Atmospheric noise on the bispectrum in optical speckle interferometry

Based on a simple picture of speckle phenomena in optical interferometry it is shown that the recent signal-to-noise ratio estimate for the so called bispectrum, due to Wirnitzer (1985), does not possess the right limit when photon statistics is unimportant. In this wave-limit, which is true for bright sources, his calculations over-estimate the signal-to-noise ratio for the bispectrum by a factor of the order of the square root of the number of speckles

Complexes of Cut (II), Ni(II) & Co(II) with 3,5-Dimethyl-I-nitroguanylpyrazole

978-98

Translational diffusion of fluorescent probes on a sphere: monte carlo simulations, theory, and fluorescence anisotropy experiment

Translational diffusion of fluorescent molecules on curved surfaces (micelles, vesicles, and proteins) depolarizes the fluorescence. A Monte Carlo simulation method was developed to obtain the fluorescence anisotropy decays for the general case of molecular dipoles tilted at an angle a to the surface normal. The method is used to obtain fluorescence anisotropy decay due to diffusion of tilted dipoles on a spherical surface, which matched well with the exact solution for the sphere. The anisotropy decay is a single exponential for α = 0° , a double exponential for α = 90° , and three exponentials for intermediate angles. The slower decay component(s) for α ≠ 0 arise due to the geometric phase factor. Although the anisotropy decay equation contains three exponentials, there are only two parameters, namely a and the rate constant, Dtr/R2, where Dtr is the translational diffusion coefficient and R is the radius of the sphere. It is therefore possible to determine the orientation angle and translational diffusion coefficient from the experimental fluorescence anisotropy data. This method was applied in interpreting the fluorescence anisotropy decay of Nile red in SDS micelles. It is necessary, however, to include two other independent mechanisms of fluorescence depolarization for molecules intercalated in micelles. These are the wobbling dynamics of the molecule about the molecular long axis, and the rotation of the spherical micelle as a whole. The fitting of the fluorescence anisotropy decay to the full equation gave the tilt angle of the molecular dipoles to be 1± 2° and the translational diffusion coefficient to be 1.3± 0.1×10-10 m2/s

Cerium Oxide Nanoparticles Inside Carbon Nanoreactors for Selective Allylic Oxidation of Cyclohexene

The confinement of cerium oxide (CeO2) nanoparticles within hollow carbon nanostructures has been achieved and harnessed to control the oxidation of cyclohexene. Graphitized carbon nanofibers (GNF) have been used as the nanoscale tubular host and filled by sublimation of the Ce(tmhd)4 complex (where tmhd = tetrakis(2,2,6,6-tetramethyl-3,5-heptanedionato)) into the internal cavity, followed by a subsequent thermal decomposition to yield the hybrid nanostructure CeO2@GNF, where nanoparticles are preferentially immobilized at the internal graphitic step-edges of the GNF. Control over the size of the CeO2 nanoparticles has been demonstrated within the range of about 4–9 nm by varying the mass ratio of the Ce(tmhd)4 precursor to GNF during the synthesis. CeO2@GNF was effective in promoting the allylic oxidation of cyclohexene in high yield with time-dependent control of product selectivity at a comparatively low loading of CeO2 of 0.13 mol %. Unlike many of the reports to date where ceria catalyzes such organic transformations, we found the encapsulated CeO2 to play the key role of radical initiator due to the presence of Ce3+ included in the structure, with the nanotube acting as both a host, preserving the high performance of the CeO2 nanoparticles anchored at the GNF step-edges over multiple uses, and an electron reservoir, maintaining the balance of Ce3+ and Ce4+ centers. Spatial confinement effects ensure excellent stability and recyclability of CeO2@GNF nanoreactors

Resolving the Inner Structure of QSO Discs by Fold Caustic Crossing Events

Though the bulk of the observed optical flux from the discs of intermediate-redshift lensed quasars is formed well outside the region of strong relativistic boosting and light-bending, relativistic effects have important influence on microlensing curves. The reason is in the divergent nature of amplification factors near fold caustics increasingly sensitive to small spatial size details. Higher-order disc images produced by strong light bending around the black hole may affect the amplification curves, making a contribution of up to several percent near maximum amplification. In accordance with theoretical predictions, some of the observed high-amplification events possess fine structure. Here we consider three putative caustic crossing events, one by SBS1520+530 and two events for individual images of the Einstein's cross (QSO J2237+0305). Using relativistic disc models allows to improve the fits, but the required inclinations are high, about 70deg or larger. Such high inclinations apparently contradict the absence of any strong absorption that is likely to arise if a disc is observed edge-on through a dust torus. Still, the high inclinations are required only for the central parts of the disc, that allows the disc itself to be initially tilted by 60-90deg with respect to the black hole and aligned toward the black hole equatorial plane near the last stable orbit radius. For SBS1520+530, an alternative explanation for the observed amplification curve is a superposition of two subsequent fold caustic crossings. While relativistic disc models favour black hole masses ~10^10 solar (several times higher than the virial estimates) or small Eddington ratios, this model is consistent with the observed distribution of galaxies over peculiar velocities only if the black hole mass is about 3 10^8 solar.Comment: 19 pages, 16 figures, 3 tables; accepted to MNRAS; small proof corrections mad

