Fractal free energy landscapes in structural glasses

Charbonneau, Patrick; Kurchan, Jorge; Parisi, G.; Urbani, Pierfrancesco; Zamponi, Francesco

doi:10.1038/ncomms4725

Cited by 463 publications

(695 citation statements)

References 78 publications

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“…This result can be derived in infinite dimension using the replica trick [29], yielding a similar result θ ≈ 0.42 that appears to be correct in any dimensions. Considering that the force distribution in flow must converge to that of jammed packings as the jamming point is approached, the minimum force f min can be easily estimated.…”

Section: Weakest Force In the Volume Csupporting

confidence: 69%

Effect of particle collisions in dense suspension flows

2016

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Effect of particle collisions in dense suspension flowsDüring, G.; Lerner, E.; Wyart, M. Published in:Physical Review E DOI:10.1103/PhysRevE.94.022601 Link to publication Citation for published version (APA):Düring, G., Lerner, E., & Wyart, M. (2016). Effect of particle collisions in dense suspension flows. Physical Review E, 94(2), [022601]. DOI: 10.1103/PhysRevE.94.022601 General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. We study nonlocal effects associated with particle collisions in dense suspension flows, in the context of the Affine Solvent Model, known to capture various aspects of the jamming transition. We show that an individual collision changes significantly the velocity field on a characteristic volume c ∼ 1/δz that diverges as jamming is approached, where δz is the deficit in coordination number required to jam the system. Such an event also affects the contact forces between particles on that same volume c , but this change is modest in relative terms, of order f coll ∼f 0.8 , wheref is the typical contact force scale. We then show that the requirement that coordination is stationary (such that a collision has a finite probability to open one contact elsewhere in the system) yields the scaling of the viscosity (or equivalently the viscous number) with coordination deficit δz. The same scaling result was derived [E. DeGiuli, G. Düring, E. Lerner, and M. Wyart, Phys. Rev. E 91, 062206 (2015)] via different arguments making an additional assumption. The present approach gives a mechanistic justification as to why the correct finite size scaling volume behaves as 1/δz and can be used to recover a marginality condition known to characterize the distributions of contact forces and gaps in jammed packings.

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Section: Weakest Force In the Volume Csupporting

confidence: 69%

Effect of particle collisions in dense suspension flows

2016

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“…We expect this approach to be fruitful in elucidating a number of outstanding aspects of the glass problem, such as the existence of the Gardner transition in finite dimensional systems [49,50], the growth of static point-to-set correlations [51][52][53] and locally-favored structures [54], measurements of configurational entropy [55], and the physics of ultrastable glasses [56].…”

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confidence: 99%

Equilibrium Sampling of Hard Spheres up to the Jamming Density and Beyond

et al. 2016

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We implement and optimize a particle-swap Monte-Carlo algorithm that allows us to thermalize a polydisperse system of hard spheres up to unprecedentedly-large volume fractions, where previous algorithms and experiments fail to equilibrate. We show that no glass singularity intervenes before the jamming density, which we independently determine through two distinct non-equilibrium protocols. We demonstrate that equilibrium fluid and non-equilibrium jammed states can have the same density, showing that the jamming transition cannot be the end-point of the fluid branch.PACS numbers: 05.20.Jj,We clarify the behavior of non-crystalline states of hard spheres at very large densities where both a glass transition (in colloidal systems) and a jamming transition (in non-Brownian systems) are observed [1][2][3]. Glass and jamming transitions are usually studied through distinct protocols, and understanding the relation between these two broad classes of phase transformations and the resulting amorphous arrested states is an important research goal [1][2][3][4][5]. These questions impact a wide range of fields, from the rheological properties of soft materials to optimization problems in computer science [1,6].Let us first consider Brownian hard spheres. When size polydispersity is introduced, crystallization can be prevented and the thermodynamic properties of the fluid studied at increasing density until a glass transition takes place, where particle diffusivity becomes very small [7]. Upon further compression, the pressure of the glass increases until a jamming transition occurs, where particles come at close contact and the pressure diverges [8]. Because the laboratory glass transition arises from using a finite observation timescale, two scenarios were proposed to describe the hypothetical situation where thermalization is no longer an issue [9]. A first possibility is that slower compressions reveal an ideal glass transition density, ϕ 0 , above which the equilibrium state is a glass, not a fluid [2]. Jamming would then be observed upon further non-equilibrium compression of these glass states [10]. Alternatively, it may be that slower compressions continuously shift the kinetic glass transition to higher densities. In this view, it is plausible that jamming becomes the end-point of the equilibrium fluid branch [11,12].Distinguishing between these two scenarios by direct numerical measurements is challenging. For a wellstudied binary mixture of hard spheres, for instance, thermalization can be achieved up to ϕ max ≈ 0.60 [9,13]. The location of the glass transition must be extrapolated using empirical fits based on activated relaxation. Values in the range ϕ 0 = 0.615 − 0.635 were obtained [9], depending on the fitting function. Fitting the relaxation times to a power law yields ϕ mct ≈ 0.59 < ϕ max , so that the associated mode-coupling transition [14] corresponds to an avoided singularity. For the same system, jamming transitions were located in the range ϕ J = 0.648 − 0.662 depending on the chosen protocol [15][1...

