Showing papers by "Tata Institute of Fundamental Research published in 1996"

Introduction to algorithms: 4. Turtle graphics

Abstract: The primary purpose of a programming language is to assist the programmer in the practice of her art. Each language is either designed for a class of problems or supports a different style of programming. In other words, a programming language turns the computer into a ‘virtual machine’ whose features and capabilities are unlimited. In this article, we illustrate these aspects through a language similar tologo. Programs are developed to draw geometric pictures using this language.

The Current State of Solar Modeling

Abstract: Data from the Global Oscillation Network Group (GONG) project and other helioseismic experiments provide a test for models of stellar interiors and for the thermodynamic and radiative properties, on which the models depend, of matter under the extreme conditions found in the sun. Current models are in agreement with the helioseismic inferences, which suggests, for example, that the disagreement between the predicted and observed fluxes of neutrinos from the sun is not caused by errors in the models. However, the GONG data reveal subtle errors in the models, such as an excess in sound speed just beneath the convection zone. These discrepancies indicate effects that have so far not been correctly accounted for; for example, it is plausible that the sound-speed differences reflect weak mixing in stellar interiors, of potential importance to the overall evolution of stars and ultimately to estimates of the age of the galaxy based on stellar evolution calculations.

Spectroscopic evidence for a pseudogap in the normal state of underdoped high- T c superconductors

Abstract: IT is well known that BCS mean-field theory is remarkably successful in describing conventional superconductors. A central concept of BCS theory is the energy gap in the electronic excitation spectrum below the superconducting transition temperature, Tc. The gap also serves as the order parameter: quite generally, long-range phase coherence and a non-zero gap go hand-in-hand1. But in underdoped high-Tc superconductors there is considerable evidence that a pseudogap (a suppression of spectral weight) is already formed in the normal state above Tc—first, from studies of the spin excitation spectrum2–5,24, which measure a 'spin gap', and later from a variety of other probes6–10. Here we present a study of underdoped Bi2Sr2CaCu2O8+δ (Bi2212) using angle-resolved photoemission spectroscopy (ARPES), which directly measures the momentum-resolved electron excitation spectrum of the CuO2 planes. We find that a pseudogap with d-wave symmetry opens up in the normal state below a temperature T* > Tc, and develops into the d-wave superconducting gap once phase coherence is established below Tc.

Differential Rotation and Dynamics of the Solar Interior

Abstract: Splitting of the sun's global oscillation frequencies by large-scale flows can be used to investigate how rotation varies with radius and latitude within the solar interior. The nearly uninterrupted observations by the Global Oscillation Network Group (GONG) yield oscillation power spectra with high duty cycles and high signal-to-noise ratios. Frequency splittings derived from GONG observations confirm that the variation of rotation rate with latitude seen at the surface carries through much of the convection zone, at the base of which is an adjustment layer leading to latitudinally independent rotation at greater depths. A distinctive shear layer just below the surface is discernible at low to mid-latitudes.

Survey of sociodemographic characteristics of tobacco use among 99,598 individuals in Bombay, India using handheld computers.

Abstract: OBJECTIVES: To study the diversity and sociodemographic characteristics of tobacco use in Bombay, India. DESIGN: Population-based, cross- sectional, house-to-house survey with face-to-face interviews in the city of Bombay during 1992-94. Data was input directly into a programmed, handheld computer (electronic diary). PARTICIPANTS: Permanent residents of the city of Bombay aged 35 years and older. MAIN OUTCOME MEASURES: Tobacco use in various smoking and smokeless forms. RESULTS: 99598 individuals were interviewed (60% women, 40% men). Among women, prevalence of tobacco use was high (57.5%) but almost solely in the smokeless form. Among men, 69.3% reported current tobacco use and 23.6% were smokers. The most common smokeless tobacco practice among women was mishri use (44.5% of smokeless users) and among men betel quid with tobacco (27.1%). About half of smokers used bidi and half smoked cigarettes. Chewing areca nut without tobacco was rare (< 0.5% of smokeless users). Educational level was inversely associated with tobacco use of all kinds except cigarette smoking. CONCLUSIONS: The pattern of tobacco use varies across India and, in Bombay, is very different from other areas. Using handheld computers to collect data in the field was successful.

Moduli for principal bundles over algebraic curves: II

Abstract: We classify principal bundles on a compact Riemann surface. A moduli space for semistable principal bundles with a reductive structure group is constructed using Mumford’s geometric invariant theory.

Eulerian Walkers as a Model of Self-Organized Criticality.

Abstract: We propose a new model of self-organized criticality. A particle is dropped at random on a lattice and moves along directions specified by arrows at each site. As it moves, it changes the direction of the arrows according to fixed rules. On closed graphs these walks generate Euler circuits. On open graphs, the particle eventually leaves the system, and a new particle is then added. The operators corresponding to particle addition generate an Abelian group, same as the group for the Abelian sandpile model on the graph. We determine the critical steady state and some critical exponents exactly, using this equivalence.

