Two Diverging Length Scales in the Structure of Jammed Packings

Hexner, Daniel; Liu, Andrea J.; Nagel, Sidney R.

doi:10.1103/PhysRevLett.121.115501

Two Diverging Length Scales in the Structure of Jammed Packings

Journal Article · Tue Sep 11 00:00:00 EDT 2018 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.121.115501· OSTI ID:1596600

Hexner, Daniel ^[1]; Liu, Andrea J. ^[2]; Nagel, Sidney R. ^[3]

Univ. of Pennsylvania, Philadelphia, PA (United States); Univ. of Chicago, IL (United States); University of Pennsylvania
Univ. of Pennsylvania, Philadelphia, PA (United States)
Univ. of Chicago, IL (United States)

Here, at densities higher than the jamming transition for athermal, frictionless repulsive spheres we find two distinct length scales, both of which diverge as a power law as the transition is approached. The first,

ξ_{Z}

, is associated with the two-point correlation function for the number of contacts on two particles as a function of the particle separation. Additionally, the second,

ξ_{f}

, is associated with contact-number fluctuations in subsystems of different sizes. On scales below

ξ_{f}

, the fluctuations are highly suppressed, similar to the phenomenon of hyperuniformity usually associated with density fluctuations. The exponents for the divergence of

ξ_{Z}

and

ξ_{f}

are different and appear to be different in two and three dimensions.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Chicago, IL (United States); Univ. of Pennsylvania, Philadelphia, PA (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division

Grant/Contract Number:: FG02-03ER46088; FG02-05ER46199

OSTI ID:: 1596600

Alternate ID(s):: OSTI ID: 1541359
OSTI ID: 1856742
OSTI ID: 1469439

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 11 Vol. 121; ISSN 0031-9007; ISSN PRLTAO

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (41)

