1
|
Charbonneau P, Hu Y, Morse PK. Dynamics and fluctuations of minimally structured glass formers. Phys Rev E 2024; 109:054905. [PMID: 38907402 DOI: 10.1103/physreve.109.054905] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/02/2024] [Accepted: 04/22/2024] [Indexed: 06/24/2024]
Abstract
The mean-field theory (MFT) of simple structural glasses, which is exact in the limit of infinite spatial dimensions, d→∞, offers theoretical insight as well as quantitative predictions about certain features of d=3 systems. In order to more systematically relate the behavior of physical systems to MFT, however, various finite-d effects need to be accounted for. Although some efforts along this direction have already been undertaken, theoretical and technical challenges hinder progress. A general approach to sidestep many of these difficulties consists of simulating minimally structured models whose behavior smoothly converges to that described by the MFT as d increases, so as to permit a controlled dimensional extrapolation. Using this approach, we here extract the small fluctuations around the dynamical MFT captured by a standard liquid-state observable, the non-Gaussian parameter α_{2}. The results provide insight into the physical origin of these fluctuations as well as a quantitative reference with which to compare observations for more realistic glass formers.
Collapse
Affiliation(s)
| | | | - Peter K Morse
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
- Princeton Institute of Materials, Princeton University, Princeton, New Jersey 08544, USA
| |
Collapse
|
2
|
Oyama N, Mizuno H, Ikeda A. Shear-induced criticality in glasses shares qualitative similarities with the Gardner phase. SOFT MATTER 2023; 19:6074-6087. [PMID: 37491980 DOI: 10.1039/d3sm00512g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/27/2023]
Abstract
Although glass phases are ubiquitously found in various soft matter systems, we are still far from a complete understanding of them. The concept of marginal stability predicted by infinite-dimensional mean-field theories is drawing attention as a candidate for a universal and distinguishing unique feature of glasses. While among theoretical predictions, the non-Debye scaling has indeed been observed universally over various classes of glasses, the Gardner phase is found only in a limited portion of them. In this work, we numerically demonstrate that plastic events observed in two-dimensional Lennard-Jones glasses under quasistatic shear exhibit statistical properties that are qualitatively consistent with the picture of an infinitely hierarchical energy landscape associated with the Gardner phase.
Collapse
Affiliation(s)
- Norihiro Oyama
- Graduate School of Arts and Sciences, The University of Tokyo, Tokyo 153-8902, Japan.
- Mathematics for Advanced Materials-OIL, AIST, Sendai 980-8577, Japan
| | - Hideyuki Mizuno
- Graduate School of Arts and Sciences, The University of Tokyo, Tokyo 153-8902, Japan.
| | - Atsushi Ikeda
- Graduate School of Arts and Sciences, The University of Tokyo, Tokyo 153-8902, Japan.
- Research Center for Complex Systems Biology, Universal Biology Institute, University of Tokyo, Komaba, Tokyo 153-8902, Japan
| |
Collapse
|
3
|
Liao Q, Berthier L, Zhou HJ, Xu N. Dynamic Gardner cross-over in a simple glass. Proc Natl Acad Sci U S A 2023; 120:e2218218120. [PMID: 37339213 PMCID: PMC10293817 DOI: 10.1073/pnas.2218218120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2022] [Accepted: 05/21/2023] [Indexed: 06/22/2023] Open
Abstract
The criticality of the jamming transition responsible for amorphous solidification has been theoretically linked to the marginal stability of a thermodynamic Gardner phase. While the critical exponents of jamming appear independent of the preparation history, the pertinence of Gardner physics far from equilibrium is an open question. To fill this gap, we numerically study the nonequilibrium dynamics of hard disks compressed toward the jamming transition using a broad variety of protocols. We show that dynamic signatures of Gardner physics can be disentangled from the aging relaxation dynamics. We thus define a generic dynamic Gardner cross-over regardless of the history. Our results show that the jamming transition is always accessed by exploring increasingly complex landscape, resulting in anomalous microscopic relaxation dynamics that remains to be understood theoretically.