Angle-resolved photoemission spectroscopy study of the superconducting gap anisotropy in Bi2Sr2CaCu2O8+x.

Abstract: We report measurements of the momentum dependence of the superconducting gap in ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}\mathrm{Ca}{\mathrm{Cu}}_{2}{\mathrm{O}}_{8+x}$ with angle-resolved photoemission spectroscopy using a dense sampling of the Brillouin zone in the vicinity of the Fermi surface. In the $Y$ quadrant of the zone, where there are no complications from ghost bands caused by the superlattice, we find a gap function consistent within error bars to the form $cos({k}_{x})\ensuremath{-}cos({k}_{y})$ expected for a $d$-wave order parameter. Similar results are found in the $X$ quadrant with the photon polarization chosen to enhance main band emission over that due to ghost bands.

The Forward muon detector of L3

Abstract: The forward-backward muon detector of the L3 experiment is presented. Intended to be used for LEP 200 physics, it consists of 96 self-calibrating drift chambers of a new design enclosing the magnet pole pieces of the L3 solenoid. The pole pieces are toroidally magnetized to form two independent analyzing spectrometers. A novel trigger is provided by resistive plate counters attached to the drift chambers. Details about the design, construction and performance of the whole system are given together with results obtained during the 1995 running at LEP.

Size-induced structural transitions in the cu-o and ce-o systems

Abstract: We have studied the effect of reducing the particle size on the crystal structures of copper oxide and cerium oxide. Below 25 nm, the cubic ${\mathrm{Cu}}_{2}$O is found to be more stable than the monoclinic CuO. This confirms an earlier conjecture that the ionic character of a solid tends to increase with a reduction in the particle size. As a result, high-symmetry crystal structures are more likely to be stable at smaller sizes. For cerium oxide, the bulk (cubic) ${\mathrm{CeO}}_{2}$ phase remains stable down to 4.8 nm and, as expected, does not undergo a transition to any of the other available structures with lower symmetry. \textcopyright{} 1996 The American Physical Society.

The Solar Acoustic Spectrum and Eigenmode Parameters

Abstract: The Global Oscillation Network Group (GONG) project estimates the frequencies, amplitudes, and linewidths of more than 250,000 acoustic resonances of the sun from data sets lasting 36 days. The frequency resolution of a single data set is 0.321 microhertz. For frequencies averaged over the azimuthal order m , the median formal error is 0.044 microhertz, and the associated median fractional error is 1.6 × 10 −5 . For a 3-year data set, the fractional error is expected to be 3 × 10 −6 . The GONG m -averaged frequency measurements differ from other helioseismic data sets by 0.03 to 0.08 microhertz. The differences arise from a combination of systematic errors, random errors, and possible changes in solar structure.

Evidence for Large-Scale Solar Magnetic Reconnection from Radio and X-Ray Measurements

Abstract: Utilizing Yohkoh Soft X-ray Telescope and Nancay radioheliograph data, we present, for the first time, observations of expanding twisted X-ray loops and a series of nonthermal radio bursts that follow the loop expansion in time and space up to ∼12′ distance. The loops were produced during a long-duration C4.7 flare close to disk center on 1994 October 25 at 1049 UT. The series of radio bursts were observed on the southern hemisphere above a weak positive-polarity region. The Kitt Peak magnetogram shows the existence of a weak negative-polarity region on the northern hemisphere at the same heliolongitude. Simultaneously with the nonthermal radio bursts, we observed the appearance of two remote X-ray brightenings and subsequent formation of two coronal holes above these weak (quiet) magnetic regions of opposite polarity, which strongly suggest the involvement of these remote regions in the event. During the 6 hr-long gradual phase of the flare, new X-ray loop connections developed among the active region and the remote quiet regions. A nonthermal radio continuum emission originating from the active region was also observed. We propose that the series of radio bursts, two remote X-ray brightenings, and new coronal loop connections were all signatures of a large-scale reconnection process between the expanding twisted flare loops and overlying transequatorial loops connecting quiet-Sun regions. The reconnection was only partial; the external part of the overlying large-scale fields were pushed out in the solar wind by the expanding twisted loops, leading to the formation of the coronal holes. The interaction between the active region and the large-scale fields seemed to be active during the entire gradual phase of the flare. This scenario may also explain the measurement of high-energy electrons in the interplanetary medium from 74° south heliolatitude as observed by Ulysses. © 1996. The American Astronomical Society. All rights reserved.

