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Stress correlations in near-crystalline packings

by Roshan Maharana and Kabir Ramola

Submission summary

Authors (as registered SciPost users): Roshan Maharana
Submission information
Preprint Link: scipost_202311_00022v2  (pdf)
Date submitted: 2024-04-16 11:45
Submitted by: Maharana, Roshan
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
Specialties:
  • Mathematical Physics
  • Statistical and Soft Matter Physics
Approaches: Theoretical, Computational

Abstract

We derive exact results for stress-correlations in near-crystalline systems in two and three dimensions. We study energy minimized configurations of particles interacting through Harmonic as well as Lennard-Jones potentials, for varying degrees of microscopic disorder and quenched forces on grains. Our findings demonstrate that the macroscopic elastic properties of such near-crystalline packings remain unchanged within a certain disorder threshold, yet they can be influenced by various factors, including packing density, pressure, and the strength of inter-particle interactions. We show that the stress-correlations in such systems display anisotropic behavior at large lengthscales and are significantly influenced by the pre-stress of the system. The anisotropic nature of these correlations remains unaffected as we increase the strength of the disorder. Additionally, we derive the large lengthscale behavior for the change in the local stress components that shows a $1/r^d$ radial decay for the case of particle size disorder and a $1/r^{d-1}$ behavior for quenched forces introduced into a crystalline network. Finally, we verify our theoretical results numerically using energy-minimised static particle configurations.

Author comments upon resubmission

We thank the Referees for their comments, and have taken them into account in our resubmission.

List of changes

Below we write the list of changes in the revised manuscript.

1. Both Figure 1 and Figure 9 are cited in the main text.

2. The sequence of figures now corresponds to the order of citation.

3. Definitions for variables such as $\lambda_{SS},\lambda_{SL},\lambda_{LL}$ in Eq. (4) and $\mathcal{P}_1,\mathcal{P}_2$ in Eq. (23) are provided in sections 2.2 and 5, respectively.

4. Figure 2 has been updated to include the variation of the difference $B_{theory}-\langle B \rangle$ and $G_{theory}-\langle G \rangle$ in logarithmic scale.

5. Previous numerical finding regarding the variation of elastic modulus with disorder is cited on Page 7 as reference [31].

6. Centrosymmetry order parameter for near-crystalline packings are measured and written in Page 8.

7. Relevant citations for measuring the centrosymmetry order parameter are included as references [67], [68], and [69].

8. Appendix D now provides a comprehensive explanation of the measurement of Inversion symmetry order parameter.

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Reports on this Submission

Anonymous Report 2 on 2024-4-17 (Invited Report)

Report

The authors have adequately addressed all questions and comments raised by the referees. Based on the revisions made, I recommend this manuscript for publication in SciPost.

Recommendation

Publish (meets expectations and criteria for this Journal)

  • validity: high
  • significance: high
  • originality: high
  • clarity: high
  • formatting: -
  • grammar: -

Anonymous Report 1 on 2024-4-17 (Invited Report)

Report

I have read the authors' rebuttal and the newest revised version of the paper. The authors did a great job in addressing all the queries of the Referees. I recommend this paper for publication in SciPost in its present form.

Recommendation

Publish (surpasses expectations and criteria for this Journal; among top 10%)

  • validity: top
  • significance: top
  • originality: top
  • clarity: top
  • formatting: excellent
  • grammar: excellent

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