Mark Shattuck Current Research
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Research Interests:  (For more information see Professor Shattuck's website) Mark Shattuck's research activities are currently in the areas of:

Granular Media: Mesoscopic Physics on a Laboratory Scale: The study of granular materials provides insight into poorly understood and vitally important industrial problems, and an unprecedented opportunity to investigate experimentally the theoretical underpinnings of statistical physics. In granular systems, collective behavior and pattern formation can occur with a small number of macroscopic particles. This property creates a unique opportunity to gain a fundamental understanding of mesoscopic systems, such as colloids, lubrication, and nanoscale porous media. The profound link between granular flows and ordinary fluids and is a cornerstone of our research.

Experimental tests of granular kinetic theory: We conduct experiments to directly test granular kinetic theory in the laboratory. From snapshots of a 2D rotating layer of spheres trapped between two glass plates, we extract the velocity field using a temporal cross-correlation technique we developed for dense granular flows. The result is shown to the left as a speed field. We measure the local statistical properties of the grains from close-up high-speed digital photography shown in the lower left image. We developed highly adaptable particle tracking software to extract the velocities of individual particles. The blue and green dots are the centers of the particles in successive frames. From this data, we calculate the histogram of the velocities (small blue dots) that shows excellent agreement with kinetic theory (solid black curve). At moderate rotation rates three flow regimes are formed a dilute gas at the top, a dense gas in the middle, and an elasto-plastic solid at the bottom. In earlier work, we have confirmed that continuum equations of motion derived using kinetic theory of dense inelastic gases give quantitative results for the dilute phase. We are now exploring their applicability to the dense phase, where we may encounter viscoelastic behavior, which is not currently included in the theory. Finally we are exploring ways of extending kinetic theory and connecting with elasto-plastic solid models to bring the entire flow regime under a unified theory.
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Experimental granular rheology: By uniformly exciting a granular media using a random sum of the container's elastic vibration modes, we can directly measure the speed of sound, thermal conductivity, and viscosity as a function of density and granular temperature in this uniformly heated steady state. Using a sinusoidally varying forcing we can measure the frequency dependence of the transport properties. Granular media as an analog for collective systems in extreme conditions: We will study the flow of uniformly heated granular media in a small channel as an analog for mesoscopic systems. We can explore phase transitions in systems of rods, in mixtures of rods and spheres, and in mixtures of different sized spheres. These studies will add to the understanding of both granular media and ordinary condensed matter under extreme situations including confined geometries, gradients that are large on the scale of the mean free path, and flow in which intrinsic mechanical stress can induce phase transitions.

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