The Annular Suspension and Pointing (ASP) system for space experiments and predicted pointing accuracies

An annular suspension and pointing system consisting of pointing assemblies for coarse and vernier pointing is described. The first assembly is attached to a carrier spacecraft (e.g., the space shuttle) and consists of an azimuth gimbal and an elevation gimbal which provide 'coarse' pointing. The second or vernier pointing assembly is made up of magnetic actuators of suspension and fine pointing, roll motor segments, and an instrument or experiment mounting plate around which is attached a continuous annular rim similar to that used in the annular momentum control device. The rim provides appropriate magnetic circuits for the actuators and the roll motor segments for any instrument roll position. The results of a study to determine the pointing accuracy of the system in the presence of crew motion disturbances are presented. Typical 3 sigma worst-case errors are found to be of the order of 0.001 arc-second

On the genericity of spacetime singularities

We consider here the genericity aspects of spacetime singularities that occur in cosmology and in gravitational collapse. The singularity theorems (that predict the occurrence of singularities in general relativity) allow the singularities of gravitational collapse to be either visible to external observers or covered by an event horizon of gravity. It is shown that the visible singularities that develop as final states of spherical collapse are generic. Some consequences of this fact are discussed.Comment: 19 pages, To be published in the Raychaudhuri Volume, eds. Naresh Dadhich, Pankaj Joshi and Probir Ro

On trapped surface formation in gravitational collapse II

Further to our consideration on trapped surfaces in gravitational collapse, where pressures were allowed to be negative while satisfying weak energy condition to avoid trapped surface formation, we discuss here several other attempts of similar nature in this direction. Certain astrophysical aspects are pointed out towards examining the physical realization of such a possibility in realistic gravitational collapse

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

Static spherically symmetric scalar field spacetimes with C^0 matching

All the classes of static massless scalar field models available currently in the Einstein theory of gravity necessarily contain a strong curvature naked singularity. We obtain here a family of solutions for static massless scalar fields coupled to gravity, which does not have any strong curvature singularity. This class of models contain a thin shell of singular matter, which has a physical interpretation. The central curvature singularity is, however, avoided which is common to all static massless scalar field spacetimes models known so far. Our result thus points out that the full class of solutions in this case may contain non-singular models, which is an intriguing possibility.Comment: revised version, 10 pages, no figures, accepted in Mod. Phys. Let.

Collapse and dispersal in massless scalar field models

The phenomena of collapse and dispersal for a massless scalar field has drawn considerable interest in recent years, mainly from a numerical perspective. We give here a sufficient condition for the dispersal to take place for a scalar field that initially begins with a collapse. It is shown that the change of the gradient of the scalar field from a timelike to a spacelike vector must be necessarily accompanied by the dispersal of the scalar field. This result holds independently of any symmetries of the spacetime. We demonstrate the result explicitly by means of an example, which is the scalar field solution given by Roberts. The implications of the result are discussed.Comment: revised version, Accepted for publication in Int. Journ. of Mod. Phys. D, 6 pages, 3 figure

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

Multimodal MRI-based Imputation of the Aβ+ in Early Mild Cognitive Impairment.

ObjectiveTo identify brain atrophy from structural-MRI and cerebral blood flow(CBF) patterns from arterial spin labeling perfusion-MRI that are best predictors of the Aβ-burden, measured as composite 18F-AV45-PET uptake, in individuals with early mild cognitive impairment(MCI). Furthermore, to assess the relative importance of imaging modalities in classification of Aβ+/Aβ- early mild cognitive impairment.MethodsSixty-seven ADNI-GO/2 participants with early-MCI were included. Voxel-wise anatomical shape variation measures were computed by estimating the initial diffeomorphic mapping momenta from an unbiased control template. CBF measures normalized to average motor cortex CBF were mapped onto the template space. Using partial least squares regression, we identified the structural and CBF signatures of Aβ after accounting for normal cofounding effects of age, sex, and education.Results18F-AV45-positive early-MCIs could be identified with 83% classification accuracy, 87% positive predictive value, and 84% negative predictive value by multidisciplinary classifiers combining demographics data, ApoE ε4-genotype, and a multimodal MRI-based Aβ score.InterpretationMultimodal-MRI can be used to predict the amyloid status of early-MCI individuals. MRI is a very attractive candidate for the identification of inexpensive and non-invasive surrogate biomarkers of Aβ deposition. Our approach is expected to have value for the identification of individuals likely to be Aβ+ in circumstances where cost or logistical problems prevent Aβ detection using cerebrospinal fluid analysis or Aβ-PET. This can also be used in clinical settings and clinical trials, aiding subject recruitment and evaluation of treatment efficacy. Imputation of the Aβ-positivity status could also complement Aβ-PET by identifying individuals who would benefit the most from this assessment