Synchronization phenomena in large populations of interacting elements are the subject of
intense research efforts in physical, biological, chemical, and social systems. A successful …

High speed dislocations have long been identified as the dominant feature governing the
plastic response of crystalline materials subjected to high strain rates, controlling …

We study the stability and evolution of various elastic defects in a flat graphene sheet and
the electronic properties of the most stable configurations. Two types of dislocations are …

We show that nonlinear continuum elasticity can be effective in modeling plastic flows in
crystals if it is viewed as a Landau theory with an infinite number of equivalent energy wells …

We study the mechanical response of a dislocation-free 2D crystal under homogenous
shear using a new mesoscopic approach to crystal plasticity, a Landau-type theory …

The present book introduces and develops mathematical techniques for the treatment of
nonlinear waves and singular perturbation methods at a level that is suitable for graduate …

The cores of edge dislocations, edge dislocation dipoles, and edge dislocation loops in
planar graphene have been studied by means of periodized discrete elasticity models. To …

Power law fluctuations and scale-free spatial patterns are known to characterize steady state
plastic flow in crystalline materials. In this Letter we study the emergence of correlations in a …

We develop a novel continuum description of lattice dynamics for a particle chain with
nearest neighbor interactions. Our continuum model interpolates discrete solutions and …

Steady plastic flows have been compared to developed turbulence because the two
phenomena share the inherent complexity of particle trajectories, the scale free spatial …