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The hydra string method: a novel means to explore potential energy surfaces and its application to granular materials

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Abstract

We present a novel means to understand granular materials, the Hydra String Method (HSM). This is an efficient and autonomous way to trawl an arbitrary potential energy surface (or any similarly high dimensional function) that enumerates the saddle points, minima, and minimum energy paths between them. In doing so, it creates a reduced dimensional network representation of this surface. We also present a series of tests to choose optimized parameters for the application of the HSM. We apply this to the potential energy function of a granular system consisting of a configuration of bi-disperse, frictionless, soft spheres. Future work will make use of the found ensemble of transition pathways to statistically predict the dynamics of a system of grains.

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Data availability

All processed data is presented in the manuscript figures.

Code availability

https://github.com/knewhall/Hydra_String.

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Acknowledgements

The authors thank Eric Vanden-Eijnden for discussions on the implementation of the string method as well as Karen Daniels, Ryan Kozlowski and Jack Featherstone for their feedback on an earlier draft of this manuscript.

Funding

This work was supported by the National Science Foundation DMS-1816394.

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Authors and Affiliations

  1. Department of Physics and Astronomy, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA

    Christopher Moakler

  2. Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA

    Katherine A. Newhall

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  1. Christopher Moakler
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  2. Katherine A. Newhall
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Correspondence to Christopher Moakler.

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Moakler, C., Newhall, K.A. The hydra string method: a novel means to explore potential energy surfaces and its application to granular materials. Granular Matter 24, 24 (2022). https://doi.org/10.1007/s10035-021-01184-5

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