Collective actuation in active solids in the presence of a polarizing field: A systematic analysis of the dynamical regimes

Collective actuation in active solids, the spontaneous condensation of the dynamics on a few elastic modes, takes place whenever the deformations of the structure reorient the forces exerted by the active units composing, or embedded in, the solid. In a companion paper, we show through a combination of model experiments, numerical simulations, and theoretical analysis that adding an external field that polarizes the active forces strongly affects the dynamical transition to collective actuation. A new oscillatory regime emerges, and a reentrance transition to collective actuation takes place. Depending on the degeneracy of the modes on which the dynamics condensates, and on the orientation of the field with respect to the stiff direction of the solid, several new dynamical regimes can be observed. The purpose of the present paper is to review these dynamical regimes in a comprehensive way, both for the single-particle dynamics and for the coarse-grained one. Whenever possible the dynamical regimes and the transition between them are described analytically, otherwise numerically.