We investigate the non-equilibrium dynamics of active bead-spring critical
percolation clusters under the action of monopolar and dipolar forces.
Previously, Langevin dynamics simulations of Rouse-type dynamics were performed
on a deterministic fractal — the Sierpinski gasket — and combined with
analytical theory [Chaos {\bf 34}, 113107 (2024)]. To study disordered
fractals, we use here the critical (bond) percolation infinite cluster of
square and triangular lattices, where beads (occupying nodes) are connected by
harmonic springs. Two types of active stochastic forces, modeled as random
telegraph processes, are considered: force monopoles, acting on individual
nodes in random directions, and force dipoles, where extensile or contractile
forces act between pairs of nodes, forming dipole links. A dynamical steady
state is reached where the network is dynamically swelled for force monopoles.
The time-averaged mean square displacement (MSD) shows sub-diffusive behavior
at intermediate times longer than the force correlation time, whose anomalous
exponent is solely controlled by the spectral dimension $(d_s)$ of the fractal
network yielding MSD $\sim t^{\nu}$, with $\nu=1-\frac{d_s}{2}$, similar to the
thermal system and in accord with the general analytic theory. In contrast,
dipolar forces require a diverging time to reach a steady state, depending on
the fraction of dipoles, and lead to network shrinkage. Within a
quasi-steady-state assumption, we find a saturation behavior at the same
temporal regime. Thereafter, a second ballistic-like rise is observed for
networks with a low fraction of dipole forces, followed by a linear, diffusive
increase. The second ballistic rise is, cependant, absent in networks fully
occupied with force dipoles. These two behaviors are argued to result from
local rotations of nodes, which are either persistent or fluctuating.

Cet article explore les excursions dans le temps et leurs implications.

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