All posts by Eric Corwin

Assistant Professor of Physics
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A Geometric View of Jamming

The jamming and packing of athermal spheres is an old and rich problem. While many studies have looked at mechanical phenomena like pressure, force networks, stress, and strain, we focus on geometric properties. Specifically, we simulate spheres at a variety of packing fractions and we look at their Voronoi cells: the portion of space closest to a given particle. These cells change shape as a packing approaches jamming. We track these changes by observing their volume, surface area, and moments of inertia, which all show signatures of the transition. This new view of jamming as a purely geometric phenomena provides new insights and quantitative measurements.

VoronoiIllustration

Fluctuation Dissipation in Non-Equilibrium Systems

Since its first observation by John B. Johnson and formulation by Harry Nyquist, Fluctuation-Dissipation Theorem has provided a mechanism for peeking into the behavior of thermodynamic systems as they are perturbed from equilibrium. However, despite the theorem’s widespread usefulness, a great portion of the world around us cannot be reduced to systems which approximate equilibrium closely enough for Fluctuation-Dissipation Theorem to apply. We attempt to help bridge this gap by exploring the statistics of highly tunable non-equilibrium systems. Towards this goal, we return to the Johnson-Nyquist system of electrons scattering around a resistor lattice—by simulating the trajectories of electrons in rapidly fluctuating lattices, we hope to establish the status of Fluctuation-Dissipation Theorem in non-equilibrium systems.

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2D Friction-driven Granular Flow Mechanics

The Janssen effect is a unique property of confined granular materials experiencing gravitational compaction in which the pressure at the bottom saturates with an increasing filling height due to frictional interactions with side walls. In this Letter, we replace gravitational compaction with frictional compaction. We study friction-compacted 2D granular materials confined within fixed boundaries on a horizontal conveyor belt. We find that even with high-friction side walls the Janssen effect completely vanishes. Our results demonstrate that gravity-compacted granular systems are inherently different from frictioncompacted systems in at least one important way: vibrations induced by sliding friction with the driving surface relax away tangential forces on the walls. Remarkably, we find that the Janssen effect can be recovered by replacing the straight side walls with a sawtooth pattern. The mechanical force introduced by varying the sawtooth angle θ can be viewed as equivalent to a tunable friction force. By construction, this mechanical friction force cannot be relaxed away by vibrations in the system.

Although granular impact dynamics have been studied extensively granular flow is still a topic of active research. Granular flow mechanics is not yet well understood and has applications to ballistics, meteor impacts and industrial processes. We have designed an experiment to study the mechanics of 2D friction-driven granular flow into a hopper as well as around a probe. We use a conveyor belt to drive a jammed packing of acrylic laser cut disks past a probe that is free to rotate about the center of mass axis. A laser cutter is used to construct different probes of varying geometry. We study, for instance, the effect of probe geometry on its rotational stability and the drag force it experiences. Using a force sensor and an optical encoder, we can measure the force on the probe and its rotational motion.
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Granular Optics

Inspired by the  lovely paper “Shock Waves in Weakly Compressed Granular Media” by van den Wildenberg, Rogier van Loo, and Martin van Hecke we investigate granular optics in the non-shock regime.

We experimentally probe wave propagation in compressed granular media. Due to the presence of a Hertzian contact potential between particles, granular media is unique in that small changes in confining pressure translate into large changes in the sounds speed.  We use this property to externally construct gradients in the effective refractive index.  This allows us to demonstrate refraction within a granular pack.  We further use this property to build acoustic lenses within a granular system using nothing more than applied confining pressure.  We measure the propagation of sound waves within the granular material using force sensitive resistors.

 

Our setup includes a 2’x2’x6” containment device (sandbox) and a variety of medium from mm glass beads (sand) to ½” stone material (rocks & gravel). By using a variety of granular medium we can further probe the refractive nature of the system. We apply steady confining pressure though metal plates.

Crossover from Ballistic to Brownian Motion

In this project we are interested in studying the ballistic diffusive crossover in a free liquid.  In 1827, Robert Brown observed a speck of pollen floating in water moving in diffusive motion.  In 1905, Albert Einstein showed that diffusive motion was caused by the pollen being hit by individual water molecules.  Fundamental to this theory is that for very short time scales the pollen is moving ballistically.  The goal of this experiment is to observe a particle, suspended in a liquid, transition from ballistic to diffusive motion. To observe this behavior we use a homemade holographic microscope in conjunction with a high-speed camera.

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Two-Dimensional Macroscopic Ideal Gas

This project brings the microscopic world into the laboratory scale.  We agitate a container full of water to produce chaotic surface waves which replicate the tumultuous thermal motion of molecules in a gas, but on a centimeter scale rather than angstrom.  We’ve shown that these waves have a temperature that is functionally identical that of a thermal gas.  This offers us a unique opportunity to study statistical mechanics in a constitutive fashion, exploring directly the dynamics of interparticle interactions, phase transitions, polymer analogs, and many other systems.