Charged elastic rings: deformation and dynamics

We report the counter-intuitive instability of charged elastic rings, and the persistence of sinusoidal deformations in the lowest-energy configurations by the combination of high-precision numerical simulations and analytical perturbation calculation. We also study the dynamical evolution of the charged ring under random disturbance, and reveal the modulation of the dominant frequencies by the electrostatic force. The purely mechanical analysis of the classical ring system presented in this work yields insights into the subtlety of long-range forces in the organization and dynamics of matter.Comment: 8 pages, 5 figure

Collective dynamics and shattering of disturbed two-dimensional Lennard-Jones crystals

Elucidating collective dynamics in crystalline systems is a common scientific question in multiple fields. In this work, by combination of high-precision numerical approach and analytical normal mode analysis, we systematically investigate the dynamical response of two-dimensional Lennard-Jones crystal as a purely classical mechanical system under random disturbance of varying strength, and reveal rich microscopic dynamics. Specifically, we observe highly symmetric velocity field composed of sharply divided coherent and disordered regions, and identify the order-disorder dynamical transition of the velocity field. Under stronger disturbance, we reveal the vacancy-driven shattering of the crystal. This featured disruption mode is fundamentally different from the dislocation-unbinding scenario in two-dimensional melting. We also examine the healing dynamics associated with vacancies of varying size. The results in this work advance our understanding about the formation of collective dynamics and crystal disruption, and may have implications in elucidating relevant non-equilibrium behaviors in a host of crystalline systems.Comment: 7 pages, 4 figure

Propagating stress-pulses and wiggling transition revealed in string dynamics

Understanding string dynamics yields insights into the intricate dynamic behaviors of various filamentary thin structures in nature and industry covering multiple length scales. In this work, we investigate the planar dynamics of a flexible string where one end is free and the other end is subject to transverse and longitudinal motions. Under transverse harmonic motion, we reveal the propagating pulse structure in the stress profile over the string, and analyze its role in bringing the system into a chaotic state. For a string where one end is under longitudinal uniform acceleration, we identify the wiggling transition, derive the analytical wiggling solution from the string equations, and present the phase diagram.Comment: 5 pages, 4 figure