Frictional hyperspheres in hyperspace

We extend the formulation of the discrete element method, which is typically used to simulate granular media, to describe arbitrarily large numbers of spatial dimensions and the collisions of frictional hyperspheres in these simulations. These higher dimensional simulations require complex visualization techniques, which are also developed here. Under uniaxial compression, we find that the stiffness of a granular medium is independent of the dimension for dimensions greater than one. In the dense flow regime, we show that the compressibility and frictional properties of higher dimensional granular materials can be described by a common rheology, with the main distinction between dimensions being the packing fraction. Results from these simulations extend our understanding of the effects of dimensionality on the behavior of granular materials, and on elastic and frictional properties in higher dimensions.