Hysteresis resulting from Lennard-Jones interactions

TL;DR

This paper investigates the origin of hysteresis in multi-stable particle systems with Lennard-Jones interactions, linking it to saddle-node bifurcations and potential energy transitions.

Contribution

It specifies the generic mechanism of hysteresis for systems with Lennard-Jones interactions, supported by a detailed case study of a four-particle system.

Findings

Identification of multi-stability in Lennard-Jones particle systems

Detailed bifurcation analysis of hysteresis scenarios

Demonstration of potential energy transitions during hysteresis

Abstract

The fundamental mechanism of hysteresis in the quasistatic limit of multi-stable systems is associated with transitions of the system from one local minimum of the potential energy to another. In this scenario, as system parameters are (quasistatically) varied, the transition is prompted when a saddle-node bifurcation eliminates the minimum where the system resides in. The objective of the present work is to specify this generic mechanism for systems of interacting particles assuming a natural single-well (Lennard-Jones) interaction potential for each pair of particles. We show multi-stability and present details of hysteresis scenarios with the associated bifurcations and transitions in a case study of constrained four-degrees-of-freedom four particle systems on the plane.