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Maire R, Plati A. Enhancing (quasi-)long-range order in a two-dimensional driven crystal. J Chem Phys 2024; 161:054902. [PMID: 39087549 DOI: 10.1063/5.0217958] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2024] [Accepted: 07/14/2024] [Indexed: 08/02/2024] Open
Abstract
It has been recently shown that 2D systems can exhibit crystalline phases with long-range translational order showcasing a striking violation of the Hohenberg-Mermin-Wagner (HMW) theorem, which is valid at equilibrium. This is made possible by athermal driving mechanisms that inject energy into the system without exciting long wavelength modes of the density field, thereby inducing hyperuniformity. However, as thermal fluctuations are superimposed on the non-equilibrium driving, long-range translational order is inevitably lost. Here, we discuss the possibility of exploiting non-equilibrium effects to suppress arbitrarily large density fluctuations even when a global thermal bath is coupled to the system. We introduce a model of a harmonic crystal driven both by a global thermal bath and by a momentum conserving noise, where the typical observables related to density fluctuations and long-range translational order can be analytically derived and put in relation. This model allows us to rationalize the violation of the HMW theorem observed in previous studies through the prediction of large-wavelength phonons, which thermalize at a vanishing effective temperature when the global bath is switched off. The conceptual framework introduced through this theory is then applied to numerical simulations of a hard-disk solid in contact with a thermal bath and driven out-of-equilibrium by active collisions. Our numerical analysis demonstrates how varying driving and dissipative parameters can lead to an arbitrary enhancement of the quasi-long-range order in the system regardless of the applied global noise amplitude. Finally, we outline a possible experimental procedure to apply our results to a realistic granular system.
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Affiliation(s)
- R Maire
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
| | - A Plati
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
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Castagnède A, Filion L, Smallenburg F. Fast event-driven simulations for soft spheres: from dynamics to Laves phase nucleation. J Chem Phys 2024; 161:024116. [PMID: 38995079 DOI: 10.1063/5.0209178] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2024] [Accepted: 05/30/2024] [Indexed: 07/13/2024] Open
Abstract
Conventional molecular dynamics (MD) simulations struggle when simulating particles with steeply varying interaction potentials due to the need to use a very short time step. Here, we demonstrate that an event-driven Monte Carlo (EDMC) approach was first introduced by Peters and de With [Phys. Rev. E 85, 026703 (2012)] and represents an excellent substitute for MD in the canonical ensemble. In addition to correctly reproducing the static thermodynamic properties of the system, the EDMC method closely mimics the dynamics of systems of particles interacting via the steeply repulsive Weeks-Chandler-Andersen (WCA) potential. In comparison to time-driven MD simulations, EDMC runs faster by over an order of magnitude at sufficiently low temperatures. Moreover, the lack of a finite time step in EDMC circumvents the need to trade accuracy against the simulation speed associated with the choice of time step in MD. We showcase the usefulness of this model to explore the phase behavior of the WCA model at extremely low temperatures and to demonstrate that spontaneous nucleation and growth of the Laves phases are possible at temperatures significantly lower than previously reported.
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Affiliation(s)
- Antoine Castagnède
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
| | - Laura Filion
- Soft Condensed Matter and Biophysics, Debye Institute for Nanomaterials Science, Utrecht University, Utrecht, Netherlands
| | - Frank Smallenburg
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
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Maire R, Plati A, Stockinger M, Trizac E, Smallenburg F, Foffi G. Interplay between an Absorbing Phase Transition and Synchronization in a Driven Granular System. PHYSICAL REVIEW LETTERS 2024; 132:238202. [PMID: 38905681 DOI: 10.1103/physrevlett.132.238202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2023] [Accepted: 04/24/2024] [Indexed: 06/23/2024]
Abstract
Absorbing phase transitions (APTs) are widespread in nonequilibrium systems, spanning condensed matter, epidemics, earthquakes, ecology, and chemical reactions. APTs feature an absorbing state in which the system becomes entrapped, along with a transition, either continuous or discontinuous, to an active state. Understanding which physical mechanisms determine the order of these transitions represents a challenging open problem in nonequilibrium statistical mechanics. Here, by numerical simulations and mean-field analysis, we show that a quasi-2D vibrofluidized granular system exhibits a novel form of APT. The absorbing phase is observed in the horizontal dynamics below a critical packing fraction, and can be continuous or discontinuous based on the emergent degree of synchronization in the vertical motion. Our results provide a direct representation of a feasible experimental scenario, showcasing a surprising interplay between dynamic phase transition and synchronization.
