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Ghimenti F, Berthier L, Szamel G, van Wijland F. Transverse forces and glassy liquids in infinite dimensions. Phys Rev E 2024; 109:064133. [PMID: 39020981 DOI: 10.1103/physreve.109.064133] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2024] [Accepted: 05/21/2024] [Indexed: 07/20/2024]
Abstract
We explore the dynamics of a simple liquid whose particles, in addition to standard potential-based interactions, are also subjected to transverse forces preserving the Boltzmann distribution. We derive the effective dynamics of one and two tracer particles in the infinite-dimensional limit. We determine the amount of acceleration of the dynamics caused by the transverse forces, in particular in the vicinity of the glass transition. We analyze the emergence and evolution of odd transport phenomena induced by the transverse forces.
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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.
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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
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Bonnet G, Charbonneau P, Folena G. Glasslike caging with random planes. Phys Rev E 2024; 109:024125. [PMID: 38491637 DOI: 10.1103/physreve.109.024125] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2023] [Accepted: 12/13/2023] [Indexed: 03/18/2024]
Abstract
The richness of the mean-field solution of simple glasses leaves many of its features challenging to interpret. A minimal model that illuminates glass physics in the same way that the random energy model clarifies spin glass behavior would therefore be beneficial. Here we propose such a real-space model that is amenable to infinite-dimensional d→∞ analysis and is exactly solvable in finite d in some regimes. By joining analysis with numerical simulations, we uncover geometrical signatures of the dynamical and jamming transitions and obtain insight into the origin of activated processes. Translating these findings into the context of standard glass formers further reveals the role played by nonconvexity in the emergence of Gardner and jamming physics.
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Affiliation(s)
- Gilles Bonnet
- Bernoulli Institute, University of Groningen, NL-9747 AG Groningen, Netherlands
- CogniGron, University of Groningen, NL-9747 AG Groningen, Netherlands
| | - Patrick Charbonneau
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
- Department of Physics, Duke University, Durham, North Carolina 27708, USA
| | - Giampaolo Folena
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
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Singh AK, Banerjee V. Phase separation of a magnetic fluid: Asymptotic states and nonequilibrium kinetics. Phys Rev E 2023; 108:064604. [PMID: 38243485 DOI: 10.1103/physreve.108.064604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2023] [Accepted: 11/15/2023] [Indexed: 01/21/2024]
Abstract
We study self-assembly in a colloidal suspension of magnetic particles by performing comprehensive molecular dynamics simulations of the Stockmayer (SM) model, which comprises spherical particles decorated by a magnetic moment. The SM potential incorporates dipole-dipole interactions along with the usual Lennard-Jones interaction and exhibits a gas-liquid phase coexistence observed experimentally in magnetic fluids. When this system is quenched from the high-temperature homogeneous phase to the coexistence region, the nonequilibrium evolution to the condensed phase proceeds with the development of spatial as well as magnetic order. We observe density-dependent coarsening mechanisms-a diffusive growth law ℓ(t)∼t^{1/3} in the nucleation regime and hydrodynamics-driven inertial growth law ℓ(t)∼t^{2/3} in the spinodal regimes. [ℓ(t) is the average size of the condensate at time t after the quench.] While the spatial growth is governed by the expected conserved order parameter dynamics, the growth of magnetic order in the spinodal regime exhibits unexpected nonconserved dynamics. The asymptotic morphologies have density-dependent shapes which typically include the isotropic sphere and spherical bubble morphologies in the nucleation region, and the anisotropic cylinder, planar slab, cylindrical bubble morphologies in the spinodal region. The structures are robust and nonvolatile, and exhibit characteristic magnetic properties. For example, the oppositely magnetized hemispheres in the spherical morphology impart the characteristics of a Janus particle to it. The observed structures have versatile applications in catalysis, drug delivery systems, memory devices, and magnetic photonic crystals, to name a few.
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Affiliation(s)
- Anuj Kumar Singh
- Department of Physics, Indian Institute of Technology Delhi, New Delhi 110016, India
| | - Varsha Banerjee
- Department of Physics, Indian Institute of Technology Delhi, New Delhi 110016, India
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Pareek P, Adhikari M, Dasgupta C, Nandi SK. Different glassy characteristics are related to either caging or dynamical heterogeneity. J Chem Phys 2023; 159:174503. [PMID: 37916596 DOI: 10.1063/5.0166404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2023] [Accepted: 10/09/2023] [Indexed: 11/03/2023] Open
Abstract
Despite the enormous theoretical and application interests, a fundamental understanding of the glassy dynamics remains elusive. The static properties of glassy and ordinary liquids are similar, but their dynamics are dramatically different. What leads to this difference is the central puzzle of the field. Even the primary defining glassy characteristics, their implications, and if they are related to a single mechanism remain unclear. This lack of clarity is a severe hindrance to theoretical progress. Here, we combine analytical arguments and simulations of various systems in different dimensions and address these questions. Our results suggest that the myriad of glassy features are manifestations of two distinct mechanisms. Particle caging controls the mean, and coexisting slow- and fast-moving regions govern the distribution of particle displacements. All the other glassy characteristics are manifestations of these two mechanisms; thus, the Fickian yet non-Gaussian nature of glassy liquids is not surprising. We discover a crossover, from stretched exponential to a power law, in the behavior of the overlap function. This crossover is prominent in simulation data and forms the basis of our analyses. Our results have crucial implications on how the glassy dynamics data are analyzed, challenge some recent suggestions on the mechanisms governing glassy dynamics, and impose strict constraints that a correct theory of glasses must have.
