Scaling ansatz for the jamming transition

Goodrich CP, Liu AJ, Sethna JP. 2016. Scaling ansatz for the jamming transition. Proceedings of the National Academy of Sciences. 113(35), 9745–9750.

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Journal Article | Published | English
Author
Goodrich, Carl PeterIST Austria ; Liu, Andrea J.; Sethna, James P.
Abstract
We propose a Widom-like scaling ansatz for the critical jamming transition. Our ansatz for the elastic energy shows that the scaling of the energy, compressive strain, shear strain, system size, pressure, shear stress, bulk modulus, and shear modulus are all related to each other via scaling relations, with only three independent scaling exponents. We extract the values of these exponents from already known numerical or theoretical results, and we numerically verify the resulting predictions of the scaling theory for the energy and residual shear stress. We also derive a scaling relation between pressure and residual shear stress that yields insight into why the shear and bulk moduli scale differently. Our theory shows that the jamming transition exhibits an emergent scale invariance, setting the stage for the potential development of a renormalization group theory for jamming.
Publishing Year
Date Published
2016-08-30
Journal Title
Proceedings of the National Academy of Sciences
Volume
113
Issue
35
Page
9745-9750
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Goodrich CP, Liu AJ, Sethna JP. Scaling ansatz for the jamming transition. Proceedings of the National Academy of Sciences. 2016;113(35):9745-9750. doi:10.1073/pnas.1601858113
Goodrich, C. P., Liu, A. J., & Sethna, J. P. (2016). Scaling ansatz for the jamming transition. Proceedings of the National Academy of Sciences. Proceedings of the National Academy of Sciences. https://doi.org/10.1073/pnas.1601858113
Goodrich, Carl Peter, Andrea J. Liu, and James P. Sethna. “Scaling Ansatz for the Jamming Transition.” Proceedings of the National Academy of Sciences. Proceedings of the National Academy of Sciences, 2016. https://doi.org/10.1073/pnas.1601858113.
C. P. Goodrich, A. J. Liu, and J. P. Sethna, “Scaling ansatz for the jamming transition,” Proceedings of the National Academy of Sciences, vol. 113, no. 35. Proceedings of the National Academy of Sciences, pp. 9745–9750, 2016.
Goodrich CP, Liu AJ, Sethna JP. 2016. Scaling ansatz for the jamming transition. Proceedings of the National Academy of Sciences. 113(35), 9745–9750.
Goodrich, Carl Peter, et al. “Scaling Ansatz for the Jamming Transition.” Proceedings of the National Academy of Sciences, vol. 113, no. 35, Proceedings of the National Academy of Sciences, 2016, pp. 9745–50, doi:10.1073/pnas.1601858113.

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