Transition graphs of interacting hysterons: structure, design, organization and statistics

Area of Science:

• Physics
• Materials Science
• Complex Systems

Background:

• Multistable media exhibit memory and sequential response, modeled by hysterons.
• Interactions between hysterons are crucial for material behavior.
• Transition graphs represent the evolution of multistable systems.

Purpose of the Study:

• To develop a general framework connecting transition graphs with microscopic parameters of interacting hysterons.
• To provide tools for managing the complexity of transition graphs.
• To understand the realizability of transition graphs within the hysteron model.

Main Methods:

• Introduction of a systematic framework using 'scaffolds' to structure transition graphs.
• Connecting transition graph topology to partial orders of microscopic parameters.
• Analysis of statistical properties and realizability of transition graphs.

Main Results:

• A framework is established linking transition graphs and hysteron interactions.
• The scaffold approach structures the combinatorial space of transition graphs.
• A connection between graph topology and microscopic parameter orders is demonstrated, enabling realizability assessment.

Conclusions:

• The developed framework deepens the theoretical understanding of memory effects in complex media.
• This approach facilitates the rational design of pathways and memory functionalities in materials.
• It provides a method to determine if a transition graph is compatible with the hysteron model.