Abate, Adam Ross

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  • Publication
    Topological Persistence and Dynamical Heterogeneities Near Jamming
    (2007-08-30) Abate, Adam Ross; Durian, Douglas
    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(τ) and XB(τ), well suited for characterizing spatially heterogeneous dynamics. These are analogous to the standard four-point dynamic susceptibility X4(l,τ), 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.
  • Publication
    Approach to Jamming in an Air-Fluidized Granular Bed
    (2006-09-25) Abate, Adam Ross; Durian, Douglas J.
    Quasi-two-dimensional bidisperse amorphous systems of steel beads are fluidized by a uniform upflow of air, so that the beads roll on a horizontal plane. The short-time ballistic motion of the beads is stochastic, with non-Gaussian speed distributions and with different average kinetic energies for the two species. The approach to jamming is studied as a function of increasing bead area fraction and also as a function of decreasing air speed. The structure of the system is measured in terms of both the Voronoi tessellation and the pair distribution function. The dynamics of the system is measured in terms of both displacement statistics and the density of vibrational states. These quantities all exhibit tell-tale features as the dynamics become more constrained closer to jamming. In particular the pair distribution function and the Voronoi cell shape distribution function both develop split peaks. And the mean-squared displacement develops a plateau of subdiffusive motion separating ballistic and diffusive regimes. Though the system is driven and athermal, this behavior is remarkably reminiscent of that in dense colloidal suspensions and supercooled liquids. One possible difference is that kurtosis of the displacement distribution peaks at the beginning of the subdiffusive regime.
  • Publication
    Effective Temperatures and Activated Dynamics for a Two-Dimensional Air-Driven Granular System on Two Approaches to Jamming
    (2008-12-10) Abate, Adam Ross; Durian, Douglas J.
    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.
  • Publication
    Avalanche Statistics and Time-Resolved Grain Dynamics for a Driven Heap
    (2007-12-05) Abate, Adam Ross; Katsuragi, Hiroaki; Durian, Douglas J.
    We probe the dynamics of intermittent avalanches caused by steady addition of grains to a quasi-twodimensional heap. To characterize the time-dependent average avalanche flow speed v(t), we image the top free surface. To characterize the grain fluctuation speed δv(t), we use speckle-visibility spectroscopy. During an avalanche, we find that the fluctuation speed is approximately one-tenth the average flow speed, δv ≈ 0.1v, 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 δv∼ v1/2.