Limit distributions of expanding translates of certain orbits on homogeneous spaces

Abstract: LetL be a Lie group and λ a lattice inL. SupposeG is a non-compact simple Lie group realized as a Lie subgroup ofL and $$\overline {GA} = L$$ . LetaeG be such that Ada is semisimple and not contained in a compact subgroup of Aut(Lie(G)). Consider the expanding horospherical subgroup ofG associated toa defined as U+ ={geG:a −n gan} →e as n → ∞. Let Ω be a non-empty open subset ofU + andn i → ∞ be any sequence. It is showed that $$\overline { \cup _{i = 1}^\infty a^n \Omega \Lambda } = L$$ . A stronger measure theoretic formulation of this result is also obtained. Among other applications of the above result, we describeG-equivariant topological factors of L/gl × G/P, where the real rank ofG is greater than 1,P is a parabolic subgroup ofG andG acts diagonally. We also describe equivariant topological factors of unipotent flows on finite volume homogeneous spaces of Lie groups.

Excitations of D-strings, Entropy and Duality

Abstract: We examine the BPS and low energy non-BPS excitations of the D-string, in terms of open strings that travel on the D-string. We use this to study the energy thresholds for exciting a long D-string, for arbitrary winding number. We also compute the leading correction to the entropy from non-BPS states for a long D-string, and observe the relation of all these quantities with the corresponding quantities for the elementary string.

Zero Energy Rotating Accretion Flows near a Black Hole

Abstract: We characterize the nature of thin, axisymmetric, inviscid, accretion flows of cold adiabatic gas with zero specific energy in the vicinity of a black hole by the specific angular momentum. Using two-dimensional hydrodynamic simulations in cylindrical geometry, we present various regimes in which the accretion flows behave distinctly differently. When the flow has a small angular momentum $(\lambda\lsim\lambda_b)$, most of the material is accreted into the black hole forming a quasi-spherical flow or a simple disk-like structure around it. When the flow has a large angular momentum (typically, larger than the marginally bound value, $\lambda\gsim\lambda_{mb}$), almost no accretion into the black hole occurs. Instead, the flow produces a stable standing shock with one or more vortices behind it and is deflected away at the shock as a conical outgoing wind of higher entropy. If the flow has an angular momentum somewhat smaller than $\lambda_{mb}$ $(\lambda_{u}\lsim\lambda\lsim\lambda_{mb})$, a fraction (typically, $5-10$\%) of the incoming material is accreted into the black hole, but the the flow structure formed is similar to that as for $\lambda\gsim\lambda_{mb}$. Some of the deflected material is accreted back into the black hole, while the rest is blown away as an outgoing wind. These two cases with $\lambda\gsim\lambda_u$ correspond those studied in the previous works by Molteni, Lanzafame, \& Chakrabarti (1994) and Ryu \etal (1995). However, the flow with an angular momentum close to the marginally stable value $(\lambda_{ms})$ is found to be unstable. More specifically, if $\lambda_b\lsim\lambda\sim\lambda_{ms}\lsim\lambda_u$, the flow displays a distinct periodicity in the sense that the inner part of the disk is built and

Superconductor-insulator transition in a disordered electronic system

Abstract: We study an electronic model of a two-dimensional $s$-wave superconductor in a random potential using quantum Monte Carlo simulations The superfluid density and the strength of the delta function in the optical conductivity are found to vanish beyond a critical disorder We calculate the temperature-dependent resistivity ${\ensuremath{\rho}}_{\mathrm{dc}}(T)$ for a highly disordered interacting Fermi system Using this we identify the nonsuperconducting state as an insulator

Measurement of the Positron to Electron Ratio in the Cosmic Rays above 5 GeV

Abstract: As part of a series of experiments to search for antimatter in cosmic rays, the New Mexico State University balloon-borne magnet spectrometer was configured for a flight to study positrons. Two completely new instruments, a transition radiation detector and a silicon-tungsten imaging calorimeter, were added to the magnet spectrometer. These two detectors provided a proton rejection factor better than 3 × 104. This instrument was flown from Fort Sumner, New Mexico, at an average depth of 4.5 g cm-2 of residual atmosphere for a period of 25 hr. We report here the measured fraction of positrons e+/(e+ + e-) from ~5 to 60 GeV at the top of the atmosphere. Our measurements do not show any compelling evidence for an increase in this ratio with energy, and our results are consistent with a constant fraction of 0.078 ± 0.016 over the entire energy region.

Direct observation of particle-hole mixing in the superconducting state by angle-resolved photoemission

Abstract: Particle-hole ($p\ensuremath{-}h$) mixing is a fundamental consequence of the existence of a pair condensate. We present direct experimental evidence for $p\ensuremath{-}h$ mixing in the angle-resolved photoemission (ARPES) spectra in the superconducting state of ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}\mathrm{Ca}{\mathrm{Cu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$. In addition to its pedagogical importance, this establishes unambiguously that the gap observed in ARPES is associated with superconductivity.