A fast algorithm for 2D Rigidity Percolation

Abstract

Rigidity Percolation is a crucial framework for describing rigidity transitions in amorphous systems. We present a new, efficient algorithm to study central-force Rigidity Percolation in two dimensions. This algorithm combines the Pebble Game algorithm, the Newman-Ziff approach to Connectivity Percolation, as well as novel rigorous results in rigidity theory, to exactly identify rigid clusters over the full bond concentration range, in a time that scales as $N^{1.02}$ for a system of $N$ nodes. Besides opening the way to accurate numerical studies of Rigidity Percolation, our work provides new insights on specific cluster merging mechanisms that distinguish it from the standard Connectivity Percolation problem.

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