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Affiliation(s)
- R Maire
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
| | - A Plati
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
| | - M Stockinger
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
- Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, 14476 Potsdam, Germany
| | - E Trizac
- LPTMS, UMR 8626, CNRS, Université Paris-Saclay, 91405 Orsay, France
- Ecole normale supérieure de Lyon, F-69364 Lyon, France
| | - F Smallenburg
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
| | - G Foffi
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
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Smallenburg F. Comment on 'Pseudo hard-sphere viscosities from equilibrium molecular dynamics'. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:228001. [PMID: 38436284 DOI: 10.1088/1361-648x/ad1f8b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/05/2023] [Accepted: 01/17/2024] [Indexed: 03/05/2024]
Abstract
In a recent article, Nicasio-Collazoet al(2023J. Phys.: Condens. Matter35425401) explore the viscosity of the pseudo-hard-sphere (PHS) model. In this comment, we highlight some discrepancies with expected behavior, and compare their results to new simulations of the same model as well as to true hard spheres. In contrast to the results of Nicasio-Collazoet al, our results follow the relation between shear, bulk, and longitudinal viscosity expected for isotropic fluids. Moreover, we observe clear differences in behavior between PHS and true hard sphere, and encourage future hard-sphere studies to focus on the true hard sphere model whenever possible.
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Affiliation(s)
- Frank Smallenburg
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
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5
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Fayen E, Filion L, Foffi G, Smallenburg F. Quasicrystal of Binary Hard Spheres on a Plane Stabilized by Configurational Entropy. PHYSICAL REVIEW LETTERS 2024; 132:048202. [PMID: 38335332 DOI: 10.1103/physrevlett.132.048202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/06/2023] [Revised: 09/08/2023] [Accepted: 01/03/2024] [Indexed: 02/12/2024]
Abstract
Because of their aperiodic nature, quasicrystals are one of the least understood phases in statistical physics. One significant complication they present in comparison to their periodic counterparts is the fact that any quasicrystal can be realized as an exponentially large number of different tilings, resulting in a significant contribution to the quasicrystal entropy. Here, we use free-energy calculations to demonstrate that it is this configurational entropy which stabilizes a dodecagonal quasicrystal in a binary mixture of hard spheres on a plane. Our calculations also allow us to quantitatively confirm that in this system all tiling realizations are essentially equally likely, with free-energy differences less than 0.0001k_{B}T per particle-an observation that could be related to the observation of only random tilings in soft-matter quasicrystals. Owing to the simplicity of the model and its available counterparts in colloidal experiments, we believe that this system is an excellent candidate to achieve the long-awaited quasicrystal self-assembly on the micron scale.
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Affiliation(s)
- Etienne Fayen
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
| | - Laura Filion
- Soft Condensed Matter, Debye Institute of Nanomaterials Science, Utrecht University, Utrecht, Netherlands
| | - Giuseppe Foffi
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
| | - Frank Smallenburg
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
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Geistfeld EC, Torres E, Schwartzentruber T. Quasi-classical trajectory analysis of three-body collision induced recombination in neutral nitrogen and oxygen. J Chem Phys 2023; 159:154111. [PMID: 37861123 DOI: 10.1063/5.0163942] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2023] [Accepted: 09/18/2023] [Indexed: 10/21/2023] Open
Abstract
We present theory and a simulation framework to model three-body collisions and gas phase recombination in dilute atom/diatom mixtures of pure oxygen (O/O2) and nitrogen (N/N2) using the Quasi-Classical Trajectory method. We formulate a three-body collision rate constant based on the lifetimes of binary collisions and initialize three-body collisions by sampling the arrival time of a third body within the lifetimes of pre-simulated binary collisions. We use this method to calculate distributions of recombined product energies, probabilities of recombination, and recombination rate constants through different collision pathways. Long-lived binary atom-diatom collisions are observed, but are too rare to play a dominant role in the recombination process for shock-heated air near the equilibrium conditions studied. The resulting recombination rate constants are within an order of magnitude of the predictions of detailed balance. Notably, the recombination simulation framework does not appeal to the principle of detailed balance and could be useful for studying conditions far from equilibrium.
