We investigate, using Langevin dynamics simulations, the Rouse-type dynamics of active harmonic bead-spring percolation clusters of square and triangular lattices. Two types of active stochastic forces, modeled as a random telegraph process with correlation time τ, are considered: force monopoles, acting on individual nodes in random directions, and force dipoles, where extensile or contractile forces act between pairs of nodes. For force monopoles, a dynamical steady state is reached where the network is dynamically swollen and the mean square displacement (MSD) shows sub-diffusive behavior at t > τ, MSD ∼ tν, with ν=1-ds2 where ds is the spectral dimension, in accord with a previously advanced general analytic theory. In contrast, dipolar forces require diverging times to reach steady state and lead to network shrinkage. Within a quasi-steady-state approximation, the MSD is found to saturate at the same temporal regime t > τ, which is followed by ballistic-like and/or diffusive behaviors. We further extend our study of dipolar forces to dilution regimes above the isostatic threshold, also known as "rigidity percolation". Here, weak dipolar forces effectively do not shrink the network in steady state. Instead, they induce "rotational swimming" of the network. Yet, for the triangular lattice, an incipient discontinuous collapse transition occurs above a critical force amplitude value. Conversely, we find a continuous crossover to a collapsed state for the non-diluted square lattice, resulting from its marginal stability. We suggest that disordered solids be poised above the isostatic point to be stable against active dipolar forces, provided that the dynamical persistent length remains lower than the spring rest length.
Majumdar et al. (Mon,) studied this question.