Topological persistence and dynamical heterogeneities near jamming

We introduce topological methods for quantifying spatially heterogeneous dynamics, and use these tools to analyze particle-tracking data for a quasi-two-dimensional granular system of air-fluidized beads on approach to jamming. In particular we define two overlap order parameters, which quantify the correlation between particle configurations at different times, based on a Voronoi construction and the persistence in the resulting cells and nearest neighbors. Temporal fluctuations in the decay of the persistent area and bond order parameters define two alternative dynamic four-point susceptibilities, XA(t) and XB(t), well-suited for characterizing spatially-heterogeneous dynamics. These are analogous to the standard four-point dynamic susceptibility X4(l,t), but where the space-dependence is fixed uniquely by topology rather than by discretionary choice of cutoff function. While these three susceptibilities yield characteristic time scales that are somewhat different, they give domain sizes for the dynamical heterogeneities that are in good agreement and that diverge on approach to jamming

The partition of energy for air-fluidized grains

The dynamics of one and two identical spheres rolling in a nearly-levitating upflow of air obey the Langevin Equation and the Fluctuation-Dissipation Relation [Ojha et al. Nature 427, 521 (2004) and Phys. Rev. E 71, 01631 (2005)]. To probe the range of validity of this statistical mechanical description, we perturb the original experiments in four ways. First, we break the circular symmetry of the confining potential by using a stadium-shaped trap, and find that the velocity distributions remain circularly symmetric. Second, we fluidize multiple spheres of different density, and find that all have the same effective temperature. Third, we fluidize two spheres of different size, and find that the thermal analogy progressively fails according to the size ratio. Fourth, we fluidize individual grains of aspherical shape, and find that the applicability of statistical mechanics depends on whether or not the grain chatters along its length, in the direction of airflow.Comment: experimen

Carbon-enhanced metal-poor stars: a window on AGB nucleosynthesis and binary evolution. II. Statistical analysis of a sample of 67 CEMP-ss stars

Many observed CEMP stars are found in binary systems and show enhanced abundances of $s$-elements. The origin of the chemical abundances of these CEMP-$s$ stars is believed to be accretion in the past of enriched material from a primary star in the AGB phase. We investigate the mechanism of mass transfer and the process of nucleosynthesis in low-metallicity AGB stars by modelling the binary systems in which the observed CEMP-$s$ stars were formed. For this purpose we compare a sample of $67$ CEMP-$s$ stars with a grid of binary stars generated by our binary evolution and nucleosynthesis model. We classify our sample CEMP-$s$ stars in three groups based on the observed abundance of europium. In CEMP$-s/r$ stars the europium-to-iron ratio is more than ten times higher than in the Sun, whereas it is lower than this threshold in CEMP$-s/nr$ stars. No measurement of europium is currently available for CEMP-$s/ur$ stars. On average our models reproduce well the abundances observed in CEMP-$s/nr$ stars, whereas in CEMP-$s/r$ stars and CEMP-$s/ur$ stars the abundances of the light-$s$ elements are systematically overpredicted by our models and in CEMP-$s/r$ stars the abundances of the heavy-$s$ elements are underestimated. In all stars our modelled abundances of sodium overestimate the observations. This discrepancy is reduced only in models that underestimate the abundances of most of the $s$-elements. Furthermore, the abundance of lead is underpredicted in most of our model stars. These results point to the limitations of our AGB nucleosynthesis model, particularly in the predictions of the element-to-element ratios. Finally, in our models CEMP-$s$ stars are typically formed in wide systems with periods above 10000 days, while most of the observed CEMP-$s$ stars are found in relatively close orbits with periods below 5000 days.Comment: 23 pages, 8 figures, accepted for publication on Astronomy & Astrophysic

Carbon-enhanced metal-poor stars: a window on AGB nucleosynthesis and binary evolution. I. Detailed analysis of 15 binary stars with known orbital periods

AGB stars are responsible for producing a variety of elements, including carbon, nitrogen, and the heavy elements produced in the slow neutron-capture process ($s$-elements). There are many uncertainties involved in modelling the evolution and nucleosynthesis of AGB stars, and this is especially the case at low metallicity, where most of the stars with high enough masses to enter the AGB have evolved to become white dwarfs and can no longer be observed. The stellar population in the Galactic halo is of low mass ($\lesssim 0.85M_{\odot}$) and only a few observed stars have evolved beyond the first giant branch. However, we have evidence that low-metallicity AGB stars in binary systems have interacted with their low-mass secondary companions in the past. The aim of this work is to investigate AGB nucleosynthesis at low metallicity by studying the surface abundances of chemically peculiar very metal-poor stars of the halo observed in binary systems. To this end we select a sample of 15 carbon- and $s$-element-enhanced metal-poor (CEMP-$s$) halo stars that are found in binary systems with measured orbital periods. With our model of binary evolution and AGB nucleosynthesis, we determine the binary configuration that best reproduces, at the same time, the observed orbital period and surface abundances of each star of the sample. The observed periods provide tight constraints on our model of wind mass transfer in binary stars, while the comparison with the observed abundances tests our model of AGB nucleosynthesis.Comment: 18 pages, 20 figures, accepted for publication on A&

