Inferring the particle-wise dynamics of amorphous solids from the local structure at the jamming point

Revealing the improved stability of amorphous boron-nitride upon carbon doping

We report on a large improvement of the thermal stability and mechanical properties of amorphous boron-nitride upon carbon doping. By generating versatile force fields using first-principles and machine learning simulations, we investigate the structural properties of amorphous boron-nitride with varying contents of carbon (from a few percent to 40 at%). We found that for 20 at% of carbon, the sp³/sp² ratio reaches a maximum with a negligible graphitisation effect, resulting in an improvement of the thermal stability by up to 20% while the bulk Young's modulus increases by about 30%. These results provide a guide to experimentalists and engineers to further tailor the growth conditions of BN-based compounds as non-conductive diffusion barriers and ultralow dielectric coefficient materials for a number of applications including interconnect technology.

Hard-sphere jamming through the lens of linear optimization

The jamming transition is ubiquitous. It is present in granular matter, foams, colloids, structural glasses, and many other systems. Yet, it defines a critical point whose properties still need to be fully understood. Recently, a major breakthrough came about when the replica formalism was extended to build a mean-field theory that provides an exact description of the jamming transition of spherical particles in the infinite-dimensional limit. While such theory explains the jamming critical behavior of both soft and hard spheres, investigating the transition in finite-dimensional systems poses very difficult and different problems, in particular from the numerical point of view. Soft particles are modeled by continuous potentials; thus, their jamming point can be reached through efficient energy minimization algorithms. In contrast, the latter methods are inapplicable to hard-sphere (HS) systems since the interaction energy among the particles is always zero by construction. To overcome these difficulties, here we recast the jamming of hard spheres as a constrained optimization problem and introduce the CALiPPSO algorithm, capable of readily producing jammed HS packings without including any effective potential. This algorithm brings a HS configuration of arbitrary dimensions to its jamming point by solving a chain of linear optimization problems. We show that there is a strict correspondence between the force balance conditions of jammed packings and the properties of the optimal solutions of CALiPPSO, whence we prove analytically that our packings are always isostatic and in mechanical equilibrium. Furthermore, using extensive numerical simulations, we show that our algorithm is able to probe the complex structure of the free-energy landscape, finding qualitative agreement with mean-field predictions. We also characterize the algorithmic complexity of CALiPPSO and provide an open-source implementation of it.

Collective Drifts in Vibrated Granular Packings: The Interplay of Friction and Structure

We simulate vertically shaken dense granular packings with horizontal periodic boundary conditions. A coordinated translating motion of the whole medium emerges when the horizontal symmetry is broken by disorder or defects in the packing and the shaking is weak enough to conserve the structure. We argue that such a drift originates in the interplay between structural symmetry breaking and frictional forces transmitted by the vibrating plate. A nonlinear ratchet model with stick slips reproduces many faces of the phenomenon. The collective motion discussed here underlies phenomena observed recently with vibrofluidized granular materials, such as persistent rotations and anomalous diffusion.

Correlation of plastic events with local structure in jammed packings across spatial dimensions

SignificanceMean-field theories, exact in the limit of infinite spatial dimensions, succeed in describing many features of glasses and amorphous solids in low dimensions, leading to considerable effort to understand how behavior evolves with dimension. Until now, all evidence has supported a picture in which "localized physics," responsible for deviations from mean-field behavior in low dimensions, fades away with rising dimension. Our work shows that rearrangements, in which particles change relative positions leading to fluid-like response, reveal a different picture of dimensional cross-over. We find that rearrangements, which are localized in two- and three-dimensional systems and correlated with local structure, remain just as correlated with local structure up to five dimensions, suggesting that local structure is important even in high dimensions.

Finite-size effects in the microscopic critical properties of jammed configurations: A comprehensive study of the effects of different types of disorder

Jamming criticality defines a universality class that includes systems as diverse as glasses, colloids, foams, amorphous solids, constraint satisfaction problems, neural networks, etc. A particularly interesting feature of this class is that small interparticle forces (f) and gaps (h) are distributed according to nontrivial power laws. A recently developed mean-field (MF) theory predicts the characteristic exponents of these distributions in the limit of very high spatial dimension, d→∞ and, remarkably, their values seemingly agree with numerical estimates in physically relevant dimensions, d=2 and 3. These exponents are further connected through a pair of inequalities derived from stability conditions, and both theoretical predictions and previous numerical investigations suggest that these inequalities are saturated. Systems at the jamming point are thus only marginally stable. Despite the key physical role played by these exponents, their systematic evaluation has yet to be attempted. Here, we carefully test their value by analyzing the finite-size scaling of the distributions of f and h for various particle-based models for jamming. Both dimension and the direction of approach to the jamming point are also considered. We show that, in all models, finite-size effects are much more pronounced in the distribution of h than in that of f. We thus conclude that gaps are correlated over considerably longer scales than forces. Additionally, remarkable agreement with MF predictions is obtained in all but one model, namely near-crystalline packings. Our results thus help to better delineate the domain of the jamming universality class. We furthermore uncover a secondary linear regime in the distribution tails of both f and h. This surprisingly robust feature is understood to follow from the (near) isostaticity of our configurations.