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Relaxation processes of dislocation systems are studied by two-dimensional dynamical simulations. In order to capture generic features, three physically different scenarios were studied and power-law decays found for various physical…
Jamming and percolation transitions in the standard random sequential adsorption of particles on regular lattices are characterized by a universal set of critical exponents. The universality class is preserved even in the presence of…
A new class of lattice gas models with trivial interactions but constrained dynamics are introduced. These are proven to exhibit a dynamical glass transition: above a critical density, rho_c, ergodicity is broken due to the appearance of an…
We report on a new behavior found in numerical simulations of spherically symmetric gravitational collapse in self-gravitating SU(2) sigma models at intermediate gravitational coupling constants: The critical solution (between black hole…
Kinetics of collision processes with linear mixing rules are investigated analytically. The velocity distribution becomes self-similar in the long time limit and the similarity functions have algebraic or stretched exponential tails. The…
We discuss the spatiotemporal behavior of local density and its relation to dynamical heterogeneity in a highly supercooled liquid by using molecular dynamics simulations of a binary mixture with different particle sizes in two dimensions.…
The site percolation on the triangular lattice stands out as one of the few exactly solved statistical systems. By initially configuring critical percolation clusters of this model and randomly reassigning the color of each percolation…
We study an abstracted model of neuronal activity via numerical simulation, and report spatiotemporal pattern formation and critical like dynamics. A population of pulse coupled, discretised, relaxation oscillators is simulated over…
We study models of spatial growth processes where initially there are sources of growth (indicated by the colour green) and sources of a growth-stopping (paralyzing) substance (indicated by red). The green sources expand and may merge with…
We present a systematic study of dynamical heterogeneity in a model for permanent gels, upon approaching the gelation threshold. We find that the fluctuations of the self intermediate scattering function are increasing functions of time,…
Crackling noise is a common feature in many systems that are pushed slowly, the most familiar instance of which is the sound made by a sheet of paper when crumpled. In percolation and regular aggregation clusters of any size merge until a…
Despite original claims of a first-order transition in the product rule model proposed by Achlioptas et al. [Science 323, 1453 (2009)], recent studies indicate that this percolation model, in fact, displays a continuous transition. The…
We prove the emergence of spatially correlated dynamics in slowly compacting dense granular media by analyzing analytically and numerically multi-point correlation functions in a simple particle model characterized by slow non-equilibrium…
Fractals emerge everywhere in nature, exhibiting intricate geometric complexities through the self-organizing patterns that span across multiple scales. Here, we investigate beyond steady-states the interplay between this geometry and the…
We derive an exact, simple relation between the average number of clusters and the wrapping probabilities for two-dimensional percolation. The relation holds for periodic lattices of any size. It generalizes a classical result of Sykes and…
Self-organized criticality is a dynamical system property where, without external tuning, a system naturally evolves towards its critical state, characterized by scale-invariant patterns and power-law distributions. In this paper, we…
Recently, a hybrid percolation transitions (HPT) that exhibits both a discontinuous transition and critical behavior at the same transition point has been observed in diverse complex systems. In spite of considerable effort to develop the…
We consider an infinite-dimensional stochastic clustering model on $\mathbb{R}$. In discrete time, each point of a unit-intensity simple point process moves halfway toward either of its left or right neighbors, chosen uniformly at random.…
In jamming systems like colloids, emulsions, foams, and biological tissues, significant deformation is essential for processes such as material scraping or wound self-healing. To adequately spread a foam or cream over a surface, external…
Percolation is the simplest fundamental model in statistical mechanics that exhibits phase transitions signaled by the emergence of a giant connected component. Despite its very simple rules, percolation theory has successfully been applied…