Related papers: Scaling in simple continued fraction
We prove a suite of dynamical results, including exactness of the transformation and piecewise-analyticity of the invariant measure, for a family of continued fraction systems, including specific examples over reals, complex numbers,…
Even though strongly correlated systems are abundant, only a few exceptional cases admit analytical solutions. In this paper we present a large class of solvable systems with strong correlations.. We consider a set of $N$ independent and…
The steady state reached by a system of particles sliding down a fluctuating surface has interesting properties. Particle clusters form and break rapidly, leading to a broad distribution of sizes and large fluctuations. The density-density…
We study scaling properties of stochastic aggregation processes in one dimension. Numerical simulations for both diffusive and ballistic transport show that the mass distribution is characterized by two independent nontrivial exponents…
In this paper, we investigate the scaling invariance of survival probability in the Caputo fractional standard map of the order $1<\alpha<2$ considered on a cylinder. We consider relatively large values of the nonlinearity parameter $K$ for…
We propose to compute physical properties by Monte Carlo calculations using conditional expectation values. The latter are obtained on top of the usual Monte Carlo sampling by partitioning the physical space in several subspaces or…
Power law scaling is observed in many physical, biological and socio-economical complex systems and is now considered as an important property of these systems. In general, power law exists in the central part of the distribution. It has…
We develop a simple computational