Shell Crossing Singularities in Quasi-Spherical Szekeres Models

We investigate the occurrence of shell crossing singularities in quasi-spherical Szekeres dust models with or without a cosmological constant. We study the conditions for shell crossing singularity both from physical and geometrical point of view and they are in agreement.Comment: 10 latex pages, RevTex style, no figure

Optimal Allocation of Reservoir Water

The purpose of this paper is to determine the optimal allocation of reservoir water among consumptive and non-consumptive uses. A non-linear mathematical programming model is developed to optimally allocate Lake Tenkiller water among competing uses that maximize the net social benefit. A mass balance is used to determine the level and volume of water in the lake. This paper examines the effect of water management on lake resources when recreational values are and are not included as control variables in the optimization process. Results show that maintaining the lake level to the ‘normal lake level’ of 632 feet during the summer months generates more recreational benefit rather than reducing the lake level by releasing water for hydro power generation.consumptive and non-consumptive use, mass balance equation, non-linear mathematical programming, optimization, recreational uses, water allocation, Resource /Energy Economics and Policy,

Is the shell-focusing singularity of Szekeres space-time visible?

The visibility of the shell-focusing singularity in Szekeres space-time - which represents quasi-spherical dust collapse - has been studied on numerous occasions in the context of the cosmic censorship conjecture. The various results derived have assumed that there exist radial null geodesics in the space-time. We show that such geodesics do not exist in general, and so previous results on the visibility of the singularity are not generally valid. More precisely, we show that the existence of a radial geodesic in Szekeres space-time implies that the space-time is axially symmetric, with the geodesic along the polar direction (i.e. along the axis of symmetry). If there is a second non-parallel radial geodesic, then the space-time is spherically symmetric, and so is a Lema\^{\i}tre-Tolman-Bondi (LTB) space-time. For the case of the polar geodesic in an axially symmetric Szekeres space-time, we give conditions on the free functions (i.e. initial data) of the space-time which lead to visibility of the singularity along this direction. Likewise, we give a sufficient condition for censorship of the singularity. We point out the complications involved in addressing the question of visibility of the singularity both for non-radial null geodesics in the axially symmetric case and in the general (non-axially symmetric) case, and suggest a possible approach.Comment: 10 page

QPO Evolution in 2005 Outburst of the Galactic Nano Quasar GRO J1655-40

GRO J1655-40 showed significant X-ray activity in the last week of February, 2005 and remained active for the next 260 days. The rising and the decline phases of this particular outburst show evidence for systematic movements of the Comptonizing region, assumed to be a CENBOL, which causes the Quasi-periodic Oscillations or QPOs. We present both the spectral and the timing results of the RXTE/PCA data taken from these two hard spectral states. Assuming that the QPOs originate from an oscillating shock CENBOL, we show how the shock slowly moves in through the accretion flow during the rising phase at a constant velocity and accelerate away outward during the later part of the decline phase. By fitting the observed frequencies with our solution, we extract time variation of various disk parameters such as the shock locations, velocity etc.Comment: 5 Pages, 2 Figures, Proceeding of the 2nd Kolkata Conference on "Observational Evidence for the Black Holes in the Universe", Published in AIP, 200