Photon redshift and the appearance of a naked singularity

In this paper we analyze the redshift as observed by an external observer receiving photons which terminate in the past at the naked singularity formed in a Tolman-Bondi dust collapse. Within the context of models considered here it is shown that photons emitted from a weak curvature naked singularity are always finitely redshifted to an external observer. Certain cases of strong curvature naked singularities, including the self-similar one, where the photons are infinitely redshifted are also pointed out.Comment: Latex file, 14 pages, no figures, one change in the reference. Accepted for publication in Phys. Rev.

Null Geodesic Expansion in Spherical Gravitational Collapse

We derive an expression for the expansion of outgoing null geodesics in spherical dust collapse and compute the limiting value of the expansion in the approach to singularity formation. An analogous expression is derived for the spherical collapse of a general form of matter. We argue on the basis of these results that the covered as well as the naked singularity solutions arising in spherical dust collapse are stable under small changes in the equation of state.Comment: 10 pages, Latex File, No figure

Analysis of curtailment at The Geysers geothermal Field, California

Geothermal energy has traditionally been viewed as a baseload energy source, but the rapid growth of intermittent renewable energy has led to a need for more flexibility in power generation to avoid mandatory curtailment imposed by grid operators. This study of curtailment at The Geysers provides insights into the magnitude, duration, frequency, temporal and spatial distribution, and potential causes of curtailment events between 2013 and 2018. Annual levels of curtailment range during this period from 9 to 47 GW h, representing 0.15 to 0.81 % of the net generation. Most curtailments occurred at the power plants connected to a lower capacity transmission line and may result from transmission constriction. There is a clear link between negative pricing and economic curtailment, especially when solar production is higher. Economic curtailment events tend to be only a few hours and vary in magnitude up to almost 300 MW, whereas transmission-related curtailment events can be up to several weeks in duration. It is likely that curtailment of geothermal power will be an increasing concern, and could be mitigated by flexible generation strategies and increases in energy storage. It is critical to know the nature of curtailment events so that flexible generation options can be assessed properly

Formulation and Evaluation of Polyherbal Anthelmintic Preparation

The present study was done with the aim to formulate an anthelmintic preparation and to evaluate anthelmintic activity of formulation containing traditionally user herbs viz., Plumbago zeylanica (leaves), Hyoscyamus niger (roots) and Abultion indicum (leaves) using adult earthworm Pheritima posthuma. The aqueous and ethanolic extract of the crude drug of different concentration were tested which involve determination of paralysis time and time to kill the worms. Piperazine citrate was used as standard and it was found that the PHFEE activity is higher than PHFAE

Compact thermally tunable silicon racetrack modulators based on an asymmetric waveguide

A compact wavelength-tunable 10-Gb/s silicon racetrack modulator with integrated thermo-optic heater is demonstrated by using a waveguide with an asymmetric cross section, combining the compact footprint of microdisk modulators with the design simplicity of regular racetrack or ring modulators. The outer perimeter of the asymmetric racetrack modulator is fully etched to maximize optical confinement, and the inner waveguide edge is shallowly etched to maintain an electrically conductive path to the embedded p-n diode and to control the propagation of the asymmetric optical mode and its coupling to the bus waveguide. The resistive heating elements based on highly doped Si strips are implemented at the outer edge of the modulator for thermo-optic control. The asymmetric modulators can be fabricated along with Si wire waveguides and shallowly etched fiber-grating couplers using a simple process flow involving just two Si-patterning steps. Devices with a bending radius of 10 mu m and a novel "T"-shaped p-n diode layout have been fabricated, and exhibit electro-optic modulation and heater efficiencies of 28 pm/V and 42 pm/mW, respectively. At 10 Gb/s, a stable extinction ratio of 10 dB is demonstrated from a 2V(pp) drive swing, which can be maintained over a wavelength range of 4.6 nm by thermally tuning the modulator. This is equivalent with a temperature variation of about 62 degrees C

Initial data and the end state of spherically symmetric gravitational collapse

Generalizing earlier results on the initial data and the final fate of dust collapse, we study here the relevance of the initial state of a spherically symmetric matter cloud towards determining its end state in the course of a continuing gravitational collapse. It is shown that given an arbitrary regular distribution of matter at the initial epoch, there always exists an evolution from this initial data which would result either in a black hole or a naked singularity depending on the allowed choice of free functions available in the solution. It follows that given any initial density and pressure profiles for the cloud, there is a non-zero measure set of configurations leading either to black holes or naked singularities, subject to the usual energy conditions ensuring the positivity of energy density. We also characterize here wide new families of black hole solutions resulting from spherically symmetric collapse without requiring the cosmic censorship assumption.Comment: Ordinary Tex file, 31 pages no figure

Mind the gap: temporal trends in inequalities in infant and child mortality in India (1992–2016)

- Temporal trends in inequalities in infant and child mortality over two and half decades in India. - Relative change in inequalities in child mortality over survey periods. - Scatter plots to identify states with largest inequalities among wealth index groups. - Concentration Index by various background characteristics. - Decomposition analysis identifying the factors contributing in inequality in infant mortality between richest and poorest groups. - Gap between the poorest and richest groups has narrowed in most states in India in recent years

Naked Singularities in Spherically Symmetric Inhomogeneous Tolman-Bondi Dust Cloud Collapse

We investigate the occurrence and nature of naked singularity for the inhomogeneous gravitational collapse of Tolman-Bondi dust clouds.It is shown that the naked singularities form at the center of the collapsing cloud in a wide class of collapse models which includes the earlier cases considered by Eardley and Smarr and Christodoulou. This class also contains self-similar as well as non-self-similar models. The structure and strength of this singularity is examined and the question is investigated as to when a non-zero measure set of non-spacelike trajectories could be emitted from the singularity as opposed to isolated trajectories coming out. It is seen that the weak energy condition and positivity of energy density ensures that the families of non-spacelike trajectories come out of the singularity. The curvature strength of the naked singularity is examined which provides an important test for its physical significance and powerful curvature growth near the naked singularity is pointed out for several subclasses considered. The conditions are discussed for the naked singularity to be globally naked. Implications for the basic issue of the final fate of gravitational collapse are considered once the inhomogeneities in the matter distribution are taken into account. It is argued that a physical formulation for the cosmic censorship may be evolved which avoids the features above. Possibilities in this direction are discussed while indicating that the analysis presented here should be useful for any possible rigorous formulation of the cosmic censorship hypothesis.Comment: 41 pages, TIFR preprint TAP 9/9