Properties of packings and dispersions of superellipse sector particles.

Superellipse sector particles (SeSPs) are segments of superelliptical curves that form a tunable set of hard-particle shapes for granular and colloidal systems. SeSPs allow for continuous parametrization of corner sharpness, aspect ratio, and particle curvature; rods, circles, rectangles, and staples are examples of shapes SeSPs can model. We compare three computational processes: pair-wise Monte Carlo simulations that explore particle-particle geometric constraints, Monte Carlo simulations that reveal how these geometric constraints play out over dispersions of many particles, and Molecular Dynamics simulations that form random loose and close packings. We investigate the dependence of critical random loose and close packing fractions on particle parameters, finding that both values increase with opening aperture and decrease with increasing corner sharpness. The identified packing fractions are compared with the mean-field prediction of the random contact model; we find deviations from the model's prediction due to correlations between particle orientations. The complex interaction of spatial proximity and orientational alignment is also explored with a generalized spatioorientational distribution area (SODA) plot, which shows how higher density packings are achieved through particles assuming a small number of preferred configurations that depend sensitively on particle shape and system preparation.

Excluded area of superellipse sector particles.

Superellipse sector particles (SeSPs) are segments of superelliptical curves that form a tunable set of hard-particle shapes for granular and colloidal systems. SeSPs allow for continuous parametrization of corner sharpness, aspect ratio, and particle curvature; rods, circles, rectangles, and staples are examples of shapes SeSPs can model. We investigate the space of allowable (nonoverlapping) configurations of two SeSPs, which depends on both the center-of-mass separation and relative orientation. Radial correlation plots of the allowed configurations reveal circular regions centered at each of the particle's two end points that indicate configurations of mutually entangled particle interactions. Simultaneous entanglement with both end points is geometrically impossible; the overlap of these two regions therefore represents an excluded area in which no particles can be placed regardless of orientation. The regions' distinct boundaries indicate a translational frustration with implications for the dynamics of particle rearrangements (e.g., under shear). Representing translational and rotational degrees of freedom as a hypervolume, we find a topological change that suggests geometric frustration arises from a phase transition in this space. The excluded area is a straightforward integration over excluded states; for arbitrary relative orientation this decreases sigmoidally with increasing opening aperture, with sharper SeSP corners resulting in a sharper decrease. Together, this work offers a path towards a unified theory for particle shape control of bulk material properties.

Elephant trunks form joints to squeeze together small objects.

Wild African elephants are voracious eaters, consuming 180 g of food per minute. One of their methods for eating at this speed is to sweep food into a pile and then pick it up. In this combined experimental and theoretical study, we elucidate the elephant's unique method of picking up a pile of food by compressing it with its trunk. To grab the smallest food items, the elephant forms a joint in its trunk, creating a pillar up to 11 cm tall that it uses to push down on food. Using a force sensor, we show the elephant applies greater force to smaller food pieces, in a manner that is required to solidify the particles into a lump solid, as calculated by Weibullian statistics. Elephants increase the height of the pillar with the force required, achieving up to 28% of the applied force using the self-weight of the pillar alone. This work shows that elephants are capable of modulating the force they apply to granular materials, taking advantage of their transition from fluid to solid. In the future, heavy robotic manipulators may also form joints to compress and lift objects together.

Ant aggregations self-heal to compensate for the Ringelmann effect.

Fire ants, Solenopsis invicta, link their bodies together to form structures such as rafts, bivouacs and bridges. Such structures are in danger of being damaged by natural disturbances such as passing water currents. In this combined experimental and theoretical study, we investigate the self-healing of ant assemblages. We press two ant aggregations together and measure the forces to pull them apart. As the group size increases, the contribution of each ant decreases. This phenomenon, known as the Ringelmann effect, or social loafing, has previously been shown for cattle and humans. In this study, we show that it is a challenge for ants as well. We rationalize this effect with an agent-based simulation which exhibits the Ringelmann effect of ants that periodically make and break links with each other, but grip with higher probability if the ants are stretched. Over time, ants compensate for the Ringelmann effect by building more links. We use a mathematical model to show that the rate of new links is proportional to the number of free ants in the cluster. The principles found here may inspire new directions in self-healing and active materials.