Chaos and threshold for irreversibility in sheared suspensions Pine, D. J.; Gollub, J. P.; Brady, J. F. Nature, Vol. 438, Issue 7070 https://doi.org/10.1038/nature04380	journal	December 2005
Hyperuniform states of matter Torquato, Salvatore Physics Reports, Vol. 745 https://doi.org/10.1016/j.physrep.2018.03.001	journal	June 2018
Charge Fluctuations in the Two-Dimensional One-Component Plasma Levesque, D.; Weis, J. -J.; Lebowitz, J. L. Journal of Statistical Physics, Vol. 100, Issue 1/2, p. 209-222 https://doi.org/10.1023/A:1018643829340	journal	January 2000
Stability of jammed packings I: the rigidity length scale Goodrich, Carl P.; Ellenbroek, Wouter G.; Liu, Andrea J. Soft Matter, Vol. 9, Issue 46 https://doi.org/10.1039/c3sm51095f	journal	January 2013
Stability of jammed packings II: the transverse length scale Schoenholz, Samuel S.; Goodrich, Carl P.; Kogan, Oleg Soft Matter, Vol. 9, Issue 46 https://doi.org/10.1039/c3sm51096d	journal	January 2013
Breakdown of continuum elasticity in amorphous solids Lerner, Edan; DeGiuli, Eric; Düring, Gustavo Soft Matter, Vol. 10, Issue 28 https://doi.org/10.1039/c4sm00311j	journal	January 2014
On the rigidity of amorphous solids Wyart, M. Annales de Physique, Vol. 30, Issue 3 https://doi.org/10.1051/anphys:2006003	journal	January 2005
Scaling ansatz for the jamming transition Goodrich, Carl P.; Liu, Andrea J.; Sethna, James P. Proceedings of the National Academy of Sciences, Vol. 113, Issue 35 https://doi.org/10.1073/pnas.1601858113	journal	August 2016
Hyperuniformity in point patterns and two-phase random heterogeneous media Zachary, Chase E.; Torquato, Salvatore Journal of Statistical Mechanics: Theory and Experiment, Vol. 2009, Issue 12 https://doi.org/10.1088/1742-5468/2009/12/P12015	journal	December 2009
Nonlinear susceptibility in glassy systems: A probe for cooperative dynamical length scales Bouchaud, Jean-Philippe; Biroli, Giulio Physical Review B, Vol. 72, Issue 6 https://doi.org/10.1103/PhysRevB.72.064204	journal	August 2005
Glass-like universe: Real-space correlation properties of standard cosmological models Gabrielli, Andrea; Joyce, Michael; Sylos Labini, Francesco Physical Review D, Vol. 65, Issue 8 https://doi.org/10.1103/PhysRevD.65.083523	journal	April 2002
Jamming at zero temperature and zero applied stress: The epitome of disorder O’Hern, Corey S.; Silbert, Leonardo E.; Liu, Andrea J. Physical Review E, Vol. 68, Issue 1 https://doi.org/10.1103/PhysRevE.68.011306	journal	July 2003
Local density fluctuations, hyperuniformity, and order metrics Torquato, Salvatore; Stillinger, Frank H. Physical Review E, Vol. 68, Issue 4 https://doi.org/10.1103/PhysRevE.68.041113	journal	October 2003
Effects of compression on the vibrational modes of marginally jammed solids Wyart, Matthieu; Silbert, Leonardo E.; Nagel, Sidney R. Physical Review E, Vol. 72, Issue 5 https://doi.org/10.1103/PhysRevE.72.051306	journal	November 2005
Long-wavelength structural anomalies in jammed systems Silbert, Leonardo E.; Silbert, Moises Physical Review E, Vol. 80, Issue 4 https://doi.org/10.1103/PhysRevE.80.041304	journal	October 2009
Experimental study of random-close-packed colloidal particles Kurita, Rei; Weeks, Eric R. Physical Review E, Vol. 82, Issue 1 https://doi.org/10.1103/PhysRevE.82.011403	journal	July 2010
Incompressibility of polydisperse random-close-packed colloidal particles Kurita, Rei; Weeks, Eric R. Physical Review E, Vol. 84, Issue 3 https://doi.org/10.1103/PhysRevE.84.030401	journal	September 2011
Thermal fluctuations, mechanical response, and hyperuniformity in jammed solids Ikeda, Atsushi; Berthier, Ludovic Physical Review E, Vol. 92, Issue 1 https://doi.org/10.1103/PhysRevE.92.012309	journal	July 2015
Elasticity of frictionless particles near jamming Karimi, Kamran; Maloney, Craig E. Physical Review E, Vol. 92, Issue 2 https://doi.org/10.1103/PhysRevE.92.022208	journal	August 2015
Search for hyperuniformity in mechanically stable packings of frictionless disks above jamming Wu, Yegang; Olsson, Peter; Teitel, S. Physical Review E, Vol. 92, Issue 5 https://doi.org/10.1103/PhysRevE.92.052206	journal	November 2015
Critical slowing down and hyperuniformity on approach to jamming Atkinson, Steven; Zhang, Ge; Hopkins, Adam B. Physical Review E, Vol. 94, Issue 1 https://doi.org/10.1103/PhysRevE.94.012902	journal	July 2016
Large-scale structure of randomly jammed spheres Ikeda, Atsushi; Berthier, Ludovic; Parisi, Giorgio Physical Review E, Vol. 95, Issue 5 https://doi.org/10.1103/PhysRevE.95.052125	journal	May 2017
Suppressed Compressibility at Large Scale in Jammed Packings of Size-Disperse Spheres Berthier, Ludovic; Chaudhuri, Pinaki; Coulais, Corentin Physical Review Letters, Vol. 106, Issue 12 https://doi.org/10.1103/PhysRevLett.106.120601	journal	March 2011
Hyperuniform Long-Range Correlations are a Signature of Disordered Jammed Hard-Particle Packings Zachary, Chase E.; Jiao, Yang; Torquato, Salvatore Physical Review Letters, Vol. 106, Issue 17 https://doi.org/10.1103/PhysRevLett.106.178001	journal	April 2011
Finite-Size Scaling at the Jamming Transition Goodrich, Carl P.; Liu, Andrea J.; Nagel, Sidney R. Physical Review Letters, Vol. 109, Issue 9 https://doi.org/10.1103/PhysRevLett.109.095704	journal	August 2012
Hyperuniformity of Critical Absorbing States Hexner, Daniel; Levine, Dov Physical Review Letters, Vol. 114, Issue 11 https://doi.org/10.1103/PhysRevLett.114.110602	journal	March 2015
Hyperuniform Density Fluctuations and Diverging Dynamic Correlations in Periodically Driven Colloidal Suspensions Tjhung, Elsen; Berthier, Ludovic Physical Review Letters, Vol. 114, Issue 14 https://doi.org/10.1103/PhysRevLett.114.148301	journal	April 2015
Nonlocal Elasticity near Jamming in Frictionless Soft Spheres Baumgarten, Karsten; Vågberg, Daniel; Tighe, Brian P. Physical Review Letters, Vol. 118, Issue 9 https://doi.org/10.1103/PhysRevLett.118.098001	journal	February 2017
Screening, Hyperuniformity, and Instability in the Sedimentation of Irregular Objects Goldfriend, Tomer; Diamant, Haim; Witten, Thomas A. Physical Review Letters, Vol. 118, Issue 15 https://doi.org/10.1103/PhysRevLett.118.158005	journal	April 2017
Exact Results for the Two-Dimensional One-Component Plasma Jancovici, B. Physical Review Letters, Vol. 46, Issue 6 https://doi.org/10.1103/PhysRevLett.46.386	journal	February 1981
Foam Mechanics at the Bubble Scale Durian, D. J. Physical Review Letters, Vol. 75, Issue 26 https://doi.org/10.1103/PhysRevLett.75.4780	journal	December 1995
Unexpected Density Fluctuations in Jammed Disordered Sphere Packings Donev, Aleksandar; Stillinger, Frank H.; Torquato, Salvatore Physical Review Letters, Vol. 95, Issue 9 https://doi.org/10.1103/PhysRevLett.95.090604	journal	August 2005
Vibrations and Diverging Length Scales Near the Unjamming Transition Silbert, Leonardo E.; Liu, Andrea J.; Nagel, Sidney R. Physical Review Letters, Vol. 95, Issue 9 https://doi.org/10.1103/PhysRevLett.95.098301	journal	August 2005
Structural Relaxation Made Simple Bitzek, Erik; Koskinen, Pekka; Gähler, Franz Physical Review Letters, Vol. 97, Issue 17 https://doi.org/10.1103/PhysRevLett.97.170201	journal	October 2006
The renormalization group: Critical phenomena and the Kondo problem Wilson, Kenneth G. Reviews of Modern Physics, Vol. 47, Issue 4 https://doi.org/10.1103/RevModPhys.47.773	journal	October 1975
Fifth-order susceptibility unveils growth of thermodynamic amorphous order in glass-formers Albert, S.; Bauer, T.; Michl, M. Science, Vol. 352, Issue 6291 https://doi.org/10.1126/science.aaf3182	journal	June 2016
Statistical Physics: Statics, Dynamics and Renormalization Kadanoff, Leo P. https://doi.org/10.1142/4016	book	January 2000
The Jamming Transition and the Marginally Jammed Solid Liu, Andrea J.; Nagel, Sidney R. Annual Review of Condensed Matter Physics, Vol. 1, Issue 1 https://doi.org/10.1146/annurev-conmatphys-070909-104045	journal	August 2010
Elastic collapse in disordered isostatic networks Moukarzel, C. F. EPL (Europhysics Letters), Vol. 97, Issue 3 https://doi.org/10.1209/0295-5075/97/36008	journal	February 2012
Geometric origin of excess low-frequency vibrational modes in weakly connected amorphous solids Wyart, M.; Nagel, S. R.; Witten, T. A. Europhysics Letters (EPL), Vol. 72, Issue 3 https://doi.org/10.1209/epl/i2005-10245-5	journal	November 2005
Exploring the jamming transition over a wide range of critical densities Ozawa, Misaki; Berthier, Ludovic; Coslovich, Daniele SciPost Physics, Vol. 3, Issue 4 https://doi.org/10.21468/SciPostPhys.3.4.027	journal	January 2017