Cosmological N-Body Simulations

In this review we discuss Cosmological N-Body codes with a special emphasis on Particle Mesh codes. We present the mathematical model for each component of N-Body codes. We compare alternative methods for computing each quantity by calculating errors for each of the components. We suggest an optimum set of components that can be combined reduce overall errors in N-Body codes.Comment: This article, published in 1997 is somewhat inaccessible; the present posting is the original versio

Mathematics of Gravitational Lensing: Multiple Imaging and Magnification

The mathematical theory of gravitational lensing has revealed many generic and global properties. Beginning with multiple imaging, we review Morse-theoretic image counting formulas and lower bound results, and complex-algebraic upper bounds in the case of single and multiple lens planes. We discuss recent advances in the mathematics of stochastic lensing, discussing a general formula for the global expected number of minimum lensed images as well as asymptotic formulas for the probability densities of the microlensing random time delay functions, random lensing maps, and random shear, and an asymptotic expression for the global expected number of micro-minima. Multiple imaging in optical geometry and a spacetime setting are treated. We review global magnification relation results for model-dependent scenarios and cover recent developments on universal local magnification relations for higher order caustics.Comment: 25 pages, 4 figures. Invited review submitted for special issue of General Relativity and Gravitatio

The Spin of the Near-Extreme Kerr Black Hole GRS 1915+105

Based on a spectral analysis of the X-ray continuum that employs a fully relativistic accretion-disk model, we conclude that the compact primary of the binary X-ray source GRS 1915+105 is a rapidly-rotating Kerr black hole. We find a lower limit on the dimensionless spin parameter of a* greater than 0.98. Our result is robust in the sense that it is independent of the details of the data analysis and insensitive to the uncertainties in the mass and distance of the black hole. Furthermore, our accretion-disk model includes an advanced treatment of spectral hardening. Our data selection relies on a rigorous and quantitative definition of the thermal state of black hole binaries, which we used to screen all of the available RXTE and ASCA data for the thermal state of GRS 1915+105. In addition, we focus on those data for which the accretion disk luminosity is less than 30% of the Eddington luminosity. We argue that these low-luminosity data are most appropriate for the thin alpha-disk model that we employ. We assume that there is zero torque at the inner edge of the disk, as is likely when the disk is thin, although we show that the presence of a significant torque does not affect our results. Our model and the model of the relativistic jets observed for this source constrain the distance and black hole mass and could thus be tested by determining a VLBA parallax distance and improving the measurement of the mass function. Finally, we comment on the significance of our results for relativistic-jet and core-collapse models, and for the detection of gravitational waves.Comment: 58 pages, 18 figures. Accepted for publication in ApJ. New in this version is a proposed observational test of our spin model and the kinematic model of the radio jet

Dark Energy and Gravity

I review the problem of dark energy focusing on the cosmological constant as the candidate and discuss its implications for the nature of gravity. Part 1 briefly overviews the currently popular `concordance cosmology' and summarises the evidence for dark energy. It also provides the observational and theoretical arguments in favour of the cosmological constant as the candidate and emphasises why no other approach really solves the conceptual problems usually attributed to the cosmological constant. Part 2 describes some of the approaches to understand the nature of the cosmological constant and attempts to extract the key ingredients which must be present in any viable solution. I argue that (i)the cosmological constant problem cannot be satisfactorily solved until gravitational action is made invariant under the shift of the matter lagrangian by a constant and (ii) this cannot happen if the metric is the dynamical variable. Hence the cosmological constant problem essentially has to do with our (mis)understanding of the nature of gravity. Part 3 discusses an alternative perspective on gravity in which the action is explicitly invariant under the above transformation. Extremizing this action leads to an equation determining the background geometry which gives Einstein's theory at the lowest order with Lanczos-Lovelock type corrections. (Condensed abstract).Comment: Invited Review for a special Gen.Rel.Grav. issue on Dark Energy, edited by G.F.R.Ellis, R.Maartens and H.Nicolai; revtex; 22 pages; 2 figure