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One way in which we can compare our experiment to models is through examining the dynamics of the particles. This is done by videotaping the particles from above and analyzing the pictures on a computer. Because photoelastic materials are transparent, it is not trivial to determine where the disks are in relation to voids in the experiment. To solve this problem, a small rectangle of opaque tape was placed on each disk. A rectangle is used so that center of mass and the orientation of each disk can be observed. Once particle velocities, positions, and orientations are known, the velocities are then averaged at certain radii to find radial, tangential and spin velocity distributions and profiles for the system.
The profiles we obtained are being used to test theoretical molecular dynamics models developed by some of our collaborators [Schoellmann]. One interesting property we have found from examining the mean tangential velocity profile is that the mean velocity falls in a roughly exponential curve as one moves radially away from the shearing surface. This implies a structure to the shear band in this material unlike the sharp cutoff in shear bands in sand or more rigid particles. We also find that the mean particle spin profile oscillates near the inner disk and falls rapidly to zero as we move radially away. If we look at the tangential velocity distributions near the shearing surface we find a non-gaussian structure that corresponds to the details of the grain motion. Looking at tangential velocity distributions farther away from the shearing surface we find the complex structure in the distribution is only obvious when the mean spin velocity is non-zero. For all the profiles and distributions above we have found invariance (within statistical fluctuations) with respect to inner disk rotation rate.  Probability distribution for particles in first radial bin In a related vein we also have begun looking at the two-dimensional density or area fraction of disks in the experiment. We discovered that lighting the system with near-UV light allows us to distiguish between the usually transparent disks and voids because they have different indeces of refraction for these wavelengths. Effects from shadows associated with the particles occur, but these can be accounted for by comparing the analytical and measured area fractions for known configurations of the disks (square lattice, hexagonally close-packed). Information on the density variation in time will give us insight into the transient density relaxation of the system. [Schoellmann] S. Schoellmann, S. Luding, H. Herrmann, to be published  Research Main PageMotivation and Experimental SetupStress Measurements
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