Cited By (6)

Mean field theory of jamming of nonspherical particles Ikeda, Harukuni; Urbani, Pierfrancesco; Zamponi, Francesco Journal of Physics A: Mathematical and Theoretical, Vol. 52, Issue 34 https://doi.org/10.1088/1751-8121/ab3079	journal	July 2019
Cluster approach to phase transitions from fluid to amorphous solids: gels, glasses and granular materials Coniglio, Antonio; Fierro, Annalisa; Pica Ciamarra, Massimo Journal of Physics A: Mathematical and Theoretical, Vol. 52, Issue 38 https://doi.org/10.1088/1751-8121/ab358a	journal	August 2019
Hyperuniformity on spherical surfaces Meyra, Ariel G.; Zarragoicoechea, Guillermo J.; Maltz, Alberto. L. Physical Review E, Vol. 100, Issue 2 https://doi.org/10.1103/physreve.100.022107	journal	August 2019
Marginally stable phases in mean-field structural glasses Scalliet, Camille; Berthier, Ludovic; Zamponi, Francesco Physical Review E, Vol. 99, Issue 1 https://doi.org/10.1103/physreve.99.012107	journal	January 2019
Marginally stable phases in mean-field structural glasses Scalliet, Camille; Berthier, Ludovic; Zamponi, Francesco arXiv https://doi.org/10.48550/arxiv.1810.01213	text	January 2018
Hyperuniformity on spherical surfaces Meyra, Ariel G.; Zarragoicoechea, Guillermo J.; Maltz, Alberto. L. arXiv https://doi.org/10.48550/arxiv.1812.04729	text	January 2018

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