Related papers: Mapping Self-Organized Criticality onto Criticalit…
We investigate the transition to Self Organized Criticality in a two-dimensional model of a flux tube with a background flow. The magnetic induction equation, represented by a partial differential equation with a stochastic source term, is…
Recent advancements in the synthesis of anisotropic macromolecules and nanoparticles have spurred an immense interest in theoretical and computational studies of self-assembly. The cornerstone of such studies is the role of shape in…
We provide a systematic approach for testing self-organization (SO) algorithms. The main challenges for such a testing domain are the strongly ramified state space, the possible error masking, the interleaving of mechanisms, and the oracle…
We do not attempt to provide yet another definition of selforganization, but explore the conditions under which we can model a system as self-organizing. These involve the dynamics of entropy, and the purpose, aspects, and description level…
It is well known that conventional simulation algorithms are inefficient for the statistical description of macroscopic systems exactly at the critical point due to the divergence of the corresponding relaxation time (critical slowing…
Lattice models of coupled dynamical systems lead to a variety of complex behaviors. Between the individual motion of independent units and the collective behavior of members of a population evolving synchronously, there exist more…
Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…
Consider the convex hull of a collection of disjoint open discs with radii $1/2$. The boundary of the convex hull consists of a finite number of line segments and arcs. Randomly choose a point in one of the arcs in the boundary so that the…
Despite broad interest in self-organizing systems, there are few quantitative, experimentally-applicable criteria for self-organization. The existing criteria all give counter-intuitive results for important cases. In this Letter, we…
The Abelian Sandpile Model (ASM) is a paradigm of self-organized criticality (SOC) which is related to $c=-2$ conformal field theory. The conformal fields corresponding to some height clusters have been suggested before. Here we derive the…
Self-Organizing Map algorithms have been used for almost 40 years across various application domains such as biology, geology, healthcare, industry and humanities as an interpretable tool to explore, cluster and visualize high-dimensional…
The precise determination of the universality classes in self-organized critical phenomena (SOC) is still an unsolved problem. Different SOC models like sandpile, linear interface depinning, and the Barkhausen effect have been investigated…
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…
We show that the coupled complex systems can evolve into a new kind of self-organized critical state where each subsystem is not critical, however, they cooperate to be critical. This criticality is different from the classical BTW…
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…
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.…
The underlying physical concept of computing out-of-time-ordered correlation (OTOC) is a significant new tool within the framework of quantum field theory, which now-a-days is treated as a measure of random fluctuations. In this paper, by…
In statistical and nonlinear systems, two qualitatively distinct parameter regions are typically identified: the regular region, characterized by smooth behavior of key quantities, and the critical region, where these quantities exhibit…
In formation control, an ensemble of autonomous agents is required to stabilize at a given configuration in the plane, doing so while agents are allowed to observe only a subset of the ensemble. As such, formation control provides a rich…
Rare events such as conformational changes in biomolecules, phase transitions, and chemical reactions are central to the behavior of many physical systems, yet they are extremely difficult to study computationally because unbiased…