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Affiliation(s)
- Puneet Pareek
- Tata Institute of Fundamental Research, Hyderabad 500046, India
| | - Monoj Adhikari
- Tata Institute of Fundamental Research, Hyderabad 500046, India
| | - Chandan Dasgupta
- Department of Physics, Indian Institute of Science, Bangalore 560012, India
- International Centre for Theoretical Sciences, TIFR, Bangalore 560089, India
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Charbonneau P, Morse PK. Jamming, relaxation, and memory in a minimally structured glass former. Phys Rev E 2023; 108:054102. [PMID: 38115479 DOI: 10.1103/physreve.108.054102] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2023] [Accepted: 10/03/2023] [Indexed: 12/21/2023]
Abstract
Structural glasses form through various out-of-equilibrium processes, including temperature quenches, rapid compression (crunches), and shear. Although each of these processes should be formally understandable within the recently formulated dynamical mean-field theory (DMFT) of glasses, the numerical tools needed to solve the DMFT equations up to the relevant physical regime do not yet exist. In this context, numerical simulations of minimally structured (and therefore mean-field-like) model glass formers can aid the search for and understanding of such solutions, thanks to their ability to disentangle structural from dimensional effects. We study here the infinite-range Mari-Kurchan model under simple out-of-equilibrium processes, and we compare results with the random Lorentz gas [J. Phys. A 55, 334001 (2022)10.1088/1751-8121/ac7f06]. Because both models are mean-field-like and formally equivalent in the limit of infinite spatial dimensions, robust features are expected to appear in the DMFT as well. The comparison provides insight into temperature and density onsets, memory, as well as anomalous relaxation. This work also further enriches the algorithmic understanding of the jamming density.
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Affiliation(s)
- Patrick Charbonneau
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
- Department of Physics, Duke University, Durham, North Carolina 27708, USA
| | - 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
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Teboul V. Dynamic phase transition induced by active molecules in a supercooled liquid. Phys Rev E 2023; 108:024605. [PMID: 37723732 DOI: 10.1103/physreve.108.024605] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2023] [Accepted: 07/21/2023] [Indexed: 09/20/2023]
Abstract
The purpose of this work is to use active particles to investigate the effect of facilitation on supercooled liquids. To this end we examine the behavior of a model supercooled liquid that is doped with a mixture of active particles and slowed particles. To simulate the facilitation mechanism, the activated particles are subjected to a force that follows the mobility of their most mobile neighboring molecule, while the slowed particles experience a friction force. Upon activation, we observe a fluidization of the entire medium along with a significant increase in dynamic heterogeneity. This effect is reminiscent of the fluidization observed experimentally when introducing molecular motors into soft materials. Interestingly, when the characteristic time τ_{μ}, used to define the mobility in the facilitation mechanism, matches the physical time t^{*} that characterizes the spontaneous cooperativity of the material, we observe a phase transition accompanied by structural aggregation of the active molecules. This transition is characterized by a sharp increase in fluidization and dynamic heterogeneity.
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Affiliation(s)
- Victor Teboul
- Laboratoire de Photonique d'Angers EA 4464, Université d'Angers, Physics Department, 2 Bd Lavoisier, 49045 Angers, France
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Folena G, Biroli G, Charbonneau P, Hu Y, Zamponi F. Equilibrium fluctuations in mean-field disordered models. Phys Rev E 2022; 106:024605. [PMID: 36109887 DOI: 10.1103/physreve.106.024605] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2022] [Accepted: 06/24/2022] [Indexed: 06/15/2023]
Abstract
Mean-field models of glasses that present a random first order transition exhibit highly nontrivial fluctuations. Building on previous studies that focused on the critical scaling regime, we here obtain a fully quantitative framework for all equilibrium conditions. By means of the replica method we evaluate Gaussian fluctuations of the overlaps around the thermodynamic limit, decomposing them in thermal fluctuations inside each state and heterogeneous fluctuations between different states. We first test and compare our analytical results with numerical simulation results for the p-spin spherical model and the random orthogonal model, and then analyze the random Lorentz gas. In all cases, a strong quantitative agreement is obtained. Our analysis thus provides a robust scheme for identifying the key finite-size (or finite-dimensional) corrections to the mean-field treatment of these paradigmatic glass models.
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Affiliation(s)
- Giampaolo Folena
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
- James Franck Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
| | - Giulio Biroli
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - Patrick Charbonneau
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
- Department of Physics, Duke University, Durham, North Carolina 27708, USA
| | - Yi Hu
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
| | - Francesco Zamponi
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
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