The MODEST questions: challenges and future directions in stellar cluster research

We present a review of some of the current major challenges in stellar cluster research, including young clusters, globular clusters, and galactic nuclei. Topics considered include: primordial mass segregation and runaway mergers, expulsion of gas from clusters, the production of stellar exotica seen in some clusters (eg blue stragglers and extreme horizontal--branch stars), binary populations within clusters, the black--hole population within stellar clusters, the final parsec problem, stellar dynamics around a massive black hole, and stellar collisions. The Modest Questions posed here are the outcome of discussions which took place at the Modest-6A workshop held in Lund, Sweden, in December, 2005. Modest-6A was organised as part of the activities of the Modest Collaboration (see www.manybody.org for further details)Comment: 24 pages, no figures, accepted for publication in New Astronom

Extreme mass ratio inspiral rates: dependence on the massive black hole mass

We study the rate at which stars spiral into a massive black hole (MBH) due to the emission of gravitational waves (GWs), as a function of the mass M of the MBH. In the context of our model, it is shown analytically that the rate approximately depends on the MBH mass as M^{-1/4}. Numerical simulations confirm this result, and show that for all MBH masses, the event rate is highest for stellar black holes, followed by white dwarfs, and lowest for neutron stars. The Laser Interferometer Space Antenna (LISA) is expected to see hundreds of these extreme mass ratio inspirals per year. Since the event rate derived here formally diverges as M->0, the model presented here cannot hold for MBHs of masses that are too low, and we discuss what the limitations of the model are.Comment: Accepted to CQG, special LISA issu

Minimum Conductivity and Evidence for Phase Transitions in Ultra-clean Bilayer Graphene

Bilayer graphene (BLG) at the charge neutrality point (CNP) is strongly susceptible to electronic interactions, and expected to undergo a phase transition into a state with spontaneous broken symmetries. By systematically investigating a large number of singly- and doubly-gated bilayer graphene (BLG) devices, we show that an insulating state appears only in devices with high mobility and low extrinsic doping. This insulating state has an associated transition temperature Tc~5K and an energy gap of ~3 meV, thus strongly suggesting a gapped broken symmetry state that is destroyed by very weak disorder. The transition to the intrinsic broken symmetry state can be tuned by disorder, out-of-plane electric field, or carrier density

On Convergence of the Inexact Rayleigh Quotient Iteration with the Lanczos Method Used for Solving Linear Systems

For the Hermitian inexact Rayleigh quotient iteration (RQI), the author has established new local general convergence results, independent of iterative solvers for inner linear systems. The theory shows that the method locally converges quadratically under a new condition, called the uniform positiveness condition. In this paper we first consider the local convergence of the inexact RQI with the unpreconditioned Lanczos method for the linear systems. Some attractive properties are derived for the residuals, whose norms are $\xi_{k+1}$'s, of the linear systems obtained by the Lanczos method. Based on them and the new general convergence results, we make a refined analysis and establish new local convergence results. It is proved that the inexact RQI with Lanczos converges quadratically provided that $\xi_{k+1}\leq\xi$ with a constant $\xi\geq 1$. The method is guaranteed to converge linearly provided that $\xi_{k+1}$ is bounded by a small multiple of the reciprocal of the residual norm $\|r_k\|$ of the current approximate eigenpair. The results are fundamentally different from the existing convergence results that always require $\xi_{k+1}<1$, and they have a strong impact on effective implementations of the method. We extend the new theory to the inexact RQI with a tuned preconditioned Lanczos for the linear systems. Based on the new theory, we can design practical criteria to control $\xi_{k+1}$ to achieve quadratic convergence and implement the method more effectively than ever before. Numerical experiments confirm our theory.Comment: 20 pages, 8 figures. arXiv admin note: text overlap with arXiv:0906.223

Superconductivity enhanced conductance fluctuations in few layer graphene nanoribbons

We investigate the mesoscopic disorder induced rms conductance variance $\delta G$ in a few layer graphene nanoribbon (FGNR) contacted by two superconducting (S) Ti/Al contacts. By sweeping the back-gate voltage, we observe pronounced conductance fluctuations superimposed on a linear background of the two terminal conductance G. The linear gate-voltage induced response can be modeled by a set of inter-layer and intra-layer capacitances. $\delta G$ depends on temperature T and source-drain voltage $V_{sd}$. $\delta G$ increases with decreasing T and $|V_{sd}|$. When lowering $|V_{sd}|$, a pronounced cross-over at a voltage corresponding to the superconducting energy gap $\Delta$ is observed. For |V_{sd}|\ltequiv \Delta the fluctuations are markedly enhanced. Expressed in the conductance variance $G_{GS}$ of one graphene-superconducutor (G-S) interface, values of 0.58 e^2/h are obtained at the base temperature of 230 mK. The conductance variance in the sub-gap region are larger by up to a factor of 1.4-1.8 compared to the normal state. The observed strong enhancement is due to phase coherent charge transfer caused by Andreev reflection at the nanoribbon-superconductor interface.Comment: 15 pages, 5 figure

TEM-STEM study of europium doped gadolinium oxide nanoparticles synthesized by spray pyrolysis

