Related papers: Exact solution of stochastic directed sandpile mod…
A dissipative stochastic sandpile model is constructed on one and two dimensional small-world networks with different shortcut densities $\phi$ where $\phi=0$ and $1$ represent a regular lattice and a random network respectively. In the…
Finite dimensional solutions to a class of stochastic partial differential equations are obtained extending the differential constraints method for deterministic PDE to the stochastic framework. A geometrical reformulation of the stochastic…
The critical exponents for a class of one-dimensional models of interface depinning in disordered media can be calculated through a mapping onto directed percolation (DP). In higher dimensions these models give rise to directed surfaces,…
We discuss various critical densities in sandpile models. The stationary density is the average expected height in the stationary state of a finite-volume model; the transition density is the critical point in the infinite-volume…
The divisible sandpile starts with i.i.d. random variables ("masses") at the vertices of an infinite, vertex-transitive graph, and redistributes mass by a local toppling rule in an attempt to make all masses at most 1. The process…
Two-component sandpile models are investigated numerically and theoretically. Monte Calro simulations are performed to show that probability distribution functions of avalanche size and lifetime obey power laws whose exponents are…
With extensive Monte Carlo simulations, we present high-precision estimates of the critical exponents of branching annihilating random walks with two offspring, a prototypical model of the directed Ising universality class in one dimension.…
The single-correlator conformal bootstrap is solved numerically for several values of dimension 4>d>2 using the available SDPB and Extremal Functional methods. Critical exponents and other conformal data of low-lying states are obtained…
We obtain an analytical solution of a one-dimensional sandpile problem in a thick flow regime, when it can be formulated in terms of linear equations. It is shown that a space periodicity takes place during the sandpile evolution even for a…
In the single-source sandpile model, a number $N$ grains of sand are positioned at a central vertex on the 2-dimensional grid $\mathbb{Z}^2$. We study the stabilisation of this configuration for a stochastic sandpile model based on a…
We study stochastic delay differential equations (SDDE) where the coefficients depend on the moving averages of the state process. As a first contribution, we provide sufficient conditions under which a linear path functional of the…
Critical properties of hulls of directed spiral percolation (DSP) clusters are studied on the square and triangular lattices in two dimensions (2D). The hull fractal dimension ($d_H$) and some of the critical exponents associated with…
We study an inhomogeneous sandpile model in which two different toppling rules are defined. For any site only one rule is applied corresponding to either the Bak, Tang and Wiesenfeld model {[}P.Bak, C. Tang, and K. Wiesenfeld, Phys. Rev.…
The BTW sandpile model is considered on three dimensional percolation lattice which is tunned with the occupation parameter $p$. Along with the three-dimensional avalanches, we study the energy propagation in two-dimensional cross-sections.…
Using Monte Carlo simulations on different system sizes we determine with high precision the critical thresholds of two families of directed percolation models on a square lattice. The thresholds decrease exponentially with the degree of…
A general maximum principle (necessary and sufficient conditions) for an optimal control problem governed by a stochastic differential equation driven by an infinite dimensional martingale is established. The solution of this equation takes…
We discuss an idea of how 3D critical exponents can be determined by Conformal Field Theory techniques.
A stochastic nonlinear partial differential equation is built for two different models exhibiting self-organized criticality, the Bak, Tang, and Wiesenfeld (BTW) sandpile model and the Zhang's model. The dynamic renormalization group (DRG)…
We propose a method of studying the continuous percolation of aligned objects as a limit of a corresponding discrete model. We show that the convergence of a discrete model to its continuous limit is controlled by a power-law dependency…
This article is based on a talk given by one of us (EVI) at the conference ``StatPhys-Taipei-1997''. It overviews the exact results in the theory of the sandpile model and discusses shortly yet unsolved problem of calculation of avalanche…