Gallery: The Spot Model with relaxation
| (a) | (b) | (c) |
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The recently proposed Spot Model provides a collective mechanism to describe random-packing dynamics for particles in a flowing amorphous material, such as sand in an hourglass. In such a material, a typical particle will be fixed in place due to packing constraints with its neighbors. When the sand flows, the particle is not free to move independently; it must move co-operatively with its neighbors.
We suggest that this motion can be described by motion of “spots”, which represent a small amount of free space spread across several particle diameters, as shown by the blue circle in (a). When the spot moves according to the blue arrow, it induces a small, correlated motion of all particles within range. This simple mechanism suffices to capture many results seen in granular drainage experiments, such as particle diffusion and spatial velocity correlations.
However, while this basic model remains simple enough for mathematical analysis, it is clear that it does not explicitly enforce packing constraints of the particles. In order to preserve valid packings, a second step has been proposed. After the block motion has been carried out, a small relaxation step is carried out, during which the particles and their nearest neighbors experience a soft-core repulsion with each other, as shown in (b). The net effect, as shown in (c), is therefore a co-operative local deformation, whose mean is roughly the original block motion.
Simulations show that this method can very accurately reproduce random-packing dynamics in granular flow, and it is hoped that this idea can also be applied to model deformations in glasses.
