Minimal descriptions of cyclic memories

Joseph D Paulsen,Nathan C Keim

doi:10.1098/rspa.2018.0874

Abstract

Many materials that are out of equilibrium can ‘learn’ one or more inputs that are repeatedly applied. Yet, a common framework for understanding such memories is lacking. Here, we construct minimal representations of cyclic memory behaviours as directed graphs, and we construct simple physically motivated models that produce the same graph structures. We show how a model of worn grass between park benches can produce multiple transient memories—a behaviour previously observed in dilute suspensions of particles and charge-density-wave conductors—and the Mullins effect. Isolating these behaviours in our simple model allows us to assess the necessary ingredients for these kinds of memory, and to quantify memory capacity. We contrast these behaviours with a simple Preisach model that produces return-point memory. Our analysis provides a unified method for comparing and diagnosing cyclic memory behaviours across different materials.

Highlights

Authors for correspondence: Department of Physics and Soft and Living Matter Program, Syracuse University, Syracuse, NY 13244, USA
In this paper we describe a novel, simple, and physically motivated model proposed by Sidney Nagel called the ‘park bench model’, which captures the distinctive aspects of multiple transient memory (MTM)
To further demonstrate the generality of our approach of describing memory behaviours as properties of graphs of memory-encoding macrostates, we develop a simple description of return-point memory (RPM)

Summary

Introduction

The existence of an equilibrium height that depends on the local driving at each patch is what allows the system to store multiple memories in the steady state. Memories of the reversal points (i.e. the amplitudes of the driving cycles) are stored as the locations of jumps in the steady-state height hi (t) as a function of patch number, i.

Results

Conclusion