Related papers: Evolutive sandpiles
Planetary systems can evolve dynamically even after the planets themselves have fully formed, and there is circumstantial evidence that most planetary systems become unstable after the disappearance of the gaseous protoplanetary disk.…
An interesting feature of growth in animals is that different parts of the body grow at approximately the same rate. This property is called proportionate growth. In this paper, we review our recent work on patterns formed by adding $N$…
The recently developed method (Paper 1) enabling one to investigate the evolution of dynamical systems with an accuracy not dependent on time is developed further. The classes of dynamical systems which can be studied by that method are…
Rapid advance of experimental techniques provides an unprecedented in-depth view into complex developmental processes. Still, little is known on how the complexity of multicellular organisms evolved by elaborating developmental programs and…
Since their introduction in the 80s, sandpile models have raised interest for their simple definition and their surprising dynamical properties. In this survey we focus on the computational complexity of the prediction problem, namely, the…
Granular materials, composed of discrete solid grains, can be modeled as simple mechanical systems. However, these materials can undergo spontaneous slow deformation, or creep, even under small forces and while in apparent mechanical…
We study a nonconservative sandpile model in one dimension, in which, if the height at any site exceeds a threshold value, the site topples by transferring one particle along each bond connecting it to its neighbours. Its height is then set…
We prove a necessary and sufficient condition for an Abelian Sandpile Model (ASM) to be avalanche-finite, namely: all unstable states of the system can be brought back to stability in finite number of topplings. The method is also…
We study a model of ``organized'' criticality, where a single avalanche propagates through an \textit{a priori} static (i.e., organized) sandpile configuration. The latter is chosen according to an i.i.d. distribution from a Borel…
We introduce the sandpile model on multiplex networks with more than one type of edge and investigate its scaling and dynamical behaviors. We find that the introduction of multiplexity does not alter the scaling behavior of avalanche…
We consider a time varying analogue of the Erd{\H o}s-R{\' e}nyi graph and study the topological variations of its associated clique complex. The dynamics of the graph are stationary and are determined by the edges, which evolve…
We define a new version of sandpile model which is very similar to Abelian Sandpile Model (ASM), but the height variables are continuous ones. With the toppling rule we define in our model, we show that the model can be mapped to ASM, so…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
The high-multiplicity exoplanet systems are generally more tightly packed when compared to the solar system. Such compact multi-planet systems are often susceptible to dynamical instability. We investigate the impact of dynamical…
We introduce a model for a sandpile, with N sites, critical height N and each site connected to every other site. It is thus a mean-field model in the spin-glass sense. We find an exact solution for the steady state probability distribution…
When the focus is on the relationships or interactions between entities, graphs offer an intuitive model for many real-world data. Such graphs are usually large and change over time, thus, requiring models and strategies that explore their…
We introduce a new lattice growth model, which we call boundary sandpile. The model amounts to potential-theoretic redistribution of a given initial mass on $\mathbb{Z}^d$ ($d\geq 2$) onto the boundary of an (a priori) unknown domain. The…
I analyse a model of an evolving network represented as a directed graph; each node corresponds to one molecular species and the links to catalytic interactions between species. Over short timescales the graph remains fixed while relative…
Multiple systems play an important role in the evolution of star clusters. First we discuss several formation mechanisms which depend on the presence of binaries, either primordial or of dynamical origin. Hierarchical configurations are…