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Granular convergence as an iterated local map.

Anna Movsheva¹, Thomas A Witten²

¹James Franck Institute, University of Chicago, 929 E. 57th Street, Chicago, IL, 60637, USA.

The European Physical Journal. E, Soft Matter

|September 18, 2023

Summary

This summary is machine-generated.

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Granular convergence, where particle packing patterns repeat after cycles of shearing, was modeled by restricting random map iterations. This approach mimics the local nature of discrete events in granular materials.

Area of Science:

Physics
Materials Science
Geophysics

Background:

Granular materials exhibit convergence, a phenomenon where microscopic configurations become periodic after cyclic quasistatic shearing.
Previous models treated granular evolution as iterations of random maps, simplifying the complex interactions within granular packs.

Purpose of the Study:

To investigate the impact of restricting randomness in map iterations on granular convergence.
To model the local nature of discrete events in granular materials more accurately.

Main Methods:

Developed a model based on iterating restricted random maps to simulate granular pack evolution.
Analyzed the number of shear cycles required for convergence and the length of the repeating period.

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Main Results:

The number of cycles needed for convergence demonstrated statistical similarities to numerical granular experiments.
The cycle count within a repeating period showed only qualitative agreement with experimental granular studies.

Conclusions:

Restricting randomness in map iterations provides a more physically grounded model for granular convergence.
The model captures key statistical behaviors of granular systems, though period length requires further refinement.