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A new kind of invasion percolation is introduced in order to take into account the inertia of the invader fluid. The inertia strength is controlled by the number N of pores (or steps) invaded after the perimeter rupture. The new model…

Hierarchically structured materials, which possess distinct features on different length scales, are ubiquitous in nature and engineering. In many cases, one structural level may be ordered while another structural level may be disordered.…

We consider a particle in one dimension submitted to amplitude and phase disorder. It can be mapped onto the complex Burgers equation, and provides a toy model for problems with interplay of interferences and disorder, such as the NSS model…

We study the creep response of solids to a constant external load in the framework of a novel fiber bundle model introduced. Analytical and numerical calculations showed that increasing the external load on a specimen a transition takes…

We investigate how the dimensionality of the embedding space affects the microscopic crackling dynamics and the macroscopic response of heterogeneous materials. Using a fiber bundle model with localized load sharing computer simulations are…

Frictional instabilities in fluid saturated granular materials underlie natural hazards, including submarine landslides and earthquake initiation. Experiments show distinct failure behaviors under subaerial and subaqueous conditions due to…

Bundles of many fibers, with statistically distributed thresholds for breakdown of individual fibers and where the load carried by a bursting fiber is equally distributed among the surviving members, are considered. During the breakdown…

We study precursors of failure in hierarchical random fuse network models which can be considered as idealizations of hierarchical (bio)materials where fibrous assemblies are held together by multi-level (hierarchical) cross-links. When…

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…

We consider driven many-particle models which have a phase transition between an active and an absorbing phase. Like previously studied models, we have particle conservation, but here we introduce an additional symmetry - when two particles…

We consider bond percolation on the square lattice with perfectly correlated random probabilities. According to scaling considerations, mapping to a random walk problem and the results of Monte Carlo simulations the critical behavior of the…

We consider the classical Turing instability in a reaction-diffusion system as the secend part of our study on pattern formation. We prove that nonlinear dynamics of a general perturbation of the Turing instability is determined by the…

The failure of 2D numerical cohesive granular steps collapsing under gravity are simulated for a large range of cohesion. Focussing on the cumulative displacement of the grains, and defining a displacement threshold, we establish a sensible…

The shearing instability of a dilute granular mixture composed of smooth inelastic hard spheres or disks is investigated. By using the Navier-Stokes hydrodynamic equations, it is shown that the scaled transversal velocity mode exhibits a…

The rheology of biological tissues is important for their function, and we would like to better understand how single cells control global tissue properties such as tissue fluidity. A confluent tissue can fluidize when cells diffuse by…

We investigate the system size scaling of the net defect number created by a rapid quench in a second-order quantum phase transition from an O(N) symmetric state to a phase of broken symmetry. Using a controlled mean-field expansion for…

We propose a generic model to describe the mechanical response and failure of systems which undergo a series of stick-slip events when subjected to an external load. We model the system as a bundle of fibers, where single fibers can…

In their letter, Andersen, Sornette, and Leung [Phys. Rev. Lett. 78, 2140 (1997)] describe possible behaviors for rupture in disordered media, based on the mean field-like democratic fiber bundle model. In this model, fibers are pulled with…

Quenched disorder - in the sense of the Harris criterion - is generally a relevant perturbation at an absorbing state phase transition point. Here using a strong disorder renormalization group framework and effective numerical methods we…

The finite-size scaling theory for continuous phase transition plays an important role in determining critical point and critical exponents from the size-dependent behaviors of quantities in the thermodynamic limit. For percolation phase…