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“…As the strain amplitude γ t increases beyond some value γ * t , particles can no longer avoid each other and the system undergoes a dynamical "absorbing state" transition from the absorbing phase to a phase in which the system continually visits new configurations. Models [3,[5][6][7][8] have linked this transition to variants of directed percolation [8][9][10], which represents a broad class of non-equilibrium phase transitions [1].Athermal glasses such as Lennard-Jones glasses, by contrast, have an extensive entropy of energy minima that are not flat [11][12][13]. At very small strain amplitudes, they exhibit elastic behavior in which they explore different configurations within the same energy minimum.…”

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confidence: 99%

Period proliferation in periodic states in cyclically sheared jammed solids

2017

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Athermal disordered systems can exhibit a remarkable response to an applied oscillatory shear: after a relatively few shearing cycles, the system falls into a configuration that had already been visited in a previous cycle. After this point the system repeats its dynamics periodically despite undergoing many particle rearrangements during each cycle. We study the behavior of orbits as we approach the jamming point in simulations of jammed particles subject to oscillatory shear at fixed pressure and zero temperature. As the pressure is lowered, we find that it becomes more common for the system to find periodic states where it takes multiple cycles before returning to a previously visited state. Thus, there is a proliferation of longer periods as the jamming point is approached.Keywords: cyclic shearing, reversibility, memory, absorbing-state phase transition, jammingOscillatory sheared athermal particle packings or suspensions can fall into periodic "absorbing states" [1] in which the system returns to a configuration previously visited during the shearing process at the same point in the cycle. Once it returns to that configuration, the dynamics repeats itself indefinitely. At low densities in the absorbing state, the particles follow the flow without ever making contact with one another so that the system moves back and forth along a flat direction in the energy landscape [2][3][4], and particles return to their original positions after a single shear cycle: T = 1. As the strain amplitude γ t increases beyond some value γ * t , particles can no longer avoid each other and the system undergoes a dynamical "absorbing state" transition from the absorbing phase to a phase in which the system continually visits new configurations. Models [3,[5][6][7][8] have linked this transition to variants of directed percolation [8][9][10], which represents a broad class of non-equilibrium phase transitions [1].Athermal glasses such as Lennard-Jones glasses, by contrast, have an extensive entropy of energy minima that are not flat [11][12][13]. At very small strain amplitudes, they exhibit elastic behavior in which they explore different configurations within the same energy minimum. As γ t increases so that the system can explore more than one minimum, one might expect the system to meander indefinitely around a hopelessly intricate energy landscape as the system is driven in an oscillatory fashion. Yet, remarkably, these systems can fall into absorbing states-they can find their way back to previously visited energy minima even as they undergo multiple particle rearrangements. Thus these systems explore many such minima [14-17] over and over again. Finally, when γ t is increased to γ * t , the system undergoes an absorbing state transition to a phase in which the system never returns to previously visited minima.In this paper we investigate the fate of absorbing states in packings of jammed spheres that can be tuned to the jamming transition, where the system loses rigidity [18,19]. Far above this transition, absorbing states...

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Fractal free energy landscapes in structural glasses

Cited by 463 publications

References 78 publications

Effect of particle collisions in dense suspension flows

Effect of particle collisions in dense suspension flows

Equilibrium Sampling of Hard Spheres up to the Jamming Density and Beyond

Period proliferation in periodic states in cyclically sheared jammed solids

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