Curvature-driven abrasion: numerical and experimental verification.
Andras Sipos (Tech U. Budapest)

While both the mathematical and the geological literature is substantial on the geometry of abrasion, little is known about the applicability and experimental verification of the mathematical models. This might be explained by the imperfect understanding of the connection between the model parameters and the physical reality. Here we study the PDE model by Firey for curvature-driven abrasion due to collisions. Even in this case our goal to make a quantitative verification required a deliberate design of the experiments. Our approach combines classical tumbler experiments with a fit of an equal volumetric superellipsoid to the abraded shape. Not only do we find good qualitative and quantitative agreement, our data helps also to verify some aspects of the more general Bloore PDE model. Beyond simulating the PDE by standard level-set technique we also compare the data to discrete-event based simulations. Although this later approach is not the direct discretization of the PDE, it exhibits good agreement of general trends. It also reflects the random fluctuations of the control parameters measured in the experiments, which is completely missing from the results of level-set simulations.