Related papers: Asymptotics of the single-source stochastic sandpi…
Recently it has been shown that when an equation that allows so-called pulled fronts in the mean-field limit is modelled with a stochastic model with a finite number $N$ of particles per correlation volume, the convergence to the speed…
We investigate the behavior of a two-state sandpile model subjected to a confining potential in one and two dimensions. From the microdynamical description of this simple model with its intrinsic exclusion mechanism, it is possible to…
We investigate the avalanche dynamics of the abelian sandpile model on arbitrarily large balls of the expanded cactus graph (the Cayley graph of the free product $\mathbb{Z}_3 * \mathbb{Z}_2$). We follow the approach of Dhar and Majumdar…
The discrete height abelian sandpile model was introduced by Bak, Tang & Wiesenfeld and Dhar as an example for the concept of self-organized criticality. When the model is modified to allow grains to disappear on each toppling, it is called…
We study the abelian sandpile growth model, where n particles are added at the origin on a stable background configuration in Z^d. Any site with at least 2d particles then topples by sending one particle to each neighbor. We find that with…
The full family of discrete logistic maps has been widely studied both as a canonical example of the period-doubling route to chaos, and as a model of natural processes. In this paper we present a study of the stochastic process described…
The Abelian Sandpile Model is a discrete diffusion process defined on graphs (Dhar \cite{DD90}, Dhar et al. \cite{DD95}) which serves as the standard model of \textit{self-organized criticality}. The transience class of a sandpile is…
This paper presents a generalization of the sandpile model, called the parallel symmetric sandpile model, which inherits the rules of the symmetric sandpile model and implements them in parallel. In this new model, at each step the…
We study the Zhang model of sandpile on a one dimensional chain of length $L$, where a random amount of energy is added at a randomly chosen site at each time step. We show that in spite of this randomness in the input energy, the…
We analyze an optimal stopping problem for random walk in random scenery on general graphs, and determine when it has a finite optimum. We use this to extend a theorem of Levine, Murugan, Peres, and Ugurcan [2016]. They proved that on a…
We study the stabilization time of two common types of influence propagation. In majority processes, nodes in a graph want to switch to the most frequent state in their neighborhood, while in minority processes, nodes want to switch to the…
We present a unified mean-field theory, based on the single site approximation to the master-equation, for stochastic self-organized critical models. In particular, we analyze in detail the properties of sandpile and forest-fire (FF)…
We approach the old-standing problem of vicinal crystal surfaces destabilized by step-down and step step-up currents from a unified modelling viewpoint with focus on both the initial and the intermediate stages of the instability. We…
We extend the model of surface granular flow proposed in \cite{bcre} to account for the effect of an external `wind', which acts as to dislodge particles from the static bed, such that a stationary state of flowing grains is reached. We…
Building on the work of Fyodorov (2004) and Fyodorov and Nadal (2012) we examine the critical behaviour of population of saddles with fixed instability index $k$ in high dimensional random energy landscapes. Such landscapes consist of a…
We study a class of stochastic processes of the type $\frac{d^n x}{dt^n}= v_0\, \sigma(t)$ where $n>0$ is a positive integer and $\sigma(t)=\pm 1$ represents an `active' telegraphic noise that flips from one state to the other with a…
In this study a stabilized finite element method for solving advection-diffusion-reaction equation with spatially variable coefficients has been carried out. Here subgrid scale approach along with algebraic approximation to the sub-scales…
Aeolian sand beds exhibit regular patterns of ripples resulting from the interaction between topography and sediment transport. Their characteristics have been so far related to reptation transport caused by the impacts on the ground of…
The dynamics of sandpile models are mapped to discrete interface equations. We study in detail the Bak-Tang-Wiesenfeld model, a stochastic model with random thresholds, and the Manna model. These are, respectively, discretizations of the…
We consider a fluid queue where the input process consists of N identical sources that turn on and off at exponential waiting times. The server works at the constant rate c and an on source generates fluid at unit rate. This model was first…