Mark D. Shattuck

Shocks in supersonic sand.

We measure time-averaged velocity, density, and temperature fields for steady granular flow past a wedge. We find the flow to be supersonic with a speed of granular pressure disturbances (sound speed) equal to about 10% of the flow speed, and we observe shocks nearly identical to those in a supersonic gas. Molecular dynamics simulations of Newtons laws yield fields in quantitative agreement with experiment. A numerical solution of Navier-Stokes-like equations agrees with a molecular dynamics simulation for experimental conditions excluding wall friction.

Crystallization of a Quasi-Two-Dimensional Granular Fluid

We experimentally investigate the crystallization of a uniformly heated quasi-2D granular fluid as a function of the filling fraction. Our experimental results for the Lindemann melting criterion, the radial distribution function, the bond order parameter, and the statistics of topological changes at the particle level are the same as those found in simulations of equilibrium hard disks. This direct mapping suggests that the study of equilibrium systems can be effectively applied to study nonequilibrium steady states such as those found in our driven and dissipative granular system.

Caging dynamics in a granular fluid

We report an experimental investigation of the caging motion in a uniformly heated granular fluid for a wide range of filling fractions, varphi. At low varphi the classic diffusive behavior of a fluid is observed. However, as varphi is increased, temporary cages develop and particles become increasingly trapped by their neighbors. We statistically analyze particle trajectories and observe a number of robust features typically associated with dense molecular liquids and colloids. Even though our monodisperse and quasi-2D system is known to not exhibit a glass transition, we still observe many of the precursors usually associated with glassy dynamics. We speculate that this is due to a process of structural arrest provided, in our case, by the presence of crystallization.

Pattern formation during mixing and segregation of flowing granular materials

Powder mixing plays an important role in a number of industries ranging from pharmaceuticals and food to ceramics and mining. Avalanches provide a mechanism for the stretching and folding needed to mix granular solids. However, unlike fluids, when particles dissimilar in size, density, or shape flow, they can spontaneously demix or segregate. Using magnetic resonance imaging, we track the transport of granular solids in a slowly rotating tube both with and without segregation effects. Compared with experiments in a 2-dimensional rotating disk partially filled with colored particles, the mixing kinematics and the granular pattern formation in a tube are changed by an axial flow instability. From simple physical principles we argue how size and density segregation mechanisms can be made to cancel, allowing good mixing of dissimilar particles, and we show experiments verifying this. Further experiments isolate the axial transport in the slowly rotating tube. Axial transport can appear faster with segregation than without.

Transport coefficients for granular media from molecular dynamics simulations

Under many conditions, macroscopic grains flow like a fluid; kinetic theory predicts continuum equations of motion for this granular fluid. In order to test the theory, we perform event-driven molecular simulations of a two-dimensional gas of inelastic hard disks, driven by contact with a heat bath. Even for strong dissipation, high densities, and small numbers of particles, we find that continuum theory describes the system well. With a bath that heats the gas homogeneously, strong velocity correlations produce a slightly smaller energy loss due to inelastic collisions than that predicted by kinetic theory. With an inhomogeneous heat bath, thermal or velocity gradients are induced. Determination of the resulting fluxes allows calculation of the thermal conductivity and shear viscosity, which are compared to the predictions of granular kinetic theory, and which can be used in continuum modeling of granular flows. The shear viscosity is close to the prediction of kinetic theory, while the thermal conductivity can be overestimated by a factor of 2; in each case, transport is lowered with increasing inelasticity.

Convection and flow in porous media. Part 1. Visualization by magnetic resonance imaging

We describe an experimental study of porous media convection (PMC) from onset to 8Ra c . The goal of this work is to provide non-invasive imaging and high-precision heat transport measurements to test theories of convection in PMC. We obtain velocity information and visualize the convection patterns using magnetic resonance imaging (MRI). We study both ordered and disordered packings of mono-disperse spheres of diameter d = 3.204 ± 0.029 mm, in circular, rectangular, and hexagonal planforms. In general, the structure of the medium plays a role which is not predicted by theories which assume a homogeneous system. Disordered media are prepared by pouring mono-disperse spheres into the container. Large ordered regions of close packing for the spheres, with grain boundaries and isolated defects, characterize these media. The defects and grain boundaries play an important role in pattern formation in disordered media. Any deviation from close packing produces a region of larger porosity, hence locally larger permeability. The result is spatial variations in the Rayleigh number, Ra. We define the critical Ra, Ra c , as the Rayleigh number at the onset of convection in the ordered regions. We find that stable localized convective regions exist around grain boundaries and defects at Ra c . These remain as pinning sites for the convection patterns in the ordered regions as Ra increases above Ra c up to 5Ra c , the highest Ra studied in the disordered media. In ordered media, spheres are packed such that the only deviations from close packing occur within a thin ( d ) region near the vertical walls. Stable localized convection begins at 0.5Ra c in the wall regions but appears to play only a weak role in the pattern formation of the interior regions (bulk), since different stable patterns are observed in the bulk at the same Ra after each cycling of Ra below Ra c , even for similar patterns of small rolls in the wall regions. The experiments provide a test of the following predictions for PMC: (i) that straight parallel rolls should be linearly stable for Ra c c ; (ii) that at onset, the rolls should have a dimensionless wavevector q c = π; (iii) that at the upper end of this range rolls should lose stability to cross-rolls; (iv) that the initial slope of the Nusselt curve should be 2; (v) that there should be a rapid decay of vertical vorticity - hence no complex flows, such as those which occur for Rayleigh- Benard convection (RBC) within the nominal regime of stable parallel rolls. These predictions are in partial agreement with our findings for the bulk convection in the ordered media. We observe roll-like structures which relax rapidly to stable patterns between Ra c and 5Ra c . However we find a wavenumber which is 0.7π compared to π derived from linear stability theory. We find an asymmetry between the size of the upfiowing regions and downfiowing regions as Ra grows above Ra c . The ratio of the volume of the upfiowing to the volume of the downfiowing regions decreases as Ra increases and leads to a novel time-dependent state, which does not consist of cross-rolls. This time-dependent state begins at 6 Ra c and is observed up to 8 Ra c , the largest Ra which we studied. It seems likely that the occurrence of this state is linked to departures from the Boussinesq approximation at higher Ra. We also find that the slope of the Nusselt curve is 0.7, which does not agree with the predicted value of 2.

