相关论文: Self-organized branching process for a one-dimensi…

With a toppling rule which generates metastable sites, we explore the properties of a gradient-driven sandpile that is minimally perturbed at one boundary. In two dimensions we find that the transport of grains takes place along deep…

This survey aims at collecting and presenting results for one-type, discrete time branching processes with random control functions. In particular, the subclass of critical migration processes with different regimes of immigration and…

A stochastic version of the Brusselator model is proposed and studied via the system size expansion. The mean-field equations are derived and shown to yield to organized Turing patterns within a specific parameters region. When determining…

A model which accounts for cracking avalanches in piles of grains subject to external load is introduced and numerically simulated. The stress is stochastically transferred from higher layers to lower ones. Cracked areas exhibit various…

A self-organized model with social percolation process is proposed to describe the propagations of information for different trading ways across a social system and the automatic formation of various groups within market traders. Based on…

We show that a large class of 1D first-order conservation PDEs can be probabilistically represented using multi-type branching processes. The representation holds when the initial conditions are linear combinations of negative exponentials.…

We introduce an external control to reduce the size of avalanches in some sandpile models exhibiting self organized criticality. This rather intuitive approach seems to be missing in the vast literature on such systems. The control action,…

Sand pile models are dynamical systems emphasizing the phenomenon of Self Organized Criticality (SOC). From N stacked grains, iterating evolution rules leads to some critical configuration where a small disturbance has deep consequences on…

We present a unified dynamical mean-field theory for stochastic self-organized critical models. We use a single site approximation and we include the details of different models by using effective parameters and constraints. We identify the…

Boundary-catalytic branching processes describe a broad class of natural phenomena where the population of diffusing particles grows due to their spontaneous binary branching (e.g., division, fission or splitting) on a catalytic boundary…

A single sandpile model with quenched random toppling matrices captures the crucial features of different models of self-organized criticality. With symmetric matrices avalanche statistics falls in the multiscaling BTW universality class.…

We construct and study branching Markov processes on the space of finite configurations of the state space of a given standard process, controlled by a branching kernel and a killing one. In particular, we may start with a superprocess,…

We examine exhaustively the behavior of avalanches in critical height sandpile models based in two- and three-dimensional lattices of various topologies. We get that for two-dimensional lattices the spatial and temporal distributions…

We study self-similarity in random binary rooted trees. In a well-understood case of Galton-Watson trees, a distribution on a space of trees is said to be self-similar if it is invariant with respect to the operation of pruning, which cuts…

We investigate a discrete model consisting of self-propelled particles that obey simple interaction rules. We show that this model can self-organize and exhibit coherent localized solutions in one- and in two-dimensions.In one-dimension,…

We extend earlier results on conditioning of super-Brownian motion to general branching rules. We obtain representations of the conditioned process, both as an $h$-transform, and as an unconditioned superprocess with immigration along a…

We introduce a model for stochastic transport on a one-dimensional substrate with particles assuming different conformations during their stepping cycles. These conformations correspond to different footprints on the substrate: in order to…

The recently introduced self-organizing height-arrow (HA) model is numerically investigated on the square lattice and analytically on the Bethe lattice. The concentration of occupied sites and critical exponents of distributions of…

We study a 2D quasi-static discrete {\it crack} anti-plane model of a tectonic plate with long range elastic forces and quenched disorder. The plate is driven at its border and the load is transfered to all elements through elastic forces.…

Motivated by applications to COVID dynamics, we describe a branching process in random environments model $\{Z_n\}$ whose characteristics change when crossing upper and lower thresholds. This introduces a cyclical path behavior involving…