Related papers: A Master Equation for Power Laws
The present paper describes a stochastic model of fracture, whose fragment size distribution can be calculated analytically as a power-law-like distribution. The model is basically cascade fracture, but incorporates the effect that each…
A simple fragmentation model is introduced and analysed. We show that, under very general conditions, an effective power law for the mass distribution arises with realistic exponent. This exponent has a universal limit, but in practice the…
A two-state master equation based decision making model has been shown to generate phase transitions, to be topologically complex and to manifest temporal complexity through an inverse power-law probability distribution function in the…
Recurrence networks are a novel tool of nonlinear time series analysis allowing the characterisation of higher-order geometric properties of complex dynamical systems based on recurrences in phase space, which are a fundamental concept in…
We study fragmentation numerically using a simple model in which an object is taken to be a set of particles that interact pairwisely via a Lennard-Jones potential while the effect of the fragmentation-induced forces is represented by some…
Power law size distribution is found to associate with fractal, self-organized behaviors and patterns of complex systems. Such distribution also emerges from natural lakes, with potentially important links to the dynamics of lake systems.…
A mapping of nonextensive statistical mechanics into Gibbs' statistical mechanics exists, which leads to a generalization of Einstein's formula for fluctuations. A unified treatment of stability of relaxed states in nonextensive statistical…
We study a few dynamical systems composed of many components whose sizes evolve according to multiplicative stochastic rules. We compare them with respect to the emergence of power laws in the size distribution of their components. We show…
A recently introduced nonlinear Fokker-Planck equation, derived directly from a master equation, comes out as a very general tool to describe phenomenologically systems presenting complex behavior, like anomalous diffusion, in the presence…
Turbulent cascades characterize the transfer of energy injected by a random force at large scales towards the small scales. In hydrodynamic turbulence, when the Reynolds number is large, the velocity field of the fluid becomes irregular and…
A mechanism is proposed for the appearance of power law distributions in various complex systems. It is shown that in a conservative mechanical system composed of subsystems with different numbers of degrees of freedom a robust power-law…
Multiplicative cascades have been introduced in turbulence to generate random or deterministic fields having intermittent values and long-range power-law correlations. Generally this is done using discrete construction rules leading to…
Collisions resulting in fragmentation are important in shaping the mass spectrum of minor bodies in the asteroid belt, the Kuiper belt, and debris disks. Models of fragmentation cascades typically find that in steady-state, the solution for…
When the complete understanding of a complex system is not available, as, e.g., for systems considered in the real-world, we need a top-down approach to complexity. In this approach one may start with the desire to understand general…
More than one billion data sampled with different frequencies from several financial instruments were investigated with the aim of testing whether they involve power law. As a result, a known power law with the power exponent around -4 was…
Starting from the model of continuous time random walk, we focus our interest on random walks in which the probability distributions of the waiting times and jumps have fat tails characterized by power laws with exponent between 0 and 1 for…
Energy cascade is ubiquitous in systems far from equilibrium. Facilitated by particle interactions and external forces, it can lead to highly complex phenomena like fully developed turbulence, characterized by power law velocity correlation…
For systems with a mixed phase space we demonstrate that dynamical tunneling universally leads to a fractional power law of the level-spacing distribution P(s) over a wide range of small spacings s. Going beyond Berry-Robnik statistics, we…
Aim of this note is to analyse branching Brownian motion within the class of models introduced in the recent paper [4] and called chemical diffusion master equations. These models provide a description for the probabilistic evolution of…
Sea ice is a complex system, and observations have shown that ice segments (i.e., floes) have a wide range of sizes, with a floe size distribution that follows a power law. However, a theory for the power law and its exponent have remained…