Le Yan

Why glass elasticity affects the thermodynamics and fragility of supercooled liquids

Supercooled liquids are characterized by their fragility: The slowing down of the dynamics under cooling is more sudden and the jump of specific heat at the glass transition is generally larger in fragile liquids than in strong ones. Despite the importance of this quantity in classifying liquids, explaining what aspects of the microscopic structure controls fragility remains a challenge. Surprisingly, experiments indicate that the linear elasticity of the glass—a purely local property of the free energy landscape—is a good predictor of fragility. In particular, materials presenting a large excess of soft elastic modes, the so-called boson peak, are strong. This is also the case for network liquids near the rigidity percolation, known to affect elasticity. Here we introduce a model of the glass transition based on the assumption that particles can organize locally into distinct configurations that are coupled spatially via elasticity. The model captures the mentioned observations connecting elasticity and fragility. We find that materials presenting an abundance of soft elastic modes have little elastic frustration: Energy is insensitive to most directions in phase space, leading to a small jump of specific heat. In this framework strong liquids turn out to lie the closest to a critical point associated with a rigidity or jamming transition, and their thermodynamic properties are related to the problem of number partitioning and to Hopfield nets in the limit of small memory.

Architecture and coevolution of allosteric materials

Significance In allosteric proteins, binding a ligand affects activity at a distant site. The physical principles allowing for such an action at a distance are not well understood. Here we introduce a numerical scheme to evolve allosteric materials in which the number of solutions, their spatial architectures, and the correlations among them can be computed. We show that allostery in these materials uses recently discovered elastic edge modes near the active site to transmit information, and that correlations generated during evolution alone can reveal key aspects of this architecture. We introduce a numerical scheme to evolve functional elastic materials that can accomplish a specified mechanical task. In this scheme, the number of solutions, their spatial architectures, and the correlations among them can be computed. As an example, we consider an “allosteric” task, which requires the material to respond specifically to a stimulus at a distant active site. We find that functioning materials evolve a less-constrained trumpet-shaped region connecting the stimulus and active sites, and that the amplitude of the elastic response varies nonmonotonically along the trumpet. As previously shown for some proteins, we find that correlations appearing during evolution alone are sufficient to identify key aspects of this design. Finally, we show that the success of this architecture stems from the emergence of soft edge modes recently found to appear near the surface of marginally connected materials. Overall, our in silico evolution experiment offers a window to study the relationship between structure, function, and correlations emerging during evolution.

On variational arguments for vibrational modes near jamming

Amorphous solids tend to present an abundance of soft elastic modes, which diminish their transport properties, generate heterogeneities in their elastic response, and affect non-linear processes like thermal activation of plasticity. This is especially true in packings of particles near their jamming transition, for which effective medium theory and variational arguments can both predict the density of vibrational modes. However, recent numerics support that one hypothesis of the variational argument does not hold. We provide a novel variational argument which overcomes this problem, and correctly predicts the scaling properties of soft modes near the jamming transition. Soft modes are shown to be related to the response to a local strain in more connected networks, and to be characterized by a volume

Model for the erosion onset of a granular bed sheared by a viscous fluid

1/\delta z

Scale-free channeling patterns near the onset of erosion of sheared granular beds

, where

Adaptive elastic networks as models of supercooled liquids.

\delta z

Dynamics and Correlations among Soft Excitations in Marginally Stable Glasses

is the excess coordination above the Maxwell threshold. These predictions are verified numerically.

Erratum: On variational arguments for vibrational modes near jamming

We study theoretically the erosion threshold of a granular bed forced by a viscous fluid. We first introduce a model of interacting particles driven on a rough substrate. It predicts a continuous transition at some threshold forcing θ_{c}, beyond which the particle current grows linearly J∼θ-θ_{c}. The stationary state is reached after a transient time t_{conv} which diverges near the transition as t_{conv}∼|θ-θ_{c}|^{-z} with z≈2.5. Both features are consistent with experiments. The model also makes quantitative testable predictions for the drainage pattern: The distribution P(σ) of local current is found to be extremely broad with P(σ)∼J/σ, and spatial correlations for the current are negligible in the direction transverse to forcing, but long-range parallel to it. We explain some of these features using a scaling argument and a mean-field approximation that builds an analogy with q models. We discuss the relationship between our erosion model and models for the plastic depinning transition of vortex lattices in dirty superconductors, where our results may also apply.

Evolution of covalent networks under cooling: contrasting the rigidity window and jamming scenarios.

Significance The response of erodible granular beds to shearing flows controls numerous natural phenomena. A central aspect is the existence of a threshold stress below which erosion stops, and whose microscopic underpinning is debated. We use an experiment where this threshold is spontaneously reached to study the spatial organization of the erosion flux. We find that erosion is heterogeneous in space and occurs along favored channels whose distribution is extremely broad, with strongly anisotropic spatial correlations. These findings can be quantitatively explained by a model incorporating both the disorder of the static bed and the interactions between mobile particles, establishing a link between erosion and dynamical phase transitions known to occur in disordered environments. Erosion shapes our landscape and occurs when a sufficient shear stress is exerted by a fluid on a sedimented layer. What controls erosion at a microscopic level remains debated, especially near the threshold forcing where it stops. Here we study, experimentally, the collective dynamics of the moving particles, using a setup where the system spontaneously evolves toward the erosion onset. We find that the spatial organization of the erosion flux is heterogeneous in space and occurs along channels of local flux σ whose distribution displays scaling near threshold and follows P(σ)≈J/σ, where J is the mean erosion flux. Channels are strongly correlated in the direction of forcing but not in the transverse direction. We show that these results quantitatively agree with a model where the dynamics is governed by the competition of disorder (which channels mobile particles) and particle interactions (which reduces channeling). These observations support that, for laminar flows, erosion is a dynamical phase transition that shares similarity with the plastic depinning transition occurring in dirty superconductors. The methodology we introduce here could be applied to probe these systems as well.

Edge mode amplification in disordered elastic networks

The thermodynamics and dynamics of supercooled liquids correlate with their elasticity. In particular for covalent networks, the jump of specific heat is small and the liquid is strong near the threshold valence where the network acquires rigidity. By contrast, the jump of specific heat and the fragility are large away from this threshold valence. In a previous work [Proc. Natl. Acad. Sci. USA 110, 6307 (2013)], we could explain these behaviors by introducing a model of supercooled liquids in which local rearrangements interact via elasticity. However, in that model the disorder characterizing elasticity was frozen, whereas it is itself a dynamic variable in supercooled liquids. Here we study numerically and theoretically adaptive elastic network models where polydisperse springs can move on a lattice, thus allowing for the geometry of the elastic network to fluctuate and evolve with temperature. We show numerically that our previous results on the relationship between structure and thermodynamics hold in these models. We introduce an approximation where redundant constraints (highly coordinated regions where the frustration is large) are treated as an ideal gas, leading to analytical predictions that are accurate in the range of parameters relevant for real materials. Overall, these results lead to a description of supercooled liquids, in which the distance to the rigidity transition controls the number of directions in phase space that cost energy and the specific heat.