@article{ed7cf1dca53e4201894a4f903eccc504,
title = "Minimal descriptions of cyclic memories",
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.",
keywords = "Charge-density waves, Cyclic driving, Memories, Mullins effect, Return-point memory, Suspensions",
author = "Paulsen, {Joseph D.} and Keim, {Nathan C.}",
note = "Funding Information: Data accessibility. Data for figure 4a, and Python code to generate all simulation results, are available in the electronic supplementary material. Authors{\textquoteright} contributions. J.D.P. and N.C.K. conceived the study, analysed the models, interpreted the results and wrote the paper. N.C.K. performed simulations. Competing interests. The authors declare no competing interests. Funding. J.D.P. gratefully acknowledges the Donors of the American Chemical Society Petroleum Research Fund for partial support of this research. This research was also supported by the National Science Foundation under grant no. PHY-1748958 to the KITP, and grant no. DMR-1708870 to N.C.K. Acknowledgements. This work was initiated at the Winter 2018 KITP program, {\textquoteleft}Memory Formation in Matter{\textquoteright}. We are grateful to Sidney Nagel for inventing the park bench model, and Muhittin Mungan for proposing and encouraging the use of graphs. We also thank Srikanth Sastry, Tom Witten and other participants in the program. Funding Information: J.D.P. gratefully acknowledges the Donors of the American Chemical Society Petroleum Research Fund for partial support of this research. This research was also supported by the National Science Foundation under grant no. PHY-1748958 to the KITP, and grant no. DMR-1708870 to N.C.K. Publisher Copyright: {\textcopyright} 2019 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License",
year = "2019",
month = jun,
day = "1",
doi = "10.1098/rspa.2018.0874",
language = "English (US)",
volume = "475",
journal = "Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences",
issn = "0080-4630",
publisher = "Royal Society of London",
number = "2226",
}