First exit times and residence times for discrete random walks on finite lattices

In this paper, we derive explicit formulas for the surface averaged first exit time of a discrete random walk on a finite lattice. We consider a wide class of random walks and lattices, including random walks in a non-trivial potential landscape. We also compute quantities of interest for modelling surface reactions and other dynamic processes, such as the residence time in a subvolume, the joint residence time of several particles and the number of hits on a reflecting surface.Comment: 19 pages, 2 figure

Another Non-segregated Blue Straggler Population in a Globular Cluster: the Case of NGC 2419

We have used a combination of ACS-HST high-resolution and wide-field SUBARU data in order to study the Blue Straggler Star (BSS) population over the entire extension of the remote Galactic globular cluster NGC 2419. The BSS population presented here is among the largest ever observed in any stellar system, with more than 230 BSS in the brightest portion of the sequence. The radial distribution of the selected BSS is essentially the same as that of the other cluster stars. In this sense the BSS radial distribution is similar to that of omega Centauri and unlike that of all Galactic globular clusters studied to date, which have highly centrally segregated distributions and, in most cases, a pronounced upturn in the external regions. As in the case of omega Centauri, this evidence indicates that NGC 2419 is not yet relaxed even in the central regions. This observational fact is in agreement with estimated half-mass relaxation time, which is of the order of the cluster age.Comment: in press in the Ap

High-latitude artificial aurora using the EISCAT high-gain HF facility

The EISCAT high-frequency (HF) transmitter facility at Ramfjord, Norway, has been used to accelerate F-region electrons sufficiently to excite the oxygen atoms and nitrogen molecules, resulting in optical emissions at 630, 557.7 and 427.8 nm. During O-mode transmissions at 5.423 MHz, using 630 MW effective radiated power, in the hours after sunset on 12 November 2001 several new observations were made, including: (1) The first high-latitude observation of an HF induced optical emission at 427.8 nm and (2) Optical rings being formed at HF on followed by their collapse into a central blob. Both discoveries remain unexplained with current theories

The surprising external upturn of the Blue Straggler radial distribution in M55

By combining high-resolution HST and wide-field ground based observations, in ultraviolet and optical bands, we study the Blue Straggler Star (BSS) population of the low density galactic globular cluster M55 (NGC 6809) over its entire radial extent. The BSS projected radial distribution is found to be bimodal, with a central peak, a broad minimum at intermediate radii, and an upturn at large radii. Similar bimodal distributions have been found in other globular clusters (M3, 47 Tucanae, NGC 6752, M5), but the external upturn in M55 is the largest found to date. This might indicate a large fraction of primordial binaries in the outer regions of M55, which seems somehow in contrast with the relatively low (\sim 10%) binary fraction recently measured in the core of this cluster.Comment: in press on Ap

Relative Frequencies of Blue Stragglers in Galactic Globular Clusters: Constraints for the Formation Mechanisms

We discuss the main properties of the Galactic globular cluster (GC) blue straggler stars (BSS), as inferred from our new catalog containing nearly 3000 BSS. The catalog has been extracted from the photometrically homogeneous V vs. (B-V) color-magnitude diagrams (CMD) of 56 GCs, based on WFPC2 images of their central cores. In our analysis we used consistent relative distances based on the same photometry and calibration. The number of BSS has been normalized to obtain relative frequencies (F_{BSS}) and specific densities (N_S) using different stellar populations extracted from the CMD. The cluster F_{BSS} is significantly smaller than the relative frequency of field BSS. We find a significant anti-correlation between the BSS relative frequency in a cluster and its total absolute luminosity (mass). There is no statistically significant trend between the BSS frequency and the expected collision rate. F_{BSS} does not depend on other cluster parameters, apart from a mild dependence on the central density. PCC clusters act like normal clusters as far as the BSS frequency is concerned. We also show that the BSS luminosity function for the most luminous clusters is significantly different, with a brighter peak and extending to brighter luminosities than in the less luminous clusters. These results imply that the efficiency of BSS production mechanisms and their relative importance vary with the cluster mass.Comment: 12 pages, 3 figures. accepted for publication in ApJ

The Apparent Fractal Conjecture: Scaling Features in Standard Cosmologies

This paper presents an analysis of the smoothness problem in cosmology by focussing on the ambiguities originated in the simplifying hypotheses aimed at observationally verifying if the large-scale distribution of galaxies is homogeneous, and conjecturing that this distribution should follow a fractal pattern in perturbed standard cosmologies. This is due to a geometrical effect, appearing when certain types of average densities are calculated along the past light cone. The paper starts reviewing the argument concerning the possibility that the galaxy distribution follows such a scaling pattern, and the premises behind the assumption that the spatial homogeneity of standard cosmology can be observable. Next, it is argued that to discuss observable homogeneity one needs to make a clear distinction between local and average relativistic densities, and showing how the different distance definitions strongly affect them, leading the various average densities to display asymptotically opposite behaviours. Then the paper revisits Ribeiro's (1995: astro-ph/9910145) results, showing that in a fully relativistic treatment some observational average densities of the flat Friedmann model are not well defined at z ~ 0.1, implying that at this range average densities behave in a fundamentally different manner as compared to the linearity of the Hubble law, well valid for z < 1. This conclusion brings into question the widespread assumption that relativistic corrections can always be neglected at low z. It is also shown how some key features of fractal cosmologies can be found in the Friedmann models. In view of those findings, it is suggested that the so-called contradiction between the cosmological principle, and the galaxy distribution forming an unlimited fractal structure, may not exist.Comment: 30 pages, 2 figures, LaTeX. This paper is a follow-up to gr-qc/9909093. Accepted for publication in "General Relativity and Gravitation

