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Center for Nonlinear Studies |
Rigidity percolation occurs when a rigid cluster first spans a sample. We review rigidity percolation on various lattices where the transition can be either first or second order. Maxwell counting (which ignores redundancy) does much better here than in other situations like connectivity percolation, because the number of redundant bonds are small at the transition, making the rigid backbone close to the isostatic point. We suggest a common language that focuses on the bond-number distribution at critically which is shown to be universal if properly scaled and includes jamming as a special case. We use an exactly soluble model (Cayley tree with a busbar) as a useful reference solution as it is solved for arbitrary degrees of freedom (g) and coordination (z).
Host: Lena Lopatina, T-1/CNLS