Dimensional Dependence of Scaling Prefactors in Overjammed Systems

Granular materials express universal properties regardless of the material properties of the individual grains. This universality of granular packings is a direct consequence of the statistics of contact forces between grains. When packing fraction changes, material properties are governed by the creation and destruction of new contacts. The number of excess contacts, packing fraction, and pressure all characterize distance to the jamming transition and are related by scaling theory made possible by the universality of granular materials. While the scalings between these parameters follow simple power laws, the prefactors to these scalings are not universal. We present measurements of these prefactors in dimensions 2-10. These prefactors depend nontrivially on dimension and differ from the asymptotic high dimensional values predicted by mean field theory.