Showing papers by "Tata Institute of Fundamental Research published in 1993"

Naked singularities in spherically symmetric inhomogeneous Tolman-Bondi dust cloud collapse

Abstract: We investigate here the occurrence and nature of a 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 are examined, and the question is investigated as to when a nonzero measure set of nonspacelike 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 nonspacelike trajectories come out of the singularity. The curvature strength of the naked singularity is examined, which provides an important test for its physical significance. This is done in terms of the strong curvature condition, which ensures that all the volume forms must be crushed to zero size in the limit of approach to the singularity, and, also, the divergence of the Kretschmann scalar $\mathcal{K}={R}^{\mathrm{abcd}}{R}_{\mathrm{abcd}}$ is pointed out. We show that the class considered here contains subclasses of solutions which admit strong curvature naked singularities in either of the senses stated above. The conditions are discussed for the naked singularity to be globally naked. An implication for the fundamental issue of the final fate of gravitational collapse is that naked singularities need not be considered as artifacts of geometric symmetries of space-time such as self-similarity, but arise in a wide range of gravitational collapse scenarios 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 suggested while indicating that the analysis presented here should be useful for any possible rigorous formulation of the cosmic censorship hypothesis.

Greed is good : approximating independent sets in sparse and bounded-degree graphs

Abstract: Theminimum-degree greedy algorithm, or Greedy for short, is a simple and well-studied method for finding independent sets in graphs. We show that it achieves a performance ratio of (Δ+2)/3 for approximating independent sets in graphs with degree bounded by Δ. The analysis yields a precise characterization of the size of the independent sets found by the algorithm as a function of the independence number, as well as a generalization of Turan's bound. We also analyze the algorithm when run in combination with a known preprocessing technique, and obtain an improved $$(2\bar d + 3)/5$$ performance ratio on graphs with average degree $$\bar d$$ , improving on the previous best $$(\bar d + 1)/2$$ of Hochbaum. Finally, we present an efficient parallel and distributed algorithm attaining the performance guarantees of Greedy.

A multiwavelength study of the eridanus soft X-ray enhancement

Abstract: We present soft X-ray, N(H), and IR maps of the Eridanus soft X-ray enhancement. Soft X-ray maps from the HEAO 1 A-2 LED experiment, processed with a maximum entropy method (MEM) algorithm, show that the enhancement consists of two distinct components: a large hook-shaped component and a small circular component at different temperatures. Both of these are located in 'holes' in the IR emission, and they correspond to N(H) features at very different velocities. The dust surrounding the X-ray enhancements appears to be associated with several high-latitude molecular clouds, which allow us to obtain a probable distance of about 130 pc to the near edge of the main enhancement. The total power emitted by the hot gas is then about 10 exp 35 to 10 exp 36 ergs/s. We consider alternative interpretations of these objects as adiabatic supernova remnants or as stellar wind bubbles and conclude that they are more likely to be stellar wind bubbles, possibly reheated by a SN explosion in the case of the main, hook-shaped object.

Factorisation of generalised theta functions. I

Abstract: We prove a version of “factorisation”, relating the space of sections of theta bundles on the moduli spaces of (parabolic, rank 2) vector bundles on curves of genusg andg−1.

Three-dimensional structure of the solar wind: Variation of density with the solar cycle

Abstract: Interplanetary Scintillation (IPS) measurements obtained from a large number of compact radio sources (nearly 150 sources) distributed over the heliocentric distance range 15–175 solar radii (R(⊙) and heliographic latitude ∼75° N-75° S have been used to study the global three-dimensional density distribution of the solar wind plasma. Contours of constant electron-density fluctuations (ΔNe) in the heliospheric plasma obtained for both the solar minimum and maximum show a strong solar latitude dependence. During low solar activity, the equatorial density-fluctuation value decreases away from the equator towards higher latitudes and is reduced by ∼2.5 times at the poles; the level of turbulence is reduced by a factor of ∼7; the solar-wind mass flux density at the poles is ∼25% lower than the equatorial value. However, during high solar activity, the average distribution of density fluctuations becomes spherically symmetric. In the ecliptic, the variation of ΔNe with the heliocentric distance follows a power law of the formR−2.2 and it does not show any change with solar activity.

