Orientational ordering in crumpled elastic sheets

We report an experimental study of the development of orientational order in a crumpled sheet, with a particular focus on the role played by the geometry of confinement. Our experiments are performed on elastomeric sheets immersed in a fluid, so that the effects of plasticity and friction are suppressed. When the sheet is crumpled either axially or radially within a cylinder, we find that the sheet aligns with the flat or the curved wall, depending on the aspect ratio of the cylinder. Nematic correlations develop between the normals of the sheets at relatively low volume fractions and the crumpled object has large density fluctuations corresponding to the stacking of parallel sheets. The aligning effect of the wall breaks symmetry and selects the direction of ordering

Large Force Fluctuations in a Flowing Granular Medium

We report the characteristics of the temporal fluctuations in the local force delivered to the wall of a 2D hopper by a granular medium flowing through it. The forces are predominantly impulsive at all flow rates for which the flow does not permanently jam. The average impulse delivered to the wall is much larger than the momentum acquired by a single particle under gravity between collisions, reflecting the fact that momentum is transferred to the walls from the bulk of the flow by collisions. At values larger than the average impulse, the probability distribution of impulses is broad and decays exponentially on the scale of the average impulse, just as it does in static granular media. At small impulse values, the probability distribution evolves continuously with flow velocity but does not show a clear signature of the transition from purely collisional flow to intermittently jamming flows. However, the time interval between collisions tends to a power law distribution, $P(\tau)\sim \tau^{-3/2}$, thus showing a clear dynamical signature of the approach to jamming.Comment: 4 pages, 3 figure

Kepler orbits of settling discs

The collective dynamics of objects moving through a viscous fluid is complex and counterintuitive. A key to understanding the role of nontrivial particle shape in this complexity is the interaction of a pair of sedimenting spheroids. We report experimental results on two discs settling at negligible Reynolds number ($\simeq 10^{-4}$), finding two classes of bound periodic orbits, each with transitions to scattering states. We account for these dynamics, at leading far-field order, through an effective Hamiltonian in which gravitational driving endows orientation with the properties of momentum. This leads to a precise correspondence with the Kepler problem of planetary motion for a wide range of initial conditions, and also to orbits with no Keplerian analogue. This notion of internal degrees of freedom manifesting themselves as an effective inertia is potentially a more general tool in Stokesian driven systems

Wrinkling in Buckling and a Thin Sheet

Module 1: Euler Buckling Learning Objectives: What is an instability? A sudden change in behaviour in response to a small change in conditions. Instabilities usually involve a change in symmetry from a more symmetric situation to a less symmetric one The mechanism for an instability usually involves two competing forces (one force stabilizing the symmetric state, and the other one destabilizing it), with one suddenly winning the contest These competing forces in thin objects are often the forces of compression (destabilizing force - favors buckling or wrinkling) and of bending (stabilizing force). Understanding by data collapse, the power of using dimensionless (unit-less) numbers, rather than dimensional parameters (measured in units of length, time, force, energy, etc). Module 2: Wrinkling Learning Objectives: What is the wavelength of a pattern? What decides the wavelength: reinforcing the idea of competition between many forces. Expanding and reinforcing concepts: What symmetry is broken in the wrinkling instability? Data collapse and dimensionless numbers You know what wrinkling is – it’s what you see when you look in mirror, or pinch the flesh on your arm. What we’re trying to do in this experiment, is to have you realize that this is an example of buckling but one that involves a repeating pattern caused by buckling

Wrinkling of a floating sheet

The objective of today’s work will be to generate wrinkle patterns on very thin polymer films using the forces generated by the surface tension of a water drop. You’ll do a few sizes of water drop and we’ll give you a couple of thicknesses of film. Digital images of the pattern will allow us to make observations of the number and size of the wrinkles generated. We will try to develop an understanding of the dependence of the pattern on the materials used and the forces applie

Heating mechanism affects equipartition in a binary granular system

Two species of particles in a binary granular system typically do not have the same mean kinetic energy, in contrast to the equipartition of energy required in equilibrium. We investigate the role of the heating mechanism in determining the extent of this non-equipartition of kinetic energy. In most experiments, different species of particle are unequally heated at the boundaries. We show by event-driven simulations that this differential heating at the boundary influences the level of non-equipartition even in the bulk of the system. This conclusion is fortified by studying a numerical model and a solvable stochastic model without spatial degrees of freedom. In both cases, even in the limit where heating events are rare compared to collisions, the effect of the heating mechanism persists