Showing papers by "Sidney R. Nagel published in 2006"

Structural signatures of the unjamming transition at zero temperature

Abstract: We study the pair correlation function $g(r)$ for zero-temperature, disordered, soft-sphere packings just above the onset of jamming. We find distinct signatures of the transition in both the first and split second peaks of this function. As the transition is approached from the jammed side (at higher packing fraction) the first peak diverges and narrows on the small-$r$ side to a $\ensuremath{\delta}$ function. On the high-$r$ side of this peak, $g(r)$ decays as a power law. In the split second peak, the two subpeaks are both singular at the transition, with power-law behavior on their low-$r$ sides and step-function drop-offs on their high-$r$ sides. These singularities at the transition are reminiscent of empirical criteria that have previously been used to distinguish glassy structures from liquid ones.

Three-dimensional shear in granular flow

Abstract: The evolution of granular shear flow is investigated as a function of height in a split-bottom Couette cell. Using particle tracking, magnetic-resonance imaging, and large-scale simulations, we find a transition in the nature of the shear as a characteristic height H* is exceeded. Below H* there is a central stationary core; above H* we observe the onset of additional axial shear associated with torsional failure. Radial and axial shear profiles are qualitatively different: the radial extent is wide and increases with height, while the axial width remains narrow and fixed.

Breakup of Air Bubbles in Water: Memory and Breakdown of Cylindrical Symmetry

Abstract: Using high-speed video, we have studied air bubbles detaching from an underwater nozzle. As a bubble distorts, it forms a thin neck which develops a singular shape as it pinches off. As in other singularities, the minimum neck radius scales with the time until the breakup. However, because the air-water interfacial tension does not drive the breakup, even small initial cylindrical asymmetries are preserved throughout the collapse. This novel, nonuniversal singularity retains a memory of the nozzle shape, size, and tilt angle. In the last stages, the air appears to tear instead of pinch.

Stability and growth of single myelin figures.

Abstract: Myelin figures are long thin cylindrical structures that typically grow as a dense tangle when water is added to the concentrated lamellar phase of certain surfactants. We show that, starting from a well-ordered initial state, single myelin figures can be produced in isolation thus allowing a detailed study of their growth and stability. These structures grow with their base at the exposed edges of bilayer stacks from which material is transported into the myelin. Myelins only form and grow in the presence of a driving stress; when the stress is removed, the myelins retract.

Splashing of liquids: interplay of surrounding gas and surface roughness

Abstract: We investigate the interplay between substrate roughness and surrounding gas pressure in controlling the dynamics of splashing when a liquid drop hits a dry solid surface. We associate two distinct forms of splashing with each of these control parameters: prompt splashing is due to surface roughness and corona splashing is due to instabilities produced by the surrounding gas. The size distribution of ejected droplets reveals the length scales of the underlying droplet-creation process in both cases.

Numerical studies of the compressible Ising spin glass

Abstract: We study a two-dimensional compressible Ising spin glass at constant volume. The spin interactions are coupled to the distance between neighboring particles in the Edwards-Anderson model with ±J interactions. We find that the energy of a given spin configuration is shifted from its incompressible value, E0, by an amount quadratic in E0 and proportional to the coupling strength. We then construct a simple model expressed only in terms of spin variables that predicts the existence of a critical value of the coupling above which the spin-glass transition cannot exist.

Spout States in the Selective Withdrawal System

Abstract: In selective withdrawal, fluid is withdrawn through a nozzle suspended above the flat interface separating two immiscible, density-separated fluids of viscosities $ u_{upper}$ and $ u_{lower} = \lambda u_{upper}$ At low withdrawal rates, the interface gently deforms into a hump At a transition withdrawal rate, a spout of the lower fluid becomes entrained with the flow of the upper one into the nozzle When $\lambda = 0005$, the spouts at the transition are very thin with features that are over an order of magnitude smaller than any observed in the humps When $\lambda = 20$, there is an intricate pattern of hysteresis and a spout appears which is qualitatively different from those seen at lower $\lambda$ No corresponding qualitative difference is seen in the hump shapes