Entangled granular media.

We study the geometrically induced cohesion of ensembles of granular "u particles" that mechanically entangle through particle interpenetration. We vary the length-to-width ratio l/w of the u particles and form them into freestanding vertical columns. In a laboratory experiment, we monitor the response of the columns to sinusoidal vibration (with peak acceleration Γ). Column collapse occurs in a characteristic time τ which follows the relation τ∝exp(Γ/Δ). Δ resembles an activation energy and is maximal at intermediate l/w. A simulation reveals that optimal strength results from competition between packing and entanglement.

Power-law flow statistics in anisometric (wedge) hoppers.

We find the probability for N particles to exit an anisometric (having unequal dimensions) hopper before jamming to have a broad power-law decay with exponent α = -2, in marked contrast to the exponential decay seen in hoppers with symmetric apertures. The transition from exponential to power law is explained by amodel that assumes particle motion is correlated over a distinct length scale. Hoppers with lengths larger than this length are modeled as a series of adjacent, statistically independent "cells." Experiments with apertures 27-37 particle diameters D long are well fit by a three-cell model, implying that the correlation length is ≈ 9-12D.

Column collapse of granular rods.

We investigate the collapse of granular rodpiles as a function of particle (length/diameter) and pile (height/radius) aspect ratio. We find that, for all particle aspect ratios below 24, there exists a critical height Hl below which the pile never collapses, maintaining its initial shape as a solid, and a second height Hu above which the pile always collapses. Intermediate heights between Hl and Hu collapse with a probability that increases linearly with increasing height. The linear increase in probability is independent of particle length, width, or aspect ratio. When piles collapse, the runoff scales as a piecewise power law with pile height, with rf ~H(1.2±0.1) for pile heights below H(c) ≈ 0.74 and r(f) ≈ H(0.6±0.1) for taller piles.

Jamming of three-dimensional prolate granular materials.

We have found that the ability of long thin rods to jam into a solidlike state in response to a local perturbation depends upon both the particle aspect ratio and the container size. The dynamic phase diagram in this parameter space reveals a broad transition region separating granular stick-slip and solidlike behavior. In this transition region the pile displays both solid and stick-slip behavior. We measure the force on a small object pulled through the pile, and find the fluctuation spectra to have power law tails with an exponent characteristic of the region. The exponent varies from beta=-2 in the stick-slip region to beta=-1 in the solid region. These values reflect the different origins--granular rearrangements vs dry friction--of the fluctuations. Finally, the packing fraction shows only a slight dependence on container size, but depends on aspect ratio in a manner predicted by mean-field theory and implies an aspect-ratio-independent contact number of =5.25 +/- 0.03.

Two-dimensional packing in prolate granular materials.

We investigate the two-dimensional packing of extremely prolate (aspect ratio alpha=L/D>10) granular materials, comparing experiments with Monte Carlo simulations. The average packing fraction of particles with aspect ratio alpha=12 is 0.68+/-0.03. We quantify the orientational correlation of particles and find a correlation length of two particle lengths. The functional form of the orientational correlation is the same in both experiments and simulations which three orders of magnitude in aspect ratio, all decaying over a distance of two particle lengths. It is possible to identify voids in the pile with sizes ranging over two orders of magnitude. The experimental void distribution function is a power law with exponent -beta=-2.43+/-0.08. Void distributions in simulated piles do not decay as a power law, but do show a broad tail. We extend the simulation to investigate the scaling at very large aspect ratios. A geometric argument predicts the pile number density to scale as alpha(-2). Simulations do indeed scale this way, but particle alignment complicates the picture, and the actual number densities are quite a bit larger than predicted.