Related papers: Pattern formation in growing sandpiles
The adoption of agroecological practices will be crucial to address the challenges of climate change and biodiversity loss. Such practices favor the cultivation of plants in complex mixtures with layouts differing from the monoculture…
We study the directed Abelian sandpile model on a square lattice, with $K$ downward neighbors per site, $K > 2$. The $K=3$ case is solved exactly, which extends the earlier known solution for the $K=2$ case. For $K>2$, the avalanche…
Solid substrates can be endued with self-organized regular stripe patterns of nanoscopic lengthscale by Langmuir-Blodgett transfer of organic monolayers. Here we consider the effect of periodically prepatterned substrates on this process of…
Active Brownian particles (ABPs) are termed out to be a successful way of modeling the moving microorganism on the substrate. In recent studies, it is shown that such organisms can sense the characteristics of the substrate. Motivated by…
The three-dimensional shapes of thin lamina such as leaves, flowers, feathers, wings etc, are driven by the differential strain induced by the relative growth. The growth takes place through variations in the Riemannian metric, given on the…
We study the abelian sandpile model on the upper half plane, and reconsider the correlations of the four height variables lying on the boundary. For more convenience, we carry out the analysis in the dissipative (massive) extension of the…
We propose a general theory for surface patterning in many different biological systems, including mite and insect cuticles, pollen grains, fungal spores, and insect eggs. The patterns of interest are often intricate and diverse, yet an…
The current literature on sandpile models mainly deals with the abelian sandpile model (ASM) and its variants. We treat a less known - but equally interesting - model, namely Zhang's sandpile. This model differs in two aspects from the ASM.…
The Abelian Sandpile Model (ASM) is a paradigm of self-organized criticality (SOC) which is related to $c=-2$ conformal field theory. The conformal fields corresponding to some height clusters have been suggested before. Here we derive the…
Pattern formation and evolution in unsynchronizable complex networks are investigated. Due to the asymmetric topology, the synchronous patterns formed in complex networks are irregular and nonstationary. For coupling strength immediately…
In this paper we study three classes of models widely used in physics, computer science and social science: the Chip Firing Game, the Abelian Sandpile Model and the Chip Firing Game on a mutating graph. We study the set of configurations…
The influence of a periodic spatial forcing on the pattern formation in a generalized Cahn-Hilliard model is studied in order to describe the pattern formation in Langmuir-Blodgett transfer onto prestructured substrates. The occurring…
We present a study of patterns, formed in drying drops of aqueous gelatin solution containing sodium sulphate. The patterns are highly complex, consisting of a hierarchical sequence of rings which form concentric bands as well as dendritic…
We numerically study the directed version of the fixed energy sandpile. On a closed square lattice, the dynamical evolution of a fixed density of sand grains is studied. The activity of the system shows a continuous phase transition around…
Abelian Cayley digraphs can be constructed by using a generalization to $Z^n$ of the concept of congruence in $Z$. Here we use this approach to present a family of such digraphs, which, for every fixed value of the degree, have…
We study erratically moving spatial structures that are found in a driven interface in a random medium at the depinning threshold. We introduce a bond-disordered variant of the Sneppen model and study the effect of extremal dynamics on the…
In this paper we derive the scaling fields in $c=-2$ conformal field theory associated with weakly allowed clusters in abelian sandpile model and show a direct relation between the two models.
We describe the surface properties of a simple lattice model of a sandpile that includes evolving structural disorder. We present a dynamical scaling hypothesis for generic sandpile automata, and additionally explore the kinetic roughening…
Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by space-time trajectories of interacting…
We report the results of three dimensional molecular dynamic simulations on the angle of repose of a sandpile formed by pouring mono-sized cohesionless spherical grains into a granular Hele-Shaw cell. In particular, we are interested to…