Stability of Naked Singularity arising in gravitational collapse of Type I matter fields

Considering gravitational collapse of Type I matter fields, we prove that, given an arbitrary $C^{2}$- mass function $\textit{M}(r,v)$ and a $C^{1}$- function $h(r,v)$ (through the corresponding $C^{1}$- metric function $\nu(t,r)$), there exist infinitely many choices of energy distribution function $b(r)$ such that the `true' initial data ($\textit{M},h(r,v)$) leads the collapse to the formation of naked singularity. We further prove that the occurrence of such a naked singularity is stable with respect to small changes in the initial data. We remark that though the initial data leading to both black hole and naked singularity form a "big" subset of the true initial data set, their occurrence is not generic. The terms `stability' and `genericity' are appropriately defined following the theory of dynamical systems. The particular case of radial pressure $p_{r}(r)$ has been illustrated in details to get clear picture of how naked singularity is formed and how, it is stable with respect to initial data.Comment: 16 pages, no figure, Latex, submitted to Praman

Comparative Studies of Photochemical and Electrochemical Methods on Mineralization of Picric Acid

The effluents generated from synthesis and processing plant of Picric acid is reported to be carcinogenic and hence needs to be treated to reduce its concentration below safe discharge limit. Present paper deals with studies on mineralization of Picric acid by adopting photochemical and electrochemical processes and the efficacy of the both processes have been explored in details. Crucial process parameters viz. pH, concentration of oxidizer and catalyst for mineralization of Picric acid are optimized. In photochemical method, It is observed that Picric acid is treated to bring down its concentration from 100 ppm to ≤ 1 ppm under Photo-Fenton process  in 2 hrs whereas same treatment carried out under Photo- catalytic process takes only 1 hr. It is also observed that TiO2 xerogel and beads of nano-TiO2 are more efficient compared to that of commercially available TiO2. The TiO2–Polysulfone (PS) beads show less efficiency than TiO2 xerogel. However, the Picric acid oxidation efficiency for TiO2–PS beads is comparable and advantage of TiO2–PS beads is that it can easily be recovered from the treated solution and can be reused in the next experiments.  Electrochemical process is user’s friendly and economical. In case of electrochemical treatments at optimized process parameters under Electro-Fenton reaction picric acid is completely mineralized below its drain discharge limit where as under Electro-peroxide reaction picric acid is mineralized upto 3 ppm within 3 hrs. The treated solution has been characterized by using UV-Visible spectrophotometer, High performance Liquid Chromatography (HPLC) and Total Organic Carbon (TOC) Analyzer. The observed results have been interpreted and reported in the present paper

Morphology and Grain Texture in As-Deposited and Heat Treated Inconel 718 Structures Produced using Laser-Based Powder Bed Fusion

With increasing interest in the use of powder bed fusion (PBF) processes for additive manufacturing, understanding the relationship between as-deposited and heat treated states and the intrinsic anisotropy of fabricated parts has become critical for its successful application. This phenomenon has been studied and reported extensively for Inconel 718 parts fabricated using PBF for aerospace applications, but few reports exist on the morphology and grain texture of Inconel 718 parts fabricated for oil and gas applications, which have different demands. This work demonstrates that the anisotropy in Inconel 718 parts produced using laser-based PBF is not entirely removed by subsequent heat treatments, and it may be an artifact of the as-deposited grain structure, whose elongated grains may stretch through several melt pools. The as-built material is observed to exhibit some texturing, with (001) being the preferential growth direction. Despite some residual anisotropy, heat treatments are sufficient to provide material qualities that meet specification, even without the use of a HIP (hot isostatic pressing) step. It is hypothesized that similarly elongated grain structures may explain the anisotropy observed in other materials systems employed in PBF additive manufacturing processes.Mechanical Engineerin

A Preliminary Examination of Variability Due to Build Location and Powder Feedstock in Additive Manufacture of Inconel 718 using Laser-Based Powder Bed Fusion

The production of metallic parts by additive manufacturing (AM) is of significant interest to industry, but in the absence of standards, practical design considerations for manufacturing engineers are not widely known. Within the context of powder bed fusion (PBF), many unknowns persist regarding variations in part quality due to part location on the build plate, process consistency, feedstock supplier, and machine manufacturer. In this paper, we investigate the mechanical property variance across the build platform and document the successful use of feedstock powders obtained from several suppliers for the manufacture of Inconel 718 tensile and Charpy specimens, built on an EOS M280 laser-based powder bed fusion system. Particular emphasis is placed on describing the manufacturing process design challenges encountered even for simple geometries. While many advocate that complexity is free when using AM, we find that AM can lead to expensive build failures given the current state of manufacturing process knowledge and that design for additive manufacture is required for successful application of AM techniques.Mechanical Engineerin