Proocedings of: Fourth Conference on the Characterization and Control of Interfaces for High Quality Advanced Materials. Kurashiki, Japan, 02-05 September 2012.Scanning-Transmission and Transmission Electron Microscopy techniques (STEM and TEM) have been applied to the characterization of nanostructured gadolinium oxides doped with europium synthesized by spray pyrolysis. The High Angle Annular Dark Field (HAADF) &- Scanning Transmission Electron Micros-copy (STEM) tools have been used to perform a tomographic study to identify morphological character-istics of nanostructured particles, and to differentiate them according to the heat treatments to which these have been subjected. With these techniques it has been possible to con&#64257;rm the hollowness and por-ous nature of samples subjected to low temperature annealing (900 ºC). Moreover, the beginning of the densi&#64257;cation and sintering processes in samples subjected to thermal treatment at higher temperature (1100 ºC) have been evaluated. Chemical analysis by electron energy loss spectroscopy (EELS) and X ray energy dispersive spectroscopy (EDS) carried out in STEM mode have allowed to con&#64257;rm the high uni-formity and the expected chemical composition. The high resolution tools either allowed to con&#64257;rm the presence of a cubic (Ia3 symmetry) and the monoclinic (c2/m symmetry) phases in the nanostructured particles.This work has been supported by the Advanced Structural Materials Program- ESTRUMAT (S2009/MAT-1585) and MAT2010-19837-C06-05. Thanks are extended to NanoPort (FEI)- Eindhoven, especially to Eng. L. Fernando Mendoza and to the Ministry of Science and Technology of Serbia (Project #142010).Publicad

Dynamical evolution of the young stars in the Galactic center: N-body simulations of the S-stars

We use N-body simulations to study the evolution of the orbital eccentricities of stars deposited near (<0.05 pc) the Milky Way massive black hole (MBH), starting from initial conditions motivated by two competing models for their origin: formation in a disk followed by inward migration; and exchange interactions involving a binary star. The first model predicts modest eccentricities, lower than those observed in the S-star cluster, while the second model predicts higher eccentricities than observed. The N-body simulations include a dense cluster of 10 M_sun stellar black holes (SBHs), expected to accumulate near the MBH by mass segregation. Perturbations from the SBHs tend to randomize the stellar orbits, partially erasing the dynamical signatures of their origin. The eccentricities of the initially highly eccentric stars evolve, in 20 Myr (the S-star lifespan), to a distribution that is consistent at the ~95 % level with the observed eccentricity distribution. In contrast, the eccentricities of the initially more circular orbits fail to evolve to the observed values in 20 Myr, arguing against the disk migration scenario. We find that 20 % - 30 % of the S-stars are tidally disrupted by the MBH over their lifetimes, and that the S-stars are not likely to be ejected as hypervelocity stars outside the central 0.05 pc by close encounters with stellar black holes.Comment: 6 pages, 2 figures. Minor corrections, Sumitted to Ap

A log-quadratic relation for predicting supermassive black hole masses from the host bulge Sersic index

We reinvestigate the correlation between black hole mass and bulge concentration. With an increased galaxy sample, updated estimates of galaxy distances, black hole masses, and Sersic indices `n' - a measure of concentration - we perform a least-squares regression analysis to obtain a relation suitable for the purpose of predicting black hole masses in other galaxies. In addition to the linear relation, log(M_bh) = 7.81(+/-0.08) + 2.69(+/-0.28)[log(n/3)] with epsilon_(intrin)=0.31 dex, we investigated the possibility of a higher order M_bh-n relation, finding the second order term in the best-fitting quadratic relation to be inconsistent with a value of zero at greater than the 99.99% confidence level. The optimal relation is given by log(M_bh) = 7.98(+/-0.09) + 3.70(+/-0.46)[log(n/3)] - 3.10(+/-0.84)[log(n/3)]^2, with epsilon_(intrin)=0.18 dex and a total absolute scatter of 0.31 dex. Extrapolating the quadratic relation, it predicts black holes with masses of ~10^3 M_sun in n=0.5 dwarf elliptical galaxies, compared to ~10^5 M_sun from the linear relation, and an upper bound on the largest black hole masses in the local universe, equal to 1.2^{+2.6}_{-0.4}x10^9 M_sun}. In addition, we show that the nuclear star clusters at the centers of low-luminosity elliptical galaxies follow an extrapolation of the same quadratic relation. Moreover, we speculate that the merger of two such nucleated galaxies, accompanied by the merger and runaway collision of their central star clusters, may result in the late-time formation of some supermassive black holes. Finally, we predict the existence of, and provide equations for, a relation between M_bh and the central surface brightness of the host bulge

On some differential-geometric aspects of the Torelli map

In this note we survey recent results on the extrinsic geometry of the Jacobian locus inside $\mathsf{A}_g$. We describe the second fundamental form of the Torelli map as a multiplication map, recall the relation between totally geodesic subvarieties and Hodge loci and survey various results related to totally geodesic subvarieties and the Jacobian locus.Comment: To appear on Boll. UMI, special volume in memory of Paolo de Bartolomei