Boundary-Mediated Phase Ordering and Collision-Free Dynamics in a Vibro-Impact Multi-Particle System

Abstract

This study investigates a mechanically realizable vibro-impact system exhibiting collision-free multi-particle motion under boundary-induced excitation. The system consists of identical spherical particles undergoing one-dimensional ballistic motion under gravity and repeated impacts with a structured vibrating boundary. While individual particles obey identical free-flight and restitution laws, experiments reveal the spontaneous emergence of temporally ordered, collision-free motion when multiple particles interact with a common impulsive base. To explain this behavior, a minimal non-smooth dynamical model is formulated using Newtonian mechanics and impact-based boundary conditions. The governing equations define an event-driven discrete impact map advancing the system between successive collisions. Although no explicit inter-particle forces are introduced, collective dynamics arise through boundary-mediated timing regulation. Under bounded excitation, the discrete update preserves temporal separation, suppresses synchronous impacts, and stabilizes staggered impact sequences as attracting configurations. The formulation extends classical single-particle bouncing-ball theory to a multi-particle setting and demonstrates how structured boundary excitation induces phase ordering in non-smooth impact systems. Numerical simulations and controlled laboratory measurements confirm the theoretical predictions. The results provide a dynamical explanation of collision-free behavior in vibro-impact systems and establish a framework for boundary-induced regulation in multi-particle impact dynamics.