Collective phenomena in non-central nuclear collisions

Recent developments in the field of anisotropic flow in nuclear collision are reviewed. The results from the top AGS energy to the top RHIC energy are discussed with emphasis on techniques, interpretation, and uncertainties in the measurements.Comment: Review paper, 56 pages, as accepted for publicatio

Effect of Flame Stabilizer Design on Performance and Exhaust Pollutants of a Two-Row Swirl-Can Combustor Operated to Near-Stoichiometric Conditions

Emissions and performance characteristics were determined for two full annulus modular combustors operated to near stoichiometric fuel air ratios. The tests were conducted to obtain stoichiometric data at inlet air temperatures from 756 to 894 K and to determine the effects of a flat plate circular flame stabilizer with upstream fuel injection and a contraswirl flame stabilizer with downstream fuel injection. Levels of unburned hydrocarbons were below 0.50 gram per kilogram of fuel for both combustors and thus there was no detectable difference in the two methods of fuel injection. The contraswirl flame stabilizer did not produce the level of mixing obtained with a flat plate circular flame stabilizer. It did produce higher levels of oxides of nitrogen, which peaked at a fuel air ratio of 0.037. For the flat plate circular flame stabilizer, oxides of nitrogen emission levels were still increasing with fuel air ratio to the maximum tested value of 0.045

Performance and Pollution Measurements of Two-Row Swirl-Can Combustor Having 72 Modules

A test program was conducted to evaluate the performance and gaseous-pollutant levels of an experimental full-annulus 72-module swirl-can combustor. A comparison of data with those for a 120-module swirl-can combustor showed no significant difference in performance or levels of gaseous pollutants. Oxides of nitrogen were correlated for the 72- and 120-swirl-can combustors by using a previously developed parameter

A tight lower bound instance for k-means++ in constant dimension

The k-means++ seeding algorithm is one of the most popular algorithms that is used for finding the initial $k$ centers when using the k-means heuristic. The algorithm is a simple sampling procedure and can be described as follows: Pick the first center randomly from the given points. For $i > 1$, pick a point to be the $i^{th}$ center with probability proportional to the square of the Euclidean distance of this point to the closest previously $(i-1)$ chosen centers. The k-means++ seeding algorithm is not only simple and fast but also gives an $O(\log{k})$ approximation in expectation as shown by Arthur and Vassilvitskii. There are datasets on which this seeding algorithm gives an approximation factor of $\Omega(\log{k})$ in expectation. However, it is not clear from these results if the algorithm achieves good approximation factor with reasonably high probability (say $1/poly(k)$). Brunsch and R\"{o}glin gave a dataset where the k-means++ seeding algorithm achieves an $O(\log{k})$ approximation ratio with probability that is exponentially small in $k$. However, this and all other known lower-bound examples are high dimensional. So, an open problem was to understand the behavior of the algorithm on low dimensional datasets. In this work, we give a simple two dimensional dataset on which the seeding algorithm achieves an $O(\log{k})$ approximation ratio with probability exponentially small in $k$. This solves open problems posed by Mahajan et al. and by Brunsch and R\"{o}glin.Comment: To appear in TAMC 2014. arXiv admin note: text overlap with arXiv:1306.420

Centrality dependence of directed and elliptic flow at the SPS

New data with a minimum bias trigger for 158 GeV/nucleon Pb + Pb have been analyzed. Directed and elliptic flow as a function of rapidity of the particles and centrality of the collision are presented. The centrality dependence of the ratio of elliptic flow to the initial space elliptic anisotropy is compared to models

Impact of surface-polish on the angular and wavelength dependence of fiber focal ratio degradation

We present measurements of how multimode fiber focal-ratio degradation (FRD) and throughput vary with levels of fiber surface polish from 60 to 0.5 micron grit. Measurements used full-beam and laser injection methods at wavelengths between 0.4 and 0.8 microns on 17 meter lengths of Polymicro FBP 300 and 400 micron core fiber. Full-beam injection probed input focal-ratios between f/3 and f/13.5, while laser injection allowed us to isolate FRD at discrete injection angles up to 17 degrees (f/1.6 marginal ray). We find (1) FRD effects decrease as grit size decreases, with the largest gains in beam quality occurring at grit sizes above 5 microns; (2) total throughput increases as grit size decreases, reaching 90% at 790 nm with the finest polishing levels; (3) total throughput is higher at redder wavelengths for coarser polishing grit, indicating surface-scattering as the primary source of loss. We also quantify the angular dependence of FRD as a function of polishing level. Our results indicate that a commonly adopted micro-bending model for FRD is a poor descriptor of the observed phenomenon.Comment: 10 pages, 7 figures, presented at SPIE Astronomical Telescopes and Instrumentation, July 201

A note on 5-cycle double covers

The strong cycle double cover conjecture states that for every circuit $C$ of a bridgeless cubic graph $G$, there is a cycle double cover of $G$ which contains $C$. We conjecture that there is even a 5-cycle double cover $S$ of $G$ which contains $C$, i.e. $C$ is a subgraph of one of the five 2-regular subgraphs of $S$. We prove a necessary and sufficient condition for a 2-regular subgraph to be contained in a 5-cycle double cover of $G$