WITHDRAWN: Recent advances in compression-coated tablets as a controlled drug delivery system

This article has been withdrawn at the request of the author(s) and/or editor. The Publisher apologizes for any inconvenience this may cause.The full Elsevier Policy on Article Withdrawal can be found at http://www.elsevier.com/locate/withdrawalpolicy

The spectrum of endstates of gravitational collapse with tangential stresses

The final state--black hole or naked singularity--of the gravitational collapse of a marginally bound matter configuration in the presence of tangential stresses is classified, in full generality, in terms of the initial data and equation of state. If the tangential pressure is sufficiently strong, configurations that would otherwise evolve to a spacelike singularity, result in a locally naked singularity, both in the homogeneous and in the general, inhomogeneous density case.Comment: 9 pages, revtex4; accepted for publication in Phys. Rev.

The final fate of spherical inhomogeneous dust collapse II: Initial data and causal structure of singularity

Further to results in [9], pointing out the role of initial density and velocity distributions towards determining the final outcome of spherical dust collapse, the causal structure of singularity is examined here in terms of evolution of the apparent horizon. We also bring out several related features which throw some useful light towards understanding the nature of this singularity, including the behaviour of geodesic families coming out and some aspects related to the stability of singularity.Comment: Latex file, uses epsf.sty, 15 pages and 3 eps figures. Paragraph on role of smooth functions rewritten. Four references added. To appear in Classical & Quantum Gravit

Singularities in gravitational collapse with radial pressure

We analyze spherical dust collapse with non-vanishing radial pressure, $\Pi$, and vanishing tangential stresses. Considering a barotropic equation of state, $\Pi=\gamma\rho$, we obtain an analytical solution in closed form---which is exact for $\gamma=-1,0$, and approximate otherwise---near the center of symmetry (where the curvature singularity forms). We study the formation, visibility, and curvature strength of singularities in the resulting spacetime. We find that visible, Tipler strong singularities can develop from generic initial data. Radial pressure alters the spectrum of possible endstates for collapse, increasing the parameter space region that contains no visible singularities, but cannot by itself prevent the formation of visible singularities for sufficiently low values of the energy density. Known results from pressureless dust are recovered in the $\gamma=0$ limit.Comment: to appear in GRG; LaTeX, 22 pages, 2 eps figure

Left ventricular remodeling and hypertrophy in patients with aortic stenosis:insights from cardiovascular magnetic resonance

<p>Abstract</p> <p>Background</p> <p>Cardiovascular magnetic resonance (CMR) is the gold standard non-invasive method for determining left ventricular (LV) mass and volume but has not been used previously to characterise the LV remodeling response in aortic stenosis. We sought to investigate the degree and patterns of hypertrophy in aortic stenosis using CMR.</p> <p>Methods</p> <p>Patients with moderate or severe aortic stenosis, normal coronary arteries and no other significant valve lesions or cardiomyopathy were scanned by CMR with valve severity assessed by planimetry and velocity mapping. The extent and patterns of hypertrophy were investigated using measurements of the LV mass index, indexed LV volumes and the LV mass/volume ratio. Asymmetric forms of remodeling and hypertrophy were defined by a regional wall thickening <b>≥</b>13 mm and >1.5-fold the thickness of the opposing myocardial segment.</p> <p>Results</p> <p>Ninety-one patients (61±21 years; 57 male) with aortic stenosis (aortic valve area 0.93±0.32cm2) were recruited. The severity of aortic stenosis was unrelated to the degree (r²=0.012, P=0.43) and pattern (P=0.22) of hypertrophy. By univariate analysis, only male sex demonstrated an association with LV mass index (P=0.02). Six patterns of LV adaption were observed: normal ventricular geometry (n=11), concentric remodeling (n=11), asymmetric remodeling (n=11), concentric hypertrophy (n=34), asymmetric hypertrophy (n=14) and LV decompensation (n=10). Asymmetric patterns displayed considerable overlap in appearances (wall thickness 17±2mm) with hypertrophic cardiomyopathy.</p> <p>Conclusions</p> <p>We have demonstrated that in patients with moderate and severe aortic stenosis, the pattern of LV adaption and degree of hypertrophy do not closely correlate with the severity of valve narrowing and that asymmetric patterns of wall thickening are common.</p> <p>Trial registration</p> <p>ClinicalTrials.gov Reference Number: NCT00930735</p