Galactic dynamos and density wave theory – II. An alternative treatment for strong non-axisymmetry

Abstract: A steady density wave in a disc-like galaxy could lead to a spiral form for the crucial α-effect term in standard dynamo theory. We had earlier studied this problem under the thin-disc approximation and by effecting an approximate separation of variables between the z-dependence and the r, φ-dependences of the magnetic field. We return to this problem by making an alternative approximation of our equations, which allows a better treatment of the case of strong departures from axisymmetry, albeit with a cruder treatment of the z-dependence. The numerical solution of the equations reveals, as in our earlier work, the existence of rapidly growing, global, bisymmetric magnetic modes, corotating with the density wave

Absolute spectrum and charge ratio of cosmic ray muons in the energy region from 0.2 GeV to 100 GeV at 600 m above sea level

Abstract: We have determined the momentum spectrum and charge ratio of muons in the region from 250 MeV/c to 100 GeV/c using a superconducting magnetic spectrometer. The absolute differential spectrum of muons obtained in this experiment at 600 m above sea level is in good agreement with the previous measurements at sea level. The differential spectrum can be represented by a power law with a varying index, which is consistent with zero below 450 MeV/c and steepens to a value of -2.7 +/- 0.1 between 20 and 100 GeV/c. The integral f1ux of muons measured in this experiment span a very large range of momentum and is in excellent agreement with the earlier results. The positive to negative muon ratio appears to be constant in the entire momentum range covered in this experiment within the errors and the mean value is 1.220 +/- 0.044. The absolute momentum spectrum and the charge ratio measured in this experiment are also consistent with the theoretical expectations. This is the only experiment which covers a wide range of nearly three decades in momentum from a very low momentum.

Genetic Studies on Dynamin Function in Drosophila

Abstract: The shibirets2 mutation of Drosophila melanogaster causes a temperature sensitive inhibition of endocytosis; this in turn leads to synaptic-vesicle depletion and consequent paralysis. Heat-pulses delivered during development of shibirets2 individuals affect the morphology of a number of adult structures. A simple screening protocol has been used to isolate several mutations that partially suppress the temperature-sensitive paralytic phenotype of shibirets2 mutant animals. All of these mutations very tightly linked to shibire and are likely to be second site intragenic mutations that restore partial activity to the shibirets2 product. The mutations suppress both behavioral, and easily-scored developmental phenotypes of shibirets2 characterized in this paper. Our results suggest that defects in endocytosis, and not in microtubule interactions, are responsible for all of the phenotypes of shibirets2 mutant Drosophila examined in this study.

Use of temporal correlation between successive frames in a hidden Markov model based speech recognizer

Abstract: The temporal correlation between successive frames is incorporated in an HMM (hidden Markov model) based speech recognizer. This is done by making the probability of the current observation vector dependent on the previous observation vectors. Preliminary results show that this approach provides significant improvement in recognition performance (with the use of temporal correlation between two successive frames alone). >

CLASSICAL FERMI FLUID AND GEOMETRIC ACTION FOR c=1

Abstract: We formulate the c=1 matrix model as a quantum fluid and discuss its classical limit in detail, emphasizing the ħ corrections. We view the fermi fluid profiles as elements of w∞-coadjoint orbit and write down a geometric action for the classical phase space. In the specific representation of fluid profiles as “strings” the action is written in a four-dimensional form in terms of gauge fields built out of the embedding of the “string” in the phase plane. We show that the collective field action can be derived from the above action provided one restricts to quadratic fluid profiles and ignores the dynamics of their “turning points”.

High-resolution radio observations of Markarian 3

Abstract: We present high-sensitivity 5-GHz MERLIN and 15-GHz VLA observations of the Seyfert nucleus of Markarian 3, with angular resolutions of 40 and 250 mas respectively. Our 5-GHz MERLIN map reveals the best example to date of a pair of highly collimated radio jets in a Seyfert nucleus. The jet system is 2 arcsec (∼ 600 pc) in extent and less than 50 mas across, and lies along P.A. 84°. Embedded in the jets are a number of compact components, and the western side terminates in a bright lobe containing a hotspot. The component at RA (1950) 06 h 09 m 48 s 423, Dec. (1950) 71°03'10″42 is unresolved and is the closest to the peak of the optical continuum emission

Further results on cerium fluoride crystals

Abstract: A systematic investigation of the properties of cerium fluoride monocrystals has been performed by the “Crystal Clear” collaboration in view of a p

On regularity of twisted spherical means and special Hermite expansions

Abstract: Regularity properties of twisted spherical means are studied in terms of certain Sobolev spaces defined using Laguerre functions. As an application we prove a localisation theorem for special Hermite expansions.

Limits on the Magnetic Field Strength at the Base of the Solar Convection Zone

Abstract: Howard (1993) finds a relationship between the tilt angles of BMRs (Bipolar Magnetic Regions) and the separation between their leading and following polarities; the tilt angle increases with polarity separation. Here we present a more detailed analysis of this relationship and show that this effect constrains the strength of the magnetic field at the bottom of the convection zone to a value between 40 and 150 kG, which confirms the constraints put by D'Silva and Choudhuri (1993) based on Joy's law (the tilt-latitude relationship), through an entirely different approach.

W∞ coherent states and path-integral derivation of bosonization of non-relativistic fermions in one dimension

Abstract: We complete the proof of bosonization of non-interacting non-relativistic fermions in one space dimension by deriving the bosonized action using W∞ coherent states in the fermion path-integral. This action was earlier derived by us using the method of co-adjoint orbits. We also discuss the classical limit of the bosonized theory and indicate the precise nature of the truncation of the full theory that leads to the collective field theory.