A microscopic Kapitza pendulum

Mode selectivity of dynamically induced conformation in many-body chainlike bead-spring models

We consider conformation of a chain consisting of beads connected by stiff springs, where the conformation is determined by the bending angles between the consecutive two springs. Stability of a conformation is determined intrinsically by a potential energy function depending on the bending angles. However, effective forces induced by excited springs can change the stability, and a conformation can stay around a local maximum or a saddle of the bending potential. A stabilized conformation was named the dynamically induced conformation in a previous work on a three-body system [Y. Y. Yamaguchi et al., Phys. Rev. E 105, 064201 (2022)2470-004510.1103/PhysRevE.105.064201]. A remarkable fact is that the stabilization by the spring motion depends on the excited normal modes, which depend on a conformation. We extend analyses of the dynamically induced conformation in many-body chainlike bead-spring systems. Simple rules are that the lowest-eigenfrequency mode contributes to the stabilization and that the higher the eigenfrequency is, the more the destabilization emerges. We verify theoretical predictions by performing numerical simulations.

Dynamically induced conformation depending on excited normal modes of fast oscillation

We present dynamical effects on conformation in a simple bead-spring model consisting of three beads connected by two stiff springs. The conformation defined by the bending angle between the two springs is determined not only by a given potential energy function depending on the bending angle, but also by fast motion of the springs which constructs the effective potential. A conformation corresponding with a local minimum of the effective potential is hence called the dynamically induced conformation. We develop a theory to derive the effective potential using multiple-scale analysis and the averaging method. A remarkable consequence is that the effective potential depends on the excited normal modes of the springs and amount of the spring energy. Efficiency of the obtained effective potential is numerically verified.

Vibrational mechanics in higher dimension: Tuning potential landscapes

This work extends the domain of vibrational mechanics to higher dimensions, with fast vibrations applied to different directions. In particular, the presented analysis considers the case of a split biharmonic drive, where harmonics of frequency ω and 2ω are applied to orthogonal directions in a two-dimensional setting. It is shown, both numerically and with analytic calculations, that this determines a highly tunable effective potential with the same symmetry as the original one. The driving allows one not only to tune the amplitude of the potential, but also to introduce an arbitrary spatial translation in the direction corresponding to the 2ω driving. The setup allows for generalization to implement translations in an arbitrary direction within the two-dimensional landscapes. The same principles also apply to three-dimensional periodic potentials.

Entropic vibrational resonance

We demonstrate the existence of vibrational resonance associated with the presence of an uneven boundary. When the motion of a Brownian particle is confined in a region with an uneven boundary, constrained to a double cavity, a high-frequency signal may produce a peak in the spectral power amplification of the other low-frequency signal and therefore to the appearance of the vibrational resonance phenomenon. The mechanism of vibrational resonance in constrained boundaries is different from that in energetic potentials and is termed entropic vibrational resonance (EVR). The EVR can be observed even if the bias force is absent in any direction. Through careful analysis, we clarify two types of mechanisms of the EVR. The one mechanism is ascribed to the transition from a bistable system to a monostable system, and the other corresponds to the match between the escape rate and the natural frequency of the low-frequency signal. Our work merges the vibrational resonance with an uneven boundary, thus extending the scope of the vibrational resonance and shedding new light on the concept of resonance.