https://doi.org/10.1140/epje/s10189-023-00343-1
Regular Article – Flowing Matter
Granular convergence as an iterated local map
James Franck Institute, University of Chicago, 929 E. 57th Street, 60637, Chicago, IL, USA
Received:
7
June
2023
Accepted:
28
August
2023
Published online:
18
September
2023
Granular convergence is a property of a granular pack as it is repeatedly sheared in a cyclic, quasistatic fashion, as the packing configuration changes via discrete events. Under suitable conditions the set of microscopic configurations encountered converges to a periodic sequence after sufficient shear cycles. Prior work modeled this evolution as the iteration of a pre-determined, random map from a set of discrete configurations into itself. Iterating such a map from a random starting point leads to similar periodic repetition. This work explores the effect of restricting the randomness of such maps in order to account for the local nature of the discrete events. The number of cycles needed for convergence shows similar statistical behavior to that of numerical granular experiments. The number of cycles in a repeating period behaves only qualitatively like these granular studies.
The authors dedicate this Festschrift article to TW’s long-time mentor and friend Phil Pincus. There are many ways one can make impact as a scientist. Phil is unique in the impact he has had in raising proteges. TW has gained lifelong benefits from being one of these proteges, dating from the late seventies. Later, Phil played a pivotal role in building Exxon’s landmark initiative into soft matter by assembling and encouraging many proteges. Phil was the inspiration behind his and TW’s soft matter text book. Many of us have felt his impact through the decades of conferences, meals, and phone calls, full of insight, wit, and encouragement.
These authors have contributed equally to this work.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
