In the present paper we give a selective review of some very recent works concerning the non-stationary regimes emerging in various one- and two- dimensional models incorporating internal rotators. In one-dimensional models, these regimes are characterized by the intense energy transfer from the outer element subject to initial or harmonic loading to the internal rotator. As for the two-dimensional models (incorporating internal rotators) we will mainly focus on the two special dynamical states, namely a state of the near complete energy transfer from longitudinal to lateral vibrations of the outer element as well as the state of a permanent, uni-directional energy locking with mild, spatial energy exchanges. In this review, we will discuss the recent theoretical and experimental advancements in the study of essentially nonlinear mechanisms governing the formation and bifurcations of the regimes of intense energy transfer. Present review will comprise the two parts. The first part will be mainly devoted to the emergence of resonant energy transfer states in one-dimensional models incorporating internal rotators, while the second part will be mainly concerned with the manifestation of various energy transfer states in the two-dimensional ones.
We analyse theoretically and by means of molecular dynamics (MD) simulations the generation of mechanical force by a polyelectrolyte (PE) chain grafted to a plane. The PE is exposed to an external electric field that favours its adsorption on the plane. The free end of the chain is linked to a deformable target body. By varying the field, one can alter the length of the non-adsorbed part of the chain. This entails variation of the deformation of the target body and hence variation of the force arising in the body. Our theoretical predictions for the generated force are in very good agreement with the MD data. Using the theory developed for the generated force, we study the effectiveness of possible PEbased nano-vices, composed of two clenching planes connected by PEs and exposed to an external electric field. We exploit the Cundall–Strack solid friction model to describe the friction between a particle and the clenching planes. We compute the diffusion coefficient of a clenched particle and show that it drastically decreases even in weak applied fields. This demonstrates the efficacy of the PE-based nano-vices, which may be a possible alternative to the existing nanotube nano-tweezers and optical tweezers.