Dynamics in a confined mass–spring chain with 1∕r repulsive potential: Strongly nonlinear regime

We present a study of the dynamics of a system of masses connected by springs and repelling by a 1∕r potential in 1D. The present study focuses on the dynamics in the regime where the repulsive force dominates the dynamics of the system. We conjecture that such a system may be approximately modeled by an alignment of repelling rigid bar magnets that are sufficiently far apart from each other. We show that except for cases where the repulsive potential is very weak, most of the energy due to a velocity perturbation at system initiation of magnitude v₀(0) generates a propagating solitary wave in the system. Dynamical simulations show that this solitary wave shows no measurable tendency to thermalize over extended simulation time scales, thereby yielding an effectively non-ergodic system. Part of the energy generates low-amplitude persistent oscillations which do not show any measurable interaction with the solitary wave. We find that the solitary wave propagation speed v_SW∝v₀ ² for various coupling strengths. We further demonstrate that owing to the repulsion between the adjacent particles, these solitary waves are mutually repulsive, i.e., they cannot cross each other and hence there is no phase change associated with their mutual interactions. We use the data driven Dynamic Mode Decomposition technique to develop a simple approximate way to represent the propagating solitary wave. Additionally, we compute fluctuations in the kinetic energy of the system at late times and show that the energy fluctuations increase drastically when the effects of v₀ and the coupling associated with the repulsive interactions become competitive.