Showing papers by "Sidney R. Nagel published in 2010"

The Jamming Transition and the Marginally Jammed Solid

Abstract: When a system jams, it undergoes a transition from a flowing to a rigid state. Despite this important change in the dynamics, the internal structure of the system remains disordered in the solid as well as the fluid phase. In this way jamming is quite different from crystallization, the other common way in which a fluid solidifies. Jamming is a paradigm for thinking about how many different types of fluids—from molecular liquids to macroscopic granular matter—develop rigidity. Here we review recent work on the jamming transition. We start with perhaps the simplest model: frictionless spheres interacting via repulsive finite-range forces at zero temperature. In this highly idealized case, the transition has aspects of both first- and second-order transitions. From studies of the normal modes of vibration for the marginally jammed solid, new physics has emerged for how a material can be rigid without having the elastic properties of a normal solid. We first survey the simulation data and theoretical argumen...

Anharmonic and quasi-localized vibrations in jammed solids—Modes for mechanical failure

Abstract: We study harmonic and anharmonic properties of the vibrational modes in 3-dimensional jammed packings of frictionless spheres interacting via repulsive, finite-range potentials. A crossover frequency is apparent in the density of states, the diffusivity and the participation ratio of the normal modes of vibration. At this frequency, which shifts to zero at the jamming threshold, the vibrational modes have a very small participation ratio implying that the modes are quasi-localized. The lowest-frequency modes are the most anharmonic, with the strongest response to pressure and the lowest-energy barriers to mechanical failure.

Viscous to Inertial Crossover in Liquid Drop Coalescence

Abstract: Using an electrical method and high-speed imaging, we probe drop coalescence down to 10 ns after the drops touch. By varying the liquid viscosity over two decades, we conclude that, at a sufficiently low approach velocity where deformation is not present, the drops coalesce with an unexpectedly late crossover time between a regime dominated by viscous and one dominated by inertial effects. We argue that the late crossover, not accounted for in the theory, can be explained by an appropriate choice of length scales present in the flow geometry.

Heat transport in model jammed solids

Abstract: We calculate numerically the normal modes of vibrations in three-dimensional jammed packings of soft spheres as a function of the packing fraction and obtain the energy diffusivity, a spectral measure of transport that controls sound propagation and thermal conductivity. The crossover frequency between weak and strong phonon scattering is controlled by the coordination and shifts to zero as the system is decompressed toward the critical packing fraction at which rigidity is lost. We present a scaling analysis that relates the packing fraction dependence of the crossover frequency to the anomalous scaling of the shear modulus with compression. Below the crossover, the diffusivity displays a power-law divergence with inverse frequency consistent with Rayleigh law, which suggests that the vibrational modes are primarily transverse waves, weakly scattered by disorder. Above it, a large number of modes appear whose diffusivity plateaus at a nearly constant value before dropping to zero above the localization frequency. The thermal conductivity of a marginally jammed solid just above the rigidity threshold is calculated and related to the one measured experimentally at room temperature for most glasses.

Thin film formation during splashing of viscous liquids.

Abstract: After impact onto a smooth dry surface, a drop of viscous liquid initially spreads in the form of a thick lamella. If the drop splashes, it first emits a thin fluid sheet that can ultimately break up into droplets causing the splash. Ambient gas is crucial for creating this thin sheet. The time for sheet ejection, ${t}_{ejt}$, depends on impact velocity, liquid viscosity, gas pressure, and molecular weight. A central air bubble is trapped below the drop at pressures even below that necessary for this sheet formation. In addition, air bubbles are entrained underneath the spreading lamella when the ejected sheet is present. Air entrainment ceases at a lamella velocity that is independent of drop impact velocity as well as ambient gas pressure.

The jamming scenario - an introduction and outlook

Abstract: The jamming scenario of disordered media, formulated about 10 years ago, has in recent years been advanced by analyzing model systems of granular media. This has led to various new concepts that are increasingly being explored in in a variety of systems. This chapter contains an introductory review of these recent developments and provides an outlook on their applicability to different physical systems and on future directions. The first part of the paper is devoted to an overview of the findings for model systems of frictionless spheres, focussing on the excess of low-frequency modes as the jamming point is approached. Particular attention is paid to a discussion of the cross-over frequency and length scales that govern this approach. We then discuss the effects of particle asphericity and static friction, the applicability to bubble models for wet foams in which the friction is dynamic, the dynamical arrest in colloids, and the implications for molecular glasses.

Glassy Dynamics in Thermally Activated List Sorting

Abstract: Sorting the integers 1 through N into an ordered list is a simple task that can be done rapidly. However, using an algorithm based on the thermally activated pairwise exchanges of neighboring list elements, we find sorting can display many features of a glass, even for lists as small as N=5. This includes memory and rejuvenation effects during aging-two hallmarks of glassy dynamics that have been difficult to reproduce in standard glass simulations.