains a large value ($\approx 100$) in the ferromagnetic insulating state. The severity of this nonlinear behavior of resistivity at high current densities is progressively enhanced with decreasing temperature, resulting ultimately, in a regime of negative differential resistivity (NDR, d$\rho$/dj < 0) for temperatures <~ 25 K. Concomitant with the build-up of the ER however, is a collapse of the MR to a small value (< 20%) even in magnetic field, H = 7 T. This demonstrates that the mechanisms that give rise to ER and MR are effectively decoupled in the ferromagnetic insulating phase of manganites. We establish that, the behavior of ferromagnetic insulating phase is distinct from the ferromagnetic metallic (FMM) phase as well as the charge ordered insulating (COI) phase, which are the two commonly realized ground state phases of manganites.Comment: 24 pages (RevTeX4 preprint), 8 figures, submitted to PR

A Minimal Model of Signaling Network Elucidates Cell-to-Cell Stochastic Variability in Apoptosis

Signaling networks are designed to sense an environmental stimulus and adapt to it. We propose and study a minimal model of signaling network that can sense and respond to external stimuli of varying strength in an adaptive manner. The structure of this minimal network is derived based on some simple assumptions on its differential response to external stimuli. We employ stochastic differential equations and probability distributions obtained from stochastic simulations to characterize differential signaling response in our minimal network model. We show that the proposed minimal signaling network displays two distinct types of response as the strength of the stimulus is decreased. The signaling network has a deterministic part that undergoes rapid activation by a strong stimulus in which case cell-to-cell fluctuations can be ignored. As the strength of the stimulus decreases, the stochastic part of the network begins dominating the signaling response where slow activation is observed with characteristic large cell-to-cell stochastic variability. Interestingly, this proposed stochastic signaling network can capture some of the essential signaling behaviors of a complex apoptotic cell death signaling network that has been studied through experiments and large-scale computer simulations. Thus we claim that the proposed signaling network is an appropriate minimal model of apoptosis signaling. Elucidating the fundamental design principles of complex cellular signaling pathways such as apoptosis signaling remains a challenging task. We demonstrate how our proposed minimal model can help elucidate the effect of a specific apoptotic inhibitor Bcl-2 on apoptotic signaling in a cell-type independent manner. We also discuss the implications of our study in elucidating the adaptive strategy of cell death signaling pathways.Comment: 9 pages, 6 figure

Electromagnetic duality in general relativity

By resolving the Riemann curvature relative to a unit timelike vector into electric and magnetic parts, we consider duality relations analogous to the electromagnetic theory. It turns out that the duality symmetry of the Einstein action implies the Einstein vacuum equation without the cosmological term. The vacuum equation is invariant under interchange of active and passive electric parts giving rise to the same vacuum solutions but the gravitational constant changes sign. Further by modifying the equation it is possible to construct interesting dual solutions to vacuum as well as to flat spacetimes.Comment: 18 pages, LaTEX versio

Non-linear IVIV characteristics in two-dimensional superconductors: Berezinskii-Kosterlitz-Thouless physics vs inhomogeneity

One of the hallmarks of the Berezinskii-Kosterlitz-Thouless (BKT) transition in two-dimensional (2D) superconductors is the universal jump of the superfluid density, that can be indirectly probed via the non-linear exponent of the current-voltage $IV$ characteristics. Here, we compare the experimental measurements of $IV$ characteristics in two cases, namely NbN thin films and SrTiO$_3$-based interfaces. While the former display a paradigmatic example of BKT-like non-linear effects, the latter do not seem to justify a BKT analysis. Rather, the observed $IV$ characteristics can be well reproduced theoretically by modelling the effect of mesoscopic inhomogeneity of the superconducting state. Our results offer an alternative perspective on the spontaneous fragmentation of the superconducting background in confined 2D systems.Comment: Final version, as publishe