Unversality and scale invariance in static granular matter

Bernard Nienhuis
Universiteit van Amsterdam

A static sand pile behaves in some aspects like a solid. It can sustain forces weaker than a certain threshold which depends on the pressure.
The density is not as uniform as a regular solid, but density fluctuations are limited. The contact forces, however, fluctuate wildly. Since the forces on each grain balance, the contact forces tend to form spatial structures known as force chains. We have discovered in simulations of two dimensional sand piles that in a well defined sense the size distribution of these force chains is scale invariant, i.e. the frequency of occurrence of a force chain varies with the number of participating grains (or forces) as a power law. The associated exponents appear to be universal: We have varied physical properties of the sandpile, such as the size distribution of the grains, the elastic nature of the material, the pressure, the regularity of the packing, the friction, and it has no effect on the value of the exponents.

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