The Unimodal Distribution Of Blue Straggler Stars in M75 (NGC 6864)

We have used a combination of multiband high-resolution and wide-field ground-based observations to image the Galactic globular cluster M75 (NGC 6864). The extensive photometric sample covers the entire cluster extension, from the very central regions out to the tidal radius, allowing us to determine the center of gravity and to construct the most extended star density profile ever published for this cluster. We also present the first detailed star counts in the very inner regions. The star density profile is well re-produced by a standard King model with core radius r_c ~ 5.4" and intermediate-high concentration c ~ 1.75. The present paper presents a detailed study of the BSS population and its radial distribution. A total number of 62 bright BSSs (with m_F255W < 21, corresponding to m_F555W < 20) has been identified, and they have been found to be highly segregated in the cluster core. No significant upturn in the BSS frequency has been observed in the outskirts of M75, in contrast to several other clusters studied with the same technique. This observational fact is quite similar to what has been found in M79 (NGC 1904) by Lanzoni et al. (2007a). Indeed the BSS radial distributions in the two clusters is qualitatively very similar, even if in M75 the relative BSS frequency seems to decrease significantly faster than in M79: indeed it decreases by a factor of 5 (from 3.4 to 0.7) within 1 r_c. Such evidence indicate that the vast majority of the cluster heavy stars (binaries) have already sunk to the core.Comment: ApJ accepted, 10 pages, 11 figures, 2 table

High-Speed PLIF Imaging of Hypersonic Transition over Discrete Cylindrical Roughness

In two separate test entries, advanced laser-based instrumentation has been developed and applied to visualize the hypersonic flow over cylindrical protrusions on a flat plate. Upstream of these trips, trace quantities of nitric oxide (NO) were seeded into the boundary layer. The protuberances were sized to force laminar-to-turbulent boundary layer transition. In the first test, a 10-Hz nitric oxide planar laser-induced fluorescence (NO PLIF) flow visualization system was used to provide wide-field-of-view, high-resolution images of the flowfield. The images had sub-microsecond time resolution. However these images, obtained with a time separation of 0.1 sec, were uncorrelated with each other. Fluorescent oil-flow visualizations were also obtained during this test. In the second experiment, a laser and camera system capable of acquiring NO PLIF measurements at 1 million frames per second (1 MHz) was used. This system had lower spatial resolution, and a smaller field of view, but the images were time correlated so that the development of the flow structures could be observed in time

Third order perturbations of a zero-pressure cosmological medium: Pure general relativistic nonlinear effects

We consider a general relativistic zero-pressure irrotational cosmological medium perturbed to the third order. We assume a flat Friedmann background but include the cosmological constant. We ignore the rotational perturbation which decays in expanding phase. In our previous studies we discovered that, to the second-order perturbation, except for the gravitational wave contributions, the relativistic equations coincide exactly with the previously known Newtonian ones. Since the Newtonian second-order equations are fully nonlinear, any nonvanishing third and higher order terms in the relativistic analyses are supposed to be pure relativistic corrections. In this work we derive such correction terms appearing in the third order. Continuing our success in the second-order perturbations we take the comoving gauge. We discover that the third-order correction terms are of $\phi_v$-order higher than the second-order terms where $\phi_v$ is a gauge-invariant combination related to the three-space curvature perturbation in the comoving gauge; compared with the Newtonian potential we have $\delta \Phi \sim {3 \over 5} \phi_v$ to the linear order. Therefore, the pure general relativistic effects are of $varphi_v$-order higher than the Newtonian ones. The corrections terms are independent of the horizon scale and depend only on the linear order gravitational potential perturbation strength. From the temperature anisotropy of cosmic microwave background we have ${\delta T \over T} \sim {1 \over 3} \delta \Phi \sim {1 \over 5} \phi_v \sim 10^{-5}$. Therefore, our present result reinforces our previous important practical implication that near current era one can use the large-scale Newtonian numerical simulation more reliably even as the simulation scale approaches near the horizon.Comment: 9 pages, no figur

The binary fraction in the globular cluster M10 (NGC 6254): comparing core and outer regions

We study the binary fraction of the globular cluster M10 (NGC 6254) as a function of radius from the cluster core to the outskirts, by means of a quan- titative analysis of the color distribution of stars relative to the fiducial main sequence. By taking advantage of two data-sets, acquired with the Advanced Camera for Survey and the Wide Field Planetary Camera 2 on board the Hubble Space Telescope, we have studied both the core and the external regions of the cluster. The binary fraction is found to decrease from 14% within the core, to 1.5% in a region between 1 and 2 half-mass radii from the cluster centre. Such a trend and the derived values are in agreement with previous results ob- tained in clusters of comparable total magnitude. The estimated binary fraction is sufficient to account for the suppression of mass segregation observed in M10, without any need to invoke the presence of an intermediate-mass black hole in its centre.Comment: Accepted for publication in ApJ (22 pages, 7 figures, 3 tables