Collapse
Affiliation(s)
- Qinyi Liao
- Chinese Academic of Sciences Key Laboratory for Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing100190, China
- Department of Physics, University of Science and Technology of China, Hefei230026, People’s Republic of China
| | - Ludovic Berthier
- Laboratoire Charles Coulomb, University of Montpellier, CNRS, Montpellier34095, France
- Yusuf Hamied Department of Chemistry, University of Cambridge, CambridgeCB2 1EW, United Kingdom
| | - Hai-Jun Zhou
- Chinese Academic of Sciences Key Laboratory for Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing100190, China
- MinJiang Collaborative Center for Theoretical Physics, MinJiang University, Fuzhou350108, China
| | - Ning Xu
- Department of Physics, University of Science and Technology of China, Hefei230026, People’s Republic of China
- Hefei National Research Center for Physical Sciences at the Microscale, Chinese Academic of Sciences Key Laboratory of Microscale Magnetic Resonance, Hefei230026, People’s Republic of China
| |
Collapse
|
4
|
Kent-Dobias J, Kurchan J. How to count in hierarchical landscapes: A full solution to mean-field complexity. Phys Rev E 2023; 107:064111. [PMID: 37464608 DOI: 10.1103/physreve.107.064111] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2022] [Accepted: 02/24/2023] [Indexed: 07/20/2023]
Abstract
We derive the general solution for counting the stationary points of mean-field complex landscapes. It incorporates Parisi's solution for the ground state, as it should. Using this solution, we count the stationary points of two models: one with multistep replica symmetry breaking and one with full replica symmetry breaking.
Collapse
Affiliation(s)
- Jaron Kent-Dobias
- Laboratoire de Physique de l'Ecole Normale Supérieure, Paris 75005, France
| | - Jorge Kurchan
- Laboratoire de Physique de l'Ecole Normale Supérieure, Paris 75005, France
| |
Collapse
|
5
|
Kool L, Charbonneau P, Daniels KE. Gardner-like crossover from variable to persistent force contacts in granular crystals. Phys Rev E 2022; 106:054901. [PMID: 36559435 DOI: 10.1103/physreve.106.054901] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2022] [Accepted: 09/29/2022] [Indexed: 06/17/2023]
Abstract
We report experimental evidence of a Gardner-like crossover from variable to persistent force contacts in a two-dimensional bidisperse granular crystal by analyzing the variability of both particle positions and force networks formed under uniaxial compression. Starting from densities just above the freezing transition and for variable amounts of additional compression, we compare configurations to both their own initial state and to an ensemble of equivalent reinitialized states. This protocol shows that force contacts are largely undetermined when the density is below a Gardner-like crossover, after which they gradually transition to being persistent, being fully so only above the jamming point. We associate the disorder that underlies this effect with the size of the microscopic asperities of the photoelastic disks used, by analogy to other mechanisms that have been previously predicted theoretically.
Collapse
Affiliation(s)
- Lars Kool
- Laboratoire de Physique et Méchanique des Milieux Hétérogènes, ESPCI, 75005 Paris, France
- Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA
| | - Patrick Charbonneau
- Department of Chemistry and Department of Physics, Duke University, Durham, North Carolina 27708, USA
| | - Karen E Daniels
- Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA
| |
Collapse
|
6
|
Chen Y, Zhang J. High-energy velocity tails in uniformly heated granular materials. Phys Rev E 2022; 106:L052903. [PMID: 36559423 DOI: 10.1103/physreve.106.l052903] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2022] [Accepted: 11/17/2022] [Indexed: 06/17/2023]
Abstract
We experimentally investigate the velocity distributions of quasi-two-dimensional granular materials uniformly heated by an electromagnetic vibrator, where the translational velocity and the rotation of a single particle are Gaussian and independent. We observe the non-Gaussian distributions of particle velocity, with the density-independent high-energy tails characterized by an exponent of β=1.50±0.03 for volume fractions of 0.111≤ϕ≤0.832, covering a wide range of structures and dynamics. Surprisingly, our results are not only in excellent agreement with the prediction of the kinetic theories of granular gas but also hold for an extremely high-volume fraction of ϕ=0.832 where the granular material forms a crystalline solid and the kinetic theory of granular gas fails fantastically. Our experiment suggests that the density-independent high-energy velocity tails of β=1.50 are a characteristic of uniformly heated granular matter.
Collapse
Affiliation(s)
- Yangrui Chen
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Jie Zhang
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
- Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
| |
Collapse
|