Velocity distributions and correlations in homogeneously heated granular media.

We compare the steady state velocity distributions from our three-dimensional inelastic hard sphere molecular dynamics simulation for homogeneously heated granular media, with the predictions of a mean field-type Enskog-Boltzmann equation for inelastic hard spheres [T. P. C. van Noije and M. H. Ernst, Granular Matter 1, 57 (1998)]. Although we find qualitative agreement for all values of density and inelasticity, the quantitative disagreement approaches approximately 40% at high inelasticity or density. By contrast the predictions of the pseudo-Maxwell molecule model [J. A. Carrillo, C. Cercignani, and I. M. Gamba, Phys. Rev. E, 62, 7700 (2000)] are both qualitatively and quantitatively different from those of our simulation. We also measure short-range and long-range velocity correlations exhibiting nonzero correlations at contact before the collision, and being consistent with a slow algebraic decay over a decade in the unit of the diameter of the particle, proportional to r(-(1+alpha)), where 0.2<alpha<0.3. The existence of these correlations implies the failure of the molecular chaos assumption and the mean field approximation, which is responsible for the quantitative disagreement of the inelastic hard sphere kinetic theory.

Experimental demonstration of nonuniform frequency distributions of granular packings.

We developed an experimental method to generate mechanically stable (MS) packings of frictionless disks and performed coordinated experiments and simulations to characterize MS packings in small systems. For a given system geometry, MS packings occur as discrete, well-separated points in configuration space with probabilities that vary by many orders of magnitude and are robust with respect to the packing preparation. Over a continuous range of system geometries, MS packings occur as distinct geometrical families and only a small fraction of families are sampled via quasistatic dynamics. These results suggest that the most frequent MS packings may dominate the structural and mechanical properties of dense granular media.

Phase bubbles and spatiotemporal chaos in granular patterns

We use inelastic hard sphere molecular dynamics simulations and laboratory experiments to study patterns in vertically oscillated granular layers. The simulations and experiments reveal that phase bubbles spontaneously nucleate in the patterns when the container acceleration amplitude exceeds a critical value, about 7 g, where the pattern is approximately hexagonal, oscillating at one-fourth the driving frequency (f/4). A phase bubble is a localized region that oscillates with a phase opposite (differing by pi) to that of the surrounding pattern; a localized phase shift is often called an arching in studies of two-dimensional systems. The simulations show that the formation of phase bubbles is triggered by undulation at the bottom of the layer on a large length scale compared to the wavelength of the pattern. Once formed, a phase bubble shrinks as if it had a surface tension, and disappears in tens to hundreds of cycles. We find that there is an oscillatory momentum transfer across a kink, and the shrinking is caused by a net collisional momentum inward across the boundary enclosing the bubble. At increasing acceleration amplitudes, the patterns evolve into randomly moving labyrinthian kinks (spatiotemporal chaos). We observe in the simulations that f/3 and f/6 subharmonic patterns emerge as primary instabilities, but that they are unstable to the undulation of the layer. Our experiments confirm the existence of transient f/3 and f/6 patterns.

Which Biomarkers Reveal Neonatal Sepsis

We address the identification of optimal biomarkers for the rapid diagnosis of neonatal sepsis. We employ both canonical correlation analysis (CCA) and sparse support vector machine (SSVM) classifiers to select the best subset of biomarkers from a large hematological data set collected from infants with suspected sepsis from Yale-New Haven Hospitals Neonatal Intensive Care Unit (NICU). CCA is used to select sets of biomarkers of increasing size that are most highly correlated with infection. The effectiveness of these biomarkers is then validated by constructing a sparse support vector machine diagnostic classifier. We find that the following set of five biomarkers capture the essential diagnostic information (in order of importance): Bands, Platelets, neutrophil CD64, White Blood Cells, and Segs. Further, the diagnostic performance of the optimal set of biomarkers is significantly higher than that of isolated individual biomarkers. These results suggest an enhanced sepsis scoring system for neonatal sepsis that includes these five biomarkers. We demonstrate the robustness of our analysis by comparing CCA with the Forward Selection method and SSVM with LASSO Logistic Regression.