Geometry and dynamics of spring networks of spherical topology

TL;DR

This study investigates the microscopic dynamics of spherical spring networks, revealing crumpling transitions and the convergence of speed distributions, providing insights into membrane shape fluctuations and structural instability.

Contribution

It introduces a detailed analysis of the dynamics of spherical spring networks, highlighting the crumpling transition and the approach to Maxwell-Boltzmann distribution.

Findings

Crumpling transition observed in strongly disturbed networks

Speed distribution rapidly converges to Maxwell-Boltzmann distribution

Lowest-energy configurations are packings of regular triangles

Abstract

The spring network model constitutes the backbone in the representations of a host of physical systems. In this work, we report the disturbance-driven microscopic dynamics of an isolated, closed spring network of spherical topology in mechanical equilibrium. The system permits self-intersection. We first show the lowest-energy configurations of the closed spring networks as packings of regular triangles. The dynamics of the disturbed spring network is analyzed from the multiple perspectives of energetics, structural instability, and speed distribution. We reveal the crumpling transition of strongly disturbed spring networks and the rapid convergence of the speed distribution toward the Maxwell-Boltzmann distribution. This work demonstrates the rich physics arising from the interplay of flexibility and dynamics. The results may yield insights into the shape fluctuation and structural instability of deformable membranes from the dynamical perspective.