Viscous Stability of Relativistic Keplerian Accretion Disks

We investigate the viscous stability of thin, Keplerian accretion disks in regions where general relativistic (GR) effects are essential. For gas pressure dominated (GPD) disks, we show that the Newtonian conclusion that such disks are viscously stable is reversed by GR modifications in the behaviors of viscous stress and surface density over a significantly large annular region not far from the innermost stable orbit at r=\rms. For slowly-rotating central objects, this region spans a range of radii 14\lo r\lo 19 in units of the central object's mass $M$. For radiation pressure dominated (RPD) disks, the Newtonian conclusion that they are viscously unstable remains valid after including the above GR modifications, except in a very small annulus around $r\approx 14M$, which has a negligible influence. Inclusion of the stabilizing effect of the mass-inflow through the disk's inner edge via a GR analogue of Roche-lobe overflow adds a small, stable region around \rms~for RPD disks, but leaves GPD disks unchanged. We mention possible astrophysical relevance of these results, particularly to the high-frequency X-ray variabilities observed by the $Rossi$ $X-ray$ $Timing$ $Explorer$.Comment: 18 pages, 3 figures, accepted by The Astrophysical Journal Letter

Kumaraswamy-Half-Cauchy Distribution: Characterizations and Related Results

We present various characterizations of a recently introduced distribution (Ghosh 2014), called Kumaraswamy- Half- Cauchy distribution based on: (i) a simple relation between two truncated moments; (ii) truncated moment of certain function of the 1st order statistic; (iii) truncated moment of certain function of the random variable; (iv) hazard function; (v) distribution of the 1st order statistic; (vi) via record values. We also provide some remarks on bivariate Gumbel copula distribution whose marginal distributions are Kumaraswamy- Half-Cauchy distributions

Planar Two-particle Coulomb Interaction: Classical and Quantum Aspects

The classical and quantum aspects of planar Coulomb interactions have been studied in detail. In the classical scenario, Action Angle Variables are introduced to handle relativistic corrections, in the scheme of time-independent perturbation theory. Complications arising due to the logarithmic nature of the potential are pointed out. In the quantum case, harmonic oscillator approximations are considered and effects of the perturbations on the excited (oscillator) states have been analysed. In both the above cases, the known 3+1-dimensional analysis is carried through side by side, for a comparison with the 2+1-dimensional (planar) results.Comment: LaTex, Figures on request, e-mail:<[email protected]

Design Issues for Generalized Linear Models: A Review

Generalized linear models (GLMs) have been used quite effectively in the modeling of a mean response under nonstandard conditions, where discrete as well as continuous data distributions can be accommodated. The choice of design for a GLM is a very important task in the development and building of an adequate model. However, one major problem that handicaps the construction of a GLM design is its dependence on the unknown parameters of the fitted model. Several approaches have been proposed in the past 25 years to solve this problem. These approaches, however, have provided only partial solutions that apply in only some special cases, and the problem, in general, remains largely unresolved. The purpose of this article is to focus attention on the aforementioned dependence problem. We provide a survey of various existing techniques dealing with the dependence problem. This survey includes discussions concerning locally optimal designs, sequential designs, Bayesian designs and the quantile dispersion graph approach for comparing designs for GLMs.Comment: Published at http://dx.doi.org/10.1214/088342306000000105 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Dirichlet Process Hidden Markov Multiple Change-point Model

This paper proposes a new Bayesian multiple change-point model which is based on the hidden Markov approach. The Dirichlet process hidden Markov model does not require the specification of the number of change-points a priori. Hence our model is robust to model specification in contrast to the fully parametric Bayesian model. We propose a general Markov chain Monte Carlo algorithm which only needs to sample the states around change-points. Simulations for a normal mean-shift model with known and unknown variance demonstrate advantages of our approach. Two applications, namely the coal-mining disaster data and the real United States Gross Domestic Product growth, are provided. We detect a single change-point for both the disaster data and US GDP growth. All the change-point locations and posterior inferences of the two applications are in line with existing methods.Comment: Published at http://dx.doi.org/10.1214/14-BA910 in the Bayesian Analysis (http://projecteuclid.org/euclid.ba) by the International Society of Bayesian Analysis (http://bayesian.org/

Three Dimensional Gauge Theory with Topological and Non-topological Mass: Hamiltonian and Lagrangian Analysis

Three dimensional (abelian) gauged massive Thirring model is bosonized in the large fermion mass limit. A further integration of the gauge field results in a non-local theory. A truncated version of that is the Maxwell Chern Simons (MCS) theory with a conventional mass term or MCS Proca theory. This gauge invariant theory is completely solved in the Hamiltonian and Lagrangian formalism, with the spectra of the modes determined. Since the vector field constituting the model is identified (via bosonization) to the fermion current, the charge current algebra, including the Schwinger term is also computed in the MCS Proca model.Comment: Eight pages, Latex, No figures

Magnetized Accretion Inside the Marginally Stable Orbit around a Black Hole

Qualitative arguments are presented to demonstrate that the energy density of magnetic fields in matter accreting onto a black hole inside the marginally stable orbit is automatically comparable to the rest-mass energy density of the accretion flow. Several consequences follow: magnetic effects must be dynamically significant, but cannot be so strong as to dominate; outward energy transport in Alfven waves may alter the effective efficiency of energy liberation; and vertical magnetic stresses in this region may contribute to "coronal" activity.Comment: to appear in Ap. J. Letter

Acid/Base Controlled Size Modulation of Capsular Phosphates, Hydroxide Encapsulation, Quantitative and Clean Extraction of Sulfate with Carbonate Capsules of a Tripodal Urea Receptor

A simple tris-(2-aminoethyl) amine based pentafluorophenyl substituted tripodal urea receptor L has been extensively studied as a versatile receptor for various anions. Combined H-1-NMR, Isothermal Titration Calorimetry (ITC) and single crystal X-ray diffraction studies reveal that mononegative anions like F-, OH- and H2PO4- are encapsulated into the pseudocapsular dimeric assemblies of L with 1 : 1 stoichiometry whereas dinegative anions like CO32-, SO42- and HPO42- form tight capsular dimeric assemblies of L with 1 : 2 stoichiometries. Single crystal X-ray diffraction study clearly depicts that the size of the dimer of H2PO4- encapsulated pseudocapsule is 13.8 angstrom whereas the size of the tight HPO42- encapsulated capsular assembly is only 9.9 angstrom. The charge dependent anion encapsulated capsular size modulation of phosphates has been demonstrated by simple acid/base treatment via solution state P-31-NMR and single crystal X-ray diffraction studies. L is also capable of encapsulating hydroxide in its C-3v-symmetric cavity that is achieved upon treating a DMSO solution of L with tetrabutylammonium (TBA) cyanide and characterized by single crystal X-ray diffraction study. To the best of our knowledge this is the first report on the encapsulation of hydroxide in a neutral synthetic receptor. The excellent property of L to quantitatively capture aerial CO2 in the form of CO32- capsules [L-2(CO3)][N(n-Bu)(4)](2) in basic DMSO solution has been utilized to study the liquid-liquid extraction of SO42- from water via anion exchange. Almost quantitative and clean extraction of SO42- from water (99% from extracted pure mass and > 95% shown gravimetrically) has been unambiguously demonstrated by NMR, FT-IR, EDX, XRD and PXRD studies. Selective SO42- extraction is also demonstrated even in the presence of H2PO4- and NO3-. On the other hand the mixtures of L and TBACl (to solubilize L in CHCl3) results impure sulfate extraction even when 1 : 1 L/TBACl is used. Similar impure SO42- extraction is also observed when organic layers containing [L(Cl)][N(n-Bu)(4)] are used as the extractant, obtained upon precipitating SO42- from the extracted mass, [L-2(SO4)][N(n-Bu)(4)](2) in the carbonate capsules method using aqueous BaCl2 solution.Department of Science and TechnologyCSIR, IndiaChemistr

Coherent States for the Non-Linear Harmonic Oscillator

Wave packets for the Quantum Non-Linear Oscillator are considered in the Generalized Coherent State framerwork. To first order in the non-linearity parameter the Coherent State behaves very similarly to its classical counterpart. The position expectation value oscillates in a simple harmonic manner. The energy-momentum uncertainty relation is time independent as in a harmonic oscillator. Various features, (such as the Squeezed State nature), of the Coherent State have been discussed