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Affiliation(s)
- Eric C Geistfeld
- Department of Aerospace Engineering and Mechanics, University of Minnesota Minneapolis, Minneapolis, Minnesota 55455, USA
| | - Erik Torres
- Department of Aerospace Engineering and Mechanics, University of Minnesota Minneapolis, Minneapolis, Minnesota 55455, USA
| | - Thomas Schwartzentruber
- Department of Aerospace Engineering and Mechanics, University of Minnesota Minneapolis, Minneapolis, Minnesota 55455, USA
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Alkemade RM, Smallenburg F, Filion L. Improving the prediction of glassy dynamics by pinpointing the local cage. J Chem Phys 2023; 158:134512. [PMID: 37031101 DOI: 10.1063/5.0144822] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/10/2023] Open
Abstract
The relationship between structure and dynamics in glassy fluids remains an intriguing open question. Recent work has shown impressive advances in our ability to predict local dynamics using structural features, most notably due to the use of advanced machine learning techniques. Here, we explore whether a simple linear regression algorithm combined with intelligently chosen structural order parameters can reach the accuracy of the current, most advanced machine learning approaches for predicting dynamic propensity. To achieve this, we introduce a method to pinpoint the cage state of the initial configuration-i.e., the configuration consisting of the average particle positions when particle rearrangement is forbidden. We find that, in comparison to both the initial state and the inherent state, the structure of the cage state is highly predictive of the long-time dynamics of the system. Moreover, by combining the cage state information with the initial state, we are able to predict dynamic propensities with unprecedentedly high accuracy over a broad regime of time scales, including the caging regime.
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Affiliation(s)
- Rinske M Alkemade
- Soft Condensed Matter, Debye Institute of Nanomaterials Science, Utrecht University, Utrecht, Netherlands
| | - Frank Smallenburg
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
| | - Laura Filion
- Soft Condensed Matter, Debye Institute of Nanomaterials Science, Utrecht University, Utrecht, Netherlands
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Fayen E, Impéror-Clerc M, Filion L, Foffi G, Smallenburg F. Self-assembly of dodecagonal and octagonal quasicrystals in hard spheres on a plane. SOFT MATTER 2023; 19:2654-2663. [PMID: 36971334 DOI: 10.1039/d3sm00179b] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
Hard spheres are one of the most fundamental model systems in soft matter physics, and have been instrumental in shedding light on nearly every aspect of classical condensed matter. Here, we add one more important phase to the list that hard spheres form: quasicrystals. Specifically, we use simulations to show that an extremely simple, purely entropic model system, consisting of two sizes of hard spheres resting on a flat plane, can spontaneously self-assemble into two distinct random-tiling quasicrystal phases. The first quasicrystal is a dodecagonal square-triangle tiling, commonly observed in a large variety of colloidal systems. The second quasicrystal has, to our knowledge, never been observed in either experiments or simulations. It exhibits octagonal symmetry, and consists of three types of tiles: triangles, small squares, and large squares, whose relative concentration can be continuously varied by tuning the number of smaller spheres present in the system. The observed tile composition of the self-assembled quasicrystals agrees very well with the theoretical prediction we obtain by considering the four-dimensional (lifted) representation of the quasicrystal. Both quasicrystal phases form reliably and rapidly over a significant part of parameter space. Our results demonstrate that entropy combined with a set of geometrically compatible, densely packed tiles can be sufficient ingredients for the self-assembly of colloidal quasicrystals.
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Affiliation(s)
- Etienne Fayen
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405, Orsay, France.
| | - Marianne Impéror-Clerc
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405, Orsay, France.
| | - Laura Filion
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Utrecht, The Netherlands
| | - Giuseppe Foffi
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405, Orsay, France.
| | - Frank Smallenburg
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405, Orsay, France.
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