Related papers: Percolation and localization in the random fuse mo…
Cohesive particles form agglomerates that are usually very porous. Their geometry, particularly their fractal dimension, depends on the agglomeration process (diffusion-limited or ballistic growth by adding single particles or…
Real networks are vulnerable to random failures and malicious attacks. However, when a node is harmed or damaged, it may remain partially functional, which helps to maintain the overall network structure and functionality. In this paper, we…
The study of percolation in so-called {\em nested subgraphs} implies a generalization of the concept of percolation since the results are not linked to specific graph process. Here the behavior of such graphs at criticallity is studied for…
We study the effect of the competition between disorder and stress enhancement in fracture processes using the local load sharing fiber bundle model, a model that hovers on the border between analytical tractability and numerical…
The precise mechanisms underlying the failure of multi-phase materials may be strongly dependent on the material's microstructural morphology. Micromechanical modeling has provided much insight into this dependence, but uncertainties remain…
We investigated two-dimensional brittle fragmentation with a flat impact experimentally, focusing on the low impact energy region near the fragmentation-critical point. We found that the universality class of fragmentation transition…
Percolation, the formation of a macroscopic connected component, is a key feature in the description of complex networks. The dynamical properties of a variety of systems can be understood in terms of percolation, including the robustness…
I report on the experimental confirmation that critical percolation statistics underlie the ordering kinetics of twisted nematic phases in the Allen-Cahn universality class. Soon after the ordering starts from a homogeneous disordered phase…
Bootstrap percolation in (random) graphs is a contagion dynamics among a set of vertices with certain threshold levels. The process is started by a set of initially infected vertices, and an initially uninfected vertex with threshold $k$…
In biological materials, strong binding despite an applied load force is often based on clusters of dynamic bonds that share the load. Different macroscopic behaviors have been described depending on whether the load is shared locally or…
We study the high-velocity regime mode-I fracture instability when small microbranches start to appear near the main crack, using large scale simulations. Some of the features of those microbranches have been reproduced qualitatively in…
We study a generalization of site percolation on a simple cubic lattice, where not only single sites are removed randomly, but also entire parallel columns of sites. We show that typical clusters near the percolation transition are very…
Percolation is an emblematic model to assess the robustness of interconnected systems when some of their components are corrupted. It is usually investigated in simple scenarios, such as the removal of the system's units in random order, or…
A theoretical model based on the molecular interactions between a growing tumor and a dynamically evolving blood vessel network describes the transformation of the regular vasculature in normal tissues into a highly inhomogeneous tumor…
Order parameter fluctuations (the largest cluster size distribution) are studied within a three-dimensional bond percolation model on small lattices. Cumulant ratios measuring the fluctuations exhibit distinct features near the percolation…
We study the competition between thermal fluctuations and stress enhancement in the failure process of a disordered system by using a local load sharing fiber bundle model. The thermal noise is introduced by defining a failure probability…
Damage nucleation from repeated dislocation absorption at a grain boundary is simulated with molecular dynamics. At the grain boundary-dislocation intersection site, atomic shuffling events determine how the free volume brought by the…
This chapter introduces the fracture nucleation process, their (extreme) statistics in disordered solids, in fiber bundle models, and in the two fractal overlap models of earthquake.
We analyze the scaling of avalanche precursors in the three dimensional random fuse model by numerical simulations. We find that both the integrated and non-integrated avalanche size distributions are in good agreement with the results of…
A particular failure mode of highly porous brittle materials consists in the propagation of cracks under uniaxial compressive loads. Such 'anticracks' have been observed in a range of materials, from snow and porous sandstone to brittle…