Baryonic acoustic oscillations simulations for the Large Synoptic Survey Telescope (LSST)

The baryonic acoustic oscillations are features in the spatial distribution of the galaxies which, if observed at different epochs, probe the nature of the dark energy. In order to be able to measure the parameters of the dark energy equation of state to high precision, a huge sample of galaxies has to be used. The Large Synoptic Survey Telescope will survey the optical sky with 6 filters from 300nm and 1100nm, such that a catalog of galaxies with photometric redshifts will be available for dark energy studies. In this article, we will give a rough estimate of the impact of the photometric redshift uncertainties on the computation of the dark energy parameter through the reconstruction of the BAO scale from a simulated photometric catalog.Comment: 4 pages, 2 figures, 10th Rencontres de Blois proceedin

Spatially Heterogeneous Dynamics in a Granular System Near Jamming

In supercooled liquids and dense colloidal suspensions, strings of correlated motion represent a dynamical correlation length that grows as the glass transition is approached. Here, we present a granular system driven close to the jamming transition that shares this hallmark dynamical feature. In analogy, it exhibits a dynamical length scale that grows as the jamming transition is approached

Effective temperatures and activated dynamics for a two-dimensional air-driven granular system on two approaches to jamming

We present experiments on several distinct effective temperatures in a granular system at a sequence of increasing packing densities and at a sequence of decreasing driving rates. This includes single-grain measurements based on the mechanical energies of both the grains and an embedded oscillator, as well as a collective measurement based on the Einstein relation between diffusivity and mobility, which all probe different time scales. Remarkably, all effective temperatures agree. Furthermore, mobility data along the two trajectories collapse when plotted vs effective temperature and exhibit an Arrhenius form with the same energy barrier as the microscopic relaxation time

Penetration depth for shallow impact cratering

We present data for the penetration of a variety of spheres, dropped from rest, into a level non-cohesive granular medium. We improve upon our earlier work [Uehara {\it et al.} Phys. Rev. Lett. {\bf 90}, 194301 (2003)] in three regards. First, we explore the behavior vs sphere diameter and density more systematically, by holding one of these parameters constant while varying the other. Second, we prepare the granular medium more reproducibly and, third, we measure the penetration depth more accurately. The new data support our previous conclusion that the penetration depth is proportional to the 1/2 power of sphere density, the 2/3 power of sphere diameter, and the 1/3 power of total drop distance

Modelling the observed properties of carbon-enhanced metal-poor stars using binary population synthesis

The stellar population in the Galactic halo is characterised by a large fraction of CEMP stars. Most CEMP stars are enriched in $s$-elements (CEMP-$s$ stars), and some of these are also enriched in $r$-elements (CEMP-$s/r$ stars). One formation scenario proposed for CEMP stars invokes wind mass transfer in the past from a TP-AGB primary star to a less massive companion star which is presently observed. We generate low-metallicity populations of binary stars to reproduce the observed CEMP-star fraction. In addition, we aim to constrain our wind mass-transfer model and investigate under which conditions our synthetic populations reproduce observed abundance distributions. We compare the CEMP fractions and the abundance distributions determined from our synthetic populations with observations. Several physical parameters of the binary stellar population of the halo are uncertain, e.g. the initial mass function, the mass-ratio and orbital-period distributions, and the binary fraction. We vary the assumptions in our model about these parameters, as well as the wind mass-transfer process, and study the consequent variations of our synthetic CEMP population. The CEMP fractions calculated in our synthetic populations vary between 7% and 17%, a range consistent with the CEMP fractions among very metal-poor stars recently derived from the SDSS/SEGUE data sample. The results of our comparison between the modelled and observed abundance distributions are different for CEMP-$s/r$ stars and for CEMP-$s$ stars. For the latter, our simulations qualitatively reproduce the observed distributions of C, Na, Sr, Ba, Eu, and Pb. Contrarily, for CEMP-$s/r$ stars our model cannot reproduce the large abundances of neutron-rich elements such as Ba, Eu, and Pb. This result is consistent with previous studies, and suggests that CEMP-$s/r$ stars experienced a different nucleosynthesis history to CEMP-$s$ stars.Comment: 17 pages, 11 figures, accepted for publication on Astronomy and Astrophysic

Avalanche statistics and time-resolved grain dynamics for a driven heap

We probe the dynamics of intermittent avalanches caused by steady addition of grains to a quasi-two dimensional heap. To characterize the time-dependent average avalanche flow speed v(t), we image the top free surface. To characterize the grain fluctuation speed dv(t), we use Speckle-Visibility Spectroscopy. During an avalanche, we find that the fluctuation speed is approximately one-tenth the average flow speed, and that these speeds are largest near the beginning of an event. We also find that the distribution of event durations is peaked, and that event sizes are correlated with the time interval since the end of the previous event. At high rates of grain addition, where successive avalanches merge into smooth continuous flow, the relationship between average and fluctuation speeds changes to dv Sqrt[v]