arXiv subjects

Le Yan

Publications and source records attributed to Le Yan.

29 records · Page 2Linked to original sources

arXiv2018

Entropy favors heterogeneous structures of networks near the rigidity threshold

The dynamical properties and mechanical functions of amorphous materials are governed by their microscopic structures, particularly the elasticity of the interaction networks, which is generally complicated by structural heterogeneity. This ubiquitous heterogeneous nature of amorphous materials is intriguingly attributed to a complex role of entropy. Here, we show in disordered networks that the vibrational entropy increases by creating phase-separated structures when the interaction connectivity is close to the onset of network rigidity. The stress-energy, which conversely penalizes the heterogeneity, finally dominates a smaller vicinity of the rigidity threshold at the glass transition and creates a homogeneous intermediate phase. This picture of structures changing between homogeneous and heterogeneous phases by varying connectivity provides an interpretation of the transitions observed in chalcogenide glasses.

cond-mat.stat-mech↗

arXiv2016

Architecture and Co-Evolution of Allosteric Materials

We introduce a numerical scheme to evolve functional 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 non-monotonically 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 new window to study the relationship between structure, function, and correlations emerging during evolution.

physics.bio-ph↗

arXiv2016

Edge Mode Amplification in Disordered Elastic Networks

We study theoretically and numerically the propagation of a displacement field imposed at the edge of a disordered elastic material. While some modes decay with some inverse penetration depth $κ$, other exponentially {\it amplify} with rate $|κ|$, where $κ$'s are Lyapounov exponents analogous to those governing electronic transport in a disordered conductors. We obtain an analytical approximation for the full distribution $g(κ)$, which decays exponentially for large $|κ|$ and is finite when $κ\rightarrow0$. Our analysis shows that isostatic materials generically act as levers with possibly very large gains, suggesting a novel principle to design molecular machines that behave as elastic amplifiers.

cond-mat.soft↗

arXiv2016

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

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 set-up 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 $P(σ)\sim J/σ$, 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 which 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.

cond-mat.soft↗

arXiv2016

On the Dynamics of Glassy Systems

Glassy systems are disordered systems characterized by extremely slow dynamics. Examples are supercooled liquids, whose dynamics slow down under cooling. The specific pattern of slowing-down depends on the material considered. This dependence is poorly understood, in particular, it remains generally unclear which aspects of the microscopic structures control the dynamics and other macroscopic properties. Attacking this question is one of the two main aspects of this dissertation. We have introduced a new class of models of supercooled liquids, which captures the central aspects of the correspondence between structure and elasticity on the one hand, the correlation of structure and thermodynamic and dynamic properties on the other. Our results shed new light on the temperature-dependence of the topology of covalent networks, in particular, on the rigidity transition that occurs when the valence is increased. Other questions appear in glassy systems at zero temperature. In that situation, a glassy system can flow if an external driving force is imposed above some threshold. The first example we will consider is the erosion of a riverbed. Experiments support the existence of a threshold forcing, below which no erosion flux is observed. In this dissertation, we present a novel microscopic model to describe the erosion near threshold. This model makes new quantitative predictions for the spatial reparation of the flux. To study further the self-organization of driven glassy systems, we investigate the athermal dynamics of mean-field spin glasses. The spin glass self-organizes into the configurations that are stable, but barely so. Such marginal stability appears with the presence of a pseudogap in soft excitations. We show that the emergence of a pseudogap is deeply related to very strong anti-correlations emerging among soft excitations.

cond-mat.dis-nn↗

arXiv2016

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 $1/δz$, where $δz$ is the excess coordination above the Maxwell threshold. These predictions are verified numerically.

cond-mat.soft↗

arXiv2015

Adaptive Elastic Networks as models of supercooled liquids

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 {\it 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. U.S.A., 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.

cond-mat.dis-nn↗

arXiv2015

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

We study theoretically the erosion threshold of a granular bed forced by a viscous fluid. We first introduce a novel 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 $J\sim θ-θ_c$, in agreement with experiments. The stationary state is reached after a transient time $t_{\rm conv}$ which diverges near the transition as $t_{\rm conv}\sim |θ-θ_c|^{-z}$ with $z\approx 2.5$. 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 $P(σ)\sim J/σ$, 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 depinning transition of vortex lattices in dirty superconductors, where our results may also apply.

cond-mat.soft↗

arXiv2015

Dynamics and Correlations among Soft Excitations in Marginally Stable Glasses

Marginal stability is the notion that stability is achieved, but only barely so. This property constrains the ensemble of configurations explored at low temperature in a variety of systems, including spin, electron and structural glasses. A key feature of marginal states is a (saturated) pseudo-gap in the distribution of soft excitations. We study how such a pseudo-gap appears dynamically in the case of the Sherrington-Kirkpatrick (SK) spin glass. After revisiting and correcting the multi-spin-flip criterion for local stability, we show that stationarity along the hysteresis loop requires that soft spins are frustrated among each other, with a correlation that diverges as $C(λ)\sim 1/λ$, where $λ$ is the larger of two considered local fields. We explain how this arises spontaneously in a marginal system and develop an analogy between the spin dynamics in the SK model and random walks in two dimensions. We discuss the applicability of these findings to hard sphere packings.

cond-mat.stat-mech↗

arXiv2014

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

We study the evolution of structural disorder under cooling in supercooled liquids, focusing on covalent networks. We introduce a model for the energy of networks that incorporates weak non-covalent interactions. We show that at low-temperature, these interactions considerably affect the network topology near the rigidity transition that occurs as the coordination increases. As a result, this transition becomes mean-field and does not present a line of critical points previously argued for, the "rigidity window". Vibrational modes are then not fractons, but instead are similar to the anomalous modes observed in packings of particles near jamming. These results suggest an alternative interpretation for the intermediate phase observed in chalcogenides.

cond-mat.dis-nn↗

arXiv2013

Why glass elasticity affects the thermodynamics and fragility of super-cooled liquids

Super-cooled 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, which 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.

cond-mat.dis-nn↗