Showing papers by "Sidney R. Nagel published in 2013"

Stability of jammed packings II: the transverse length scale

Abstract: As a function of packing fraction at zero temperature and applied stress, an amorphous packing of spheres exhibits a jamming transition where the system is sensitive to boundary conditions even in the thermodynamic limit. Upon further compression, the system should become insensitive to boundary conditions provided it is sufficiently large. Here we explore the linear response to a large class of boundary perturbations in 2 and 3 dimensions. We consider each finite packing with periodic-boundary conditions as the basis of an infinite square or cubic lattice and study properties of vibrational modes at arbitrary wave vector. We find that the stability of such modes can be understood in terms of a competition between plane waves and the anomalous vibrational modes associated with the jamming transition; infinitesimal boundary perturbations become irrelevant for systems that are larger than a length scale that characterizes the transverse excitations. This previously identified length diverges at the jamming transition.

Multiple transient memories in sheared suspensions: robustness, structure, and routes to plasticity

Abstract: Multiple transient memories, originally discovered in charge-density-wave conductors, are a remarkable and initially counterintuitive example of how a system can store information about its driving. In this class of memories, a system can learn multiple driving inputs, nearly all of which are eventually forgotten despite their continual input. If sufficient noise is present, the system regains plasticity so that it can continue to learn new memories indefinitely. Recently, Keim and Nagel [Phys. Rev. Lett. 107, 010603 (2011)] showed how multiple transient memories could be generalized to a generic driven disordered system with noise, giving as an example simulations of a simple model of a sheared non-Brownian suspension. Here, we further explore simulation models of suspensions under cyclic shear, focusing on three main themes: robustness, structure, and overdriving. We show that multiple transient memories are a robust feature independent of many details of the model. The steady-state spatial distribution of the particles is sensitive to the driving algorithm; nonetheless, the memory formation is independent of such a change in particle correlations. Finally, we demonstrate that overdriving provides another means for controlling memory formation and retention.

Observation and characterization of the vestige of the jamming transition in a thermal three-dimensional system.

Abstract: We study the dependence on the packing fraction of the pair-correlation function $g(r)$ and particle mobility in a dense three-dimensional packing of soft colloids made of poly N-isopropyl acrylamide (pNIPAM), a thermosensitive gel. We find that $g(r)$ for our samples is qualitatively like that of a liquid at all packing fractions. There is a peak in ${g}_{1}$, the height of the first peak of $g(r)$, as a function of the packing fraction. This peak is identified as a vestige, which remains at finite temperature, of the divergence found at the jamming transition in simulations of soft frictionless spheres at zero temperature. As the density is increased, the particle dynamics slow down and near the packing fraction where there is a peak in ${g}_{1}$ the particles become arrested on the time scale of the experiment.

Energy loss at propagating jamming fronts in granular gas clusters.

Abstract: We explore the initial moments of impact between two dense granular clusters in a two-dimensional geometry. The particles are composed of solid CO(2) and are levitated on a hot surface. Upon collision, the propagation of a dynamic "jamming front" produces a distinct regime for energy dissipation in a granular gas in which the translational kinetic energy decreases by over 90%. Experiments and associated simulations show that the initial loss of kinetic energy obeys a power law in time ΔE = -Kt(3/2), a form that can be predicted from kinetic arguments.

Still Water: Dead Zones and Collimated Ejecta from the Impact of Granular Jets

Abstract: When a dense granular jet hits a target, it forms a large dead zone and ejects a highly collimated conical sheet with a well-defined opening angle. Using experiments, simulations, and continuum modeling, we find that this opening angle is insensitive to the precise target shape and the dissipation mechanisms in the flow. We show that this surprising insensitivity arises because dense granular jet impact, though highly dissipative, is nonetheless controlled by the limit of perfect fluid flow.

Collision dynamics of particle clusters in a two-dimensional granular gas.

Abstract: In a granular gas, inelastic collisions produce an instability in which the constituent particles cluster heterogeneously. These clusters then interact with each other, further decreasing their kinetic energy. We report experiments of the free collisions of dense clusters of particles in a two-dimensional geometry. The particles are composed of solid CO${}_{2}$, which float nearly frictionlessly on a hot surface due to sublimated vapor. After two dense clusters of $\ensuremath{\approx}$100 particles collide, there are two distinct stages of evolution. First, the translational kinetic energy rapidly decreases by over 90% as a ``jamming front'' sweeps across each cluster. Subsequently, the kinetic energy decreases more slowly as the particles approach the container boundaries. In this regime, the measured velocity distributions are non-Gaussian with long tails. Finally, we compare our experiments to computer simulations of colliding, two-dimensional, granular clusters composed of circular, viscoelastic particles with friction.

Transient Memories in Experiments on Sheared Non-Brownian Suspensions

Abstract: A system with multiple transient memories can remember a set of inputs but subsequently forgets almost all of them, even as they are continually applied. If noise is added, the system can store all memories indefinitely. The phenomenon has recently been predicted for cyclically sheared non-Brownian suspensions. Here we present experiments on such suspensions, finding behavior consistent with multiple transient memories and showing how memories can be stabilized by noise.

Vibration and Nonlinear Resonance in the Break-up of an Underwater Bubble

Abstract: We use high-speed X-ray phase-contrast imaging, weakly nonlinear analysis and boundary integral simulations to characterize the final stage of underwater bubble break-up The X-ray imaging study shows that an initial azimuthal perturbation to the shape of the bubble neck gives rise to oscillations that increasingly distort the cross-section shape These oscillations terminate in a pinch-off where the bubble surface develops concave regions that contact similar to what occurs when two liquid drops coalesce We also present a weakly nonlinear analysis that shows that this coalescence-like mode of pinch-off occurs when the initial shape oscillation interferes constructively with the higher harmonics it generates and thus reinforce each other's effects in bringing about bubble break-up Finally we present numerical results that confirm the weakly nonlinear analysis scenario as well as provide insight into observed shape reversals They demonstrate that when the oscillations interfere destructively, a qualitatively different mode of pinch-off results where the cross-section profile of the bubble neck develops sharply-curved regions

Stability of jammed packings II: the transverse length scale

Abstract: As a function of packing fraction at zero temperature and applied stress, an amorphous packing of spheres exhibits a jamming transition where the system is sensitive to boundary conditions even in the thermodynamic limit. Upon further compression, the system should become insensitive to boundary conditions provided it is sufficiently large. Here we explore the linear response to a large class of boundary perturbations in 2 and 3 dimensions. We consider each finite packing with periodic-boundary conditions as the basis of an infinite square or cubic lattice and study properties of vibrational modes at arbitrary wave vector. We find that the stability of such modes be understood in terms of a competition between plane waves and the anomalous vibrational modes associated with the jamming transition; infinitesimal boundary perturbations become irrelevant for systems that are larger than a length scale that characterizes the transverse excitations. This previously identified length diverges at the jamming transition.