Toughness and strength of nanocrystalline graphene.

Pristine monocrystalline graphene is claimed to be the strongest material known with remarkable mechanical and electrical properties. However, graphene made with scalable fabrication techniques is polycrystalline and contains inherent nanoscale line and point defects--grain boundaries and grain-boundary triple junctions--that lead to significant statistical fluctuations in toughness and strength. These fluctuations become particularly pronounced for nanocrystalline graphene where the density of defects is high.

Improving extreme value statistics.

The rate of convergence in extreme value statistics is nonuniversal and can be arbitrarily slow. Further, the relative error can be unbounded in the tail of the approximation, leading to difficulty in extrapolating the extreme value fit beyond the available data. We introduce the T method, and show that by using simple nonlinear transformations the extreme value approximation can be rendered rapidly convergent in the bulk, and asymptotic in the tail, thus fixing both issues.

Imaging atomic rearrangements in two-dimensional silica glass: watching silica's dance.

Structural rearrangements control a wide range of behavior in amorphous materials, and visualizing these atomic-scale rearrangements is critical for developing and refining models for how glasses bend, break, and melt. It is difficult, however, to directly image atomic motion in disordered solids. We demonstrate that using aberration-corrected transmission electron microscopy, we can excite and image atomic rearrangements in a two-dimensional silica glass-revealing a complex dance of elastic and plastic deformations, phase transitions, and their interplay.

From damage percolation to crack nucleation through finite size criticality.

We present a unified theory of fracture in disordered brittle media that reconciles apparently conflicting results reported in the literature. Our renormalization group based approach yields a phase diagram in which the percolation fixed point, expected for infinite disorder, is unstable for finite disorder and flows to a zero-disorder nucleation-type fixed point, thus showing that fracture has a mixed first order and continuous character. In a region of intermediate disorder and finite system sizes, we predict a crossover with mean-field avalanche scaling.

Fracture strength of disordered media: universality, interactions, and tail asymptotics.

We study the asymptotic properties of fracture strength distributions of disordered elastic media by a combination of renormalization group, extreme value theory, and numerical simulation. We investigate the validity of the "weakest-link hypothesis" in the presence of realistic long-ranged interactions in the random fuse model. Numerical simulations indicate that the fracture strength is well-described by the Duxbury-Leath-Beale (DLB) distribution which is shown to flow asymptotically to the Gumbel distribution.

Dielectric breakdown and avalanches at nonequilibrium metal-insulator transitions.

Motivated by recent experiments on the finite temperature Mott transition in VO(2) films, we propose a classical coarse-grained dielectric breakdown model where each degree of freedom represents a nanograin which transitions from insulator to metal with increasing temperature and voltage at random thresholds due to quenched disorder. We describe the properties of the resulting nonequilibrium metal-insulator transition and explain the universal characteristics of the resistance jump distribution. We predict that by tuning voltage, another critical point is approached, which separates a phase of boltlike avalanches from percolationlike ones.