Related papers: Self-organized criticality as an absorbing-state p…

The avalanche properties of models that exhibit 'self-organized criticality' (SOC) are still mostly awaiting theoretical explanations. A recent mapping (Europhys. Lett.~53, 569) of many sandpile models to interface depinning is presented…

Self-organized criticality elucidates the conditions under which physical and biological systems tune themselves to the edge of a second-order phase transition, with scale invariance. Motivated by the empirical observation of bimodal…

This paper applies the theory of continuous phase transitions of statistical mechanics to a slider-block model. The slider-block model is chosen as a representative of systems with avalanches. Similar behavior can be observed in a…

Kinetic equations, which explicitly take into account the branching nature of sandpile avalanches, are derived. The dynamics of the sandpile model is described by the generating functions of a branching process. Having used the results…

We study the critical behavior of the dissipative abelian sandpile model on Z with dissipative sites at arbitrary positions (x_k). This is equivalent to studying whether the expected stopping time of a trapped random walk on Z is finite.…

We study a one-dimensional fixed-energy version (that is, with no input or loss of particles), of Manna's stochastic sandpile model. The system has a continuous transition to an absorbing state at a critical value $\zeta_c$ of the particle…

Rotational constraint representing a local external bias generally has non-trivial effect on the critical behavior of lattice statistical models in equilibrium critical phenomena. In order to study the effect of rotational bias in a out of…

The origin of self-organized criticality in a model without conservation law (Olami, Feder, and Christensen, Phys. Rev. Lett. {\bf 68}, 1244 (1992)) is studied. The homogeneous system with periodic boundary condition is found to be periodic…

In this thesis we present few theoretical studies of the models of self-organized criticality. Following a brief introduction of self-organized criticality, we discuss three main problems. The first problem is about growing patterns formed…

The theory of a flux steady-state related to avalanche formation is presented for the simplest model of a sand pile within framework of the Lorenz approach. The stationary values of sand velocity and sand pile slope are derived as functions…

Spatial self-similarity is a hallmark of critical phenomena. We study the dynamic process of percolation, in which bonds are incrementally added to an initially empty lattice until the system becomes fully occupied. By tracking the gap --…

Self-organizing system is studied whose behavior is governed by field of an order parameter, a fluctuation amplitude of conjugate field and a couple of Grassmannian conjugated fields that define the entropy as a control parameter. Within…

We discuss mean-field theories for self-organized criticality and the connection with the general theory of branching processes. We point out that the nature of the self-organization is not addressed properly by the previously proposed…

The Stock Market is a complex self-interacting system, characterized by an intermittent behaviour. Periods of high activity alternate with periods of relative calm. In the present work we investigate empirically about the possibility that…

Extremal dynamics represents a path to self-organized criticality in which the order parameter is tuned to a value of zero. The order parameter is associated with a phase transition to an absorbing state. Given a process that exhibits a…

This paper develops a Hall-Sandpile model of economic instability that combines a Hall-like transversal stress mechanism with sandpile threshold dynamics on a real production-network substrate. In analogy with the physical Hall effect,…

Self-organized criticality (SOC) refers to the ability of complex systems to evolve towards a 2nd-order phase transition at which interactions between system components lead to scale-invariant events beneficial for system performance. For…

We review the properties of the self-organized critical (SOC) forest-fire model. The paradigm of self-organized criticality refers to the tendency of certain large dissipative systems to drive themselves into a critical state independent of…

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 review some recent results on the relations between sandpiles and a class of absorbing state phase transitions. We use the concept of fixed energy sandpiles (FES), in which external driving and dissipation are absent. FES are shown to…