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We investigate the statistics of record breaking events in the time series of crackling bursts in a fiber bundle model of the creep rupture of heterogeneous materials. In the model fibers break due to two mechanisms: slowly accumulating…

Although impurities are unavoidable in real-world and experimental systems, most numerical studies on nucleation focus on pure (impurity-free) systems. As a result, the role of impurities in phase transitions remains poorly understood,…

We consider the growth of a vicinal crystal surface in the presence of a step-edge barrier. For any value of the barrier strength, measured by the length l_es, nucleation of islands on terraces is always able to destroy asymptotically…

Notwithstanding the evidence against them, classical variational phase-field models continue to be used and pursued in an attempt to describe fracture nucleation in elastic brittle materials. In this context, the main objective of this…

While network abrupt breakdowns due to overloads and cascading failures have been studied extensively, the critical exponents and the universality class of such phase transitions have not been discussed. Here, we study breakdowns triggered…

We study a system composed from two interdependent networks A and B, where a fraction of the nodes in network A depends on the nodes of network B and a fraction of the nodes in network B depends on the nodes of network A. Due to the…

We investigate the gravity driven rapid failure of a granular step composed of non-cohesive steel beads. The step is initially held together with electromagnets, and released when the current is switched off. We visualize the surface and…

We discuss the relevance of methods of graph theory for the study of damage in simple model materials described by the random fuse model. While such methods are not commonly used when dealing with regular random lattices, which mimic…

We study numerically the failure of an interface joining two elastic materials under load using a fiber bundle model connected to an elastic half space. We find that the breakdown process follows the equal load sharing fiber bundle model…

We investigate the breakdown of disordered networks under the action of an increasing external---mechanical or electrical---force. We perform a mean-field analysis and estimate scaling exponents for the approach to the instability. By…

We present a linear stability analysis to demonstrate that a flat coherent phase boundary formed by the (de)intercalation of solutes into a compound is unstable against perturbations with wavelengths larger than a critical wavelength. This…

A bundle of many fibers with stochastically distributed breaking thresholds is considered as a model of composite materials. The fibers are assumed to share the load equally, and to obey Hookean elasticity up to the breaking point. The…

This paper studies growth, percolation, and correlations in disordered fiber networks. We start by introducing a 2D continuum deposition model with effective fiber-fiber interactions represented by a parameter $p$ which controls the degree…

We investigate the fragmentation process of solid materials with crystalline and amorphous phases using the discrete element method. Damage initiates inside spherical samples above the contact zone in a region where the circumferential…

We study diffusion of particles in large-scale simulations of one-dimensional stochastic sandpiles, in both the restricted and unrestricted versions. The results indicate that the diffusion constant scales in the same manner as the activity…

Dynamical friction governs the orbital decay of massive perturbers within galaxies and dark matter halos, yet its standard Chandrasekhar formulation fails in systems with cores of (roughly) constant density, where inspiral can halt or even…

We perform a probabilistic investigation on the effect of systematically removing imperfections on the buckling behavior of pressurized thin, elastic, hemispherical shells containing a distribution of defects. We employ finite element…

$k$-Core percolation has served as a paradigmatic model of discontinuous percolation for a long time. Recently it was revealed that the order parameter of $k$-core percolation of random networks additionally exhibits critical behavior. Thus…

We investigate the scaling properties of the sources of crackling noise in a fully-dynamic numerical model of sedimentary rocks subject to uniaxial compression. The model is initiated by filling a cylindrical container with randomly-sized…

We revisit a simple dynamical model of rupture in random media with long-range elasticity to test whether rupture can be seen as a first-order or a critical transition. We find a clear scaling of the macroscopic modulus as a function of…