We study the patterns formed by adding N sand grains at a single site in the abelian sandpile model on an infinite square lattice, when in the initial configuration all sites have same height. When this height is 2, stable heights being 0–3, we show that the perturbed region is a square, whose...

We recently proposed a mechanism for inducing a Turing instability by alternation of reaction–diffusion dynamics each of which is pattern-free. Herein we shed light on the question of which particular switching schemes produce that instability and which do not. We also consider a particular...

A foam is a space-filling cellular pattern, that can be decomposed into successive layers or strata. Each layer contains all cells at the same topological distance to an origin (cell, cluster of cells, or basal layer). The disorder of the underlying structure imposes a characteristic roughening...

After a brief introduction we review the nonperturbative weak noise approach to the Kardar–Parisi–Zhang (KPZ) equation in one dimension. We argue that the strong coupling aspects of the KPZ equation are related to the existence of localized propagating domain walls or solitons representing...

We analyze a system of reacting elements harmonically coupled to nearest neighbors in the continuum limit. An analytic solution is found for traveling waves. The procedure is used to find oscillatory as well as solitary waves. A comparison is made between exact solutions and solutions of the...

We report numerical simulations of the structure of advancing burning fronts under conditions where the dominating transport mechanisms is the diffusion of oxygen and heat. The model we study describes the interplay between two diffusive fields: one which accounts for the destabilizing mechanism...

We study the effect of external harmonic forcing on a one-dimensional complex Ginzburg–Landau equation (CGLE). For a sufficiently large forcing amplitude, a homogeneous state with no spatial structure is observed. As the forcing amplitude decreases, the state becomes unstable, forming a...

Our experiments on a vertically oscillated granular layer reveal that spatial patterns emerge in two stages following a change of parameter into the pattern-forming regime: an initial, domain-forming stage and a later stage in which domains coarsen to form ultimately an extended regular pattern....