Related papers: Self-organized criticality via stochastic partial …
The propagator for the activity in a broad class of self-organized critical models obeys an imaginary-time Schr\"odinger equation with a nonlocal, history-dependent potential representing memory. Consequently, the probability for an…
Controlling self-organizing systems is challenging because the system responds to the controller. Here we develop a model that captures the essential self-organizing mechanisms of Bak-Tang-Wiesenfeld (BTW) sandpiles on networks, a…
The "Self-organized criticality" (SOC), introduced in 1987 by Bak, Tang and Wiesenfeld, was an attempt to explain the 1/f noise, but it rapidly evolved towards a more ambitious scope: explaining scale invariant avalanches. In two decades,…
In this lecture we present an overview of the physics of irreversible fractal growth process, with particular emphasis on a class of models characterized by {\em quenched disorder}. These models exhibit self-organization, with critical…
Large scale organization in ensembles of events of atmospheric convection can be generated by the combined effect of forcing and of the interaction between the raising plumes and the environment. Here the "large scale" refers to the space…
We study the critical dynamics of a real scalar field in two dimensions near a continuous phase transition. We have built up and solved Dynamical Renormalization Group equations at one-loop approximation. We have found that, different form…
We study the discrete nonlinear Schr\"oinger equation with weak disorder, focusing on the regime when the nonlinearity is, on the one hand, weak enough for the normal modes of the linear problem to remain well resolved, but on the other,…
The concept of Self-Organized Criticality (SOC) was proposed in an attempt to explain the widespread appearance of power-law in nature. It describes a mechanism in which a system reaches spontaneously a state where the characteristic events…
We consider simple examples of self-organized critical systems on one-dimensional superlattices without local particle conservation laws. The set of all recurrence states are also found in these examples using a method similar to the…
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…
A dynamic scaling Ansatz for the approach to the Self-Organized Critical (SOC) regime is proposed and tested by means of extensive simulations applied to the Bak-Sneppen model (BS), which exhibits robust SOC behavior. Considering the…
In this paper we study singular kinetic equations on $\mathbb{R}^{2d}$ by the paracontrolled distribution method introduced in \cite{GIP15}. We first develop paracontrolled calculus in the kinetic setting, and use it to establish the global…
A self-organized branching process is introduced to describe one-dimensional ricepile model with stochastic topplings. Although the branching processes are generally supposed to describe well the systems in high dimension, our modification…
We present the first solvable non-conservative sandpile-like critical model of Self-Organized Criticality (SOC), and thereby substantiate the suggestion by Vespignani and Zapperi [A. Vespignani and S. Zapperi, Phys. Rev. E 57, 6345 (1998)]…
The concept of "self-organized criticality" (SOC) has been introduced by Bak, Tang, and Wiesenfeld (1987) to describe the statistics of avalanches on the surface of a sandpile with a critical slope, which produces a scale-free powerlaw size…
The concept of percolation is combined with a self-consistent treatment of the interaction between the dynamics on a lattice and the external drive. Such a treatment can provide a mechanism by which the system evolves to criticality without…
The hypothesis of self-organized criticality explains the existence of long-range `space-time' correlations, observed inseparably in many natural dynamical systems. A simple link between these correlations is yet unclear, particularly in…
We have investigated the essential ingredients allowing a system to show Self Organized Criticality (SOC) in its collective behavior. Using the Bak-Sneppen model of biological evolution as our paradigm, we show that the random microscopic…
New weak and strong existence and weak and strong uniqueness results for multi-dimensional stochastic McKean--Vlasov equations are established under relaxed regularity conditions. Weak existence is a variation of Krylov's weak existence for…
We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex and the the variable control has two components, the first being absolutely continuous and the second singular. The system is…