Profusion of Transition Pathways for Interacting Hysterons

TL;DR

This paper investigates how interactions among hysterons significantly alter transition pathways and memory effects, revealing complex behaviors beyond traditional models, with implications for designing pathways and information processing in complex media.

Contribution

It demonstrates that interacting hysterons produce a vast array of pathways, many violating classical memory rules, expanding understanding beyond the Preisach model.

Findings

Over 15,000 transition graphs from three interacting hysterons

Most pathways violate return point memory

Interactions lead to complex, distinct transition behaviors

Abstract

The response, pathways and memory effects of cyclically driven complex media can be captured by hysteretic elements called hysterons. Here we demonstrate the profound impact of hysteron interactions on pathways and memory. Specifically, while the Preisach model of independent hysterons features a restricted class of pathways which always satisfy return point memory, we show that three interacting hysterons generate more than 15,000 transition graphs, with most violating return point memory and having features completely distinct from the Preisach model. Exploring these opens a route to designer pathways and information processing in complex matter.