Spherical Dust Collapse in Higher Dimensions

We consider here the question if it is possible to recover cosmic censorship when a transition is made to higher dimensional spacetimes, by studying the spherically symmetric dust collapse in an arbitrary higher spacetime dimension. It is pointed out that if only black holes are to result as end state of a continual gravitational collapse, several conditions must be imposed on the collapsing configuration, some of which may appear to be restrictive, and we need to study carefully if these can be suitably motivated physically in a realistic collapse scenario. It would appear that in a generic higher dimensional dust collapse, both black holes and naked singularities would develop as end states as indicated by the results here. The mathematical approach developed here generalizes and unifies the earlier available results on higher dimensional dust collapse as we point out. Further, the dependence of black hole or naked singularity end states as collapse outcomes, on the nature of the initial data from which the collapse develops, is brought out explicitly and in a transparent manner as we show here. Our method also allows us to consider here in some detail the genericity and stability aspects related to the occurrence of naked singularities in gravitational collapse.Comment: Revtex4, Title changed, To appear in Physical Review

Robust autoresonant excitation in the plasma beat-wave accelerator: a theoretical study

A modified version of the Plasma Beat-Wave Accelerator scheme is introduced and analyzed, which is based on autoresonant phase-locking of the nonlinear Langmuir wave to the slowly chirped beat frequency of the driving lasers via adiabatic passage through resonance. This new scheme is designed to overcome some of the well-known limitations of previous approaches, namely relativistic detuning and nonlinear modulation or other non-uniformity or non-stationarity in the driven Langmuir wave amplitude, and sensitivity to frequency mismatch due to measurement uncertainties and density fluctuations and inhomogeneities

On the global visibility of singularity in quasi-spherical collapse

We analyze here the issue of local versus the global visibility of a singularity that forms in gravitational collapse of a dust cloud, which has important implications for the weak and strong versions of the cosmic censorship hypothesis. We find conditions as to when a singularity will be only locally naked, rather than being globally visible, thus preseving the weak censorship hypothesis. The conditions for formation of a black hole or naked singularity in the Szekeres quasi-spherical collapse models are worked out. The causal behaviour of the singularity curve is studied by examining the outgoing radial null geodesics, and the final outcome of collapse is related to the nature of the regular initial data specified on an initial hypersurface from which the collapse evolves. An interesting feature that emerges is the singularity in Szekeres spacetimes can be ``directionally naked''.Comment: Latex file, 32 pages, 12 postscript figures. To appear in the Journal of General Relativity and Gravitatio

Magnetic and Transport Properties of Ternary Indides of type R2CoIn8 (R = Ce, Pr and Dy)

We have synthesized and investigated the magnetic and transport properties of a series of compounds, R2CoIn8 (R = rare earth). Compounds form in single phase with a tetragonal structure (space group P4/mmm, no. 162). The Ce compound shows heavy fermion behavior. The magnetic susceptibility of Pr2CoIn8 shows a marked deviation from the Curie-Weiss behavior at low temperatures, which is attributed to the crystalline electric field effects. Heat capacity and magnetization measurements show that Dy2CoIn8 undergoes a magnetic transition at 17 K and a second transition near 5 K, the latter of which may be due to spin reorientation. Magnetization of this compound shows two metamagnetic transitions approximately at 3.6 T and 8.3 T.Comment: Total 7 pages of text and figure

Mappings preserving locations of movable poles: a new extension of the truncation method to ordinary differential equations

The truncation method is a collective name for techniques that arise from truncating a Laurent series expansion (with leading term) of generic solutions of nonlinear partial differential equations (PDEs). Despite its utility in finding Backlund transformations and other remarkable properties of integrable PDEs, it has not been generally extended to ordinary differential equations (ODEs). Here we give a new general method that provides such an extension and show how to apply it to the classical nonlinear ODEs called the Painleve equations. Our main new idea is to consider mappings that preserve the locations of a natural subset of the movable poles admitted by the equation. In this way we are able to recover all known fundamental Backlund transformations for the equations considered. We are also able to derive Backlund transformations onto other ODEs in the Painleve classification.Comment: To appear in Nonlinearity (22 pages

Singular normal form for the Painlev\'e equation P1

We show that there exists a rational change of coordinates of Painlev\'e's P1 equation $y''=6y^2+x$ and of the elliptic equation $y''=6y^2$ after which these two equations become analytically equivalent in a region in the complex phase space where $y$ and $y'$ are unbounded. The region of equivalence comprises all singularities of solutions of P1 (i.e. outside the region of equivalence, solutions are analytic). The Painlev\'e property of P1 (that the only movable singularities are poles) follows as a corollary. Conversely, we argue that the Painlev\'e property is crucial in reducing P1, in a singular regime, to an equation integrable by quadratures

Spherical gravitational collapse in N-dimensions

We investigate here spherically symmetric gravitational collapse in a spacetime with an arbitrary number of dimensions and with a general {\it type I} matter field, which is a broad class that includes most of the physically reasonable matter forms. We show that given the initial data for matter in terms of the initial density and pressure profiles at an initial surface $t=t_i$ from which the collapse evolves, there exist rest of the initial data functions and classes of solutions of Einstein equations which we construct here, such that the spacetime evolution goes to a final state which is either a black hole or a naked singularity, depending on the nature of initial data and evolutions chosen, and subject to validity of the weak energy condition. The results are discussed and analyzed in the light of the cosmic censorship hypothesis in black hole physics. The formalism here combines the earlier results on gravitational collapse in four dimensions in a unified treatment. Also the earlier work is generalized to higher dimensional spacetimes to allow a study of the effect of number of dimensions on the possible final outcome of the collapse in terms of either a black hole or naked singularity. No restriction is adopted on the number of dimensions, and other limiting assumptions such as self-similarity of spacetime are avoided, in order to keep the treatment general. Our methodology allows to consider to an extent the genericity and stability aspects related to the occurrence of naked singularities in gravitational collapse.Comment: Revtex4, The replaced version matches the published on

SIMULTANEOUS ESTIMATION & VALIDATION OF PARACETAMOL, PHENYLEPHRINE HYDROCHLORIDE AND CHLORPHENIRAMINE MALEATE IN TABLETS BY SPECTROPHOTOMETRIC METHOD

The present work describes two methods for simultaneous estimation of phenylephrine hydrochloride and chlorpheniramine maleate in pure and solid dosage forms. First method employs the application of simultaneous equation and second, is a multi-wavelength spectrophotometric analysis method. Both methods utilize 0.1N NaOH as solvent. Simultaneous equation develops using 256.8 nm, 236.8 nm and 222.4 nm as the max of paracetamol, phenylephrine hydrochloride and chlorpheniramine maleate respectively. Calibration curves were linear over the concentration ranges of 0-35 μg/mL for all drugs. The results demonstrated that the procedure is accurate, precise and reproducible (relative standard deviation < 1 %), while being simple, cheap and less time consuming, and hence can be suitably applied for simultaneous determination of three drugs in laboratory prepared mixtures and in commercial tablet preparation

Research Notes : United States : Evaluation of soybean germplasm for stress tolerance and biological efficiency : To evaluate soybean germplasm for biological efficiency in - Harvest Index

Two hundred soybean plant introductions and cultivars in each of maturity groups III, IV, and V were evaluated during the 1983 planting season. Data collection consisted of days from emergence to maturity, final plant height, and oven-dried weights of stems and pod walls and seeds from four plants removed from each plot. Seed yield was determined by clipping off the end 30 cm of each plot and harvesting the remaining 1 m of the three rows. This report is limited to data on seed yield efficiency (SYE) values only