Critical dynamics of a dilute central force network with partial bond bending forces

Abstract

Numerical results are presented for the dynamical properties of a dilute, central force, triangular network with 60 degrees bond bending forces. The rigidity percolation threshold P_R for such a network lies between the connectivity percolation threshold and the central force rigidity percolation threshold. A LU factorisation technique is used to determine the eigenvalues of the dynamical matrix and the results combined with finite size scaling to yield values for P_R and the fracton dimensionality d of 0.40R<or=0.405 and 1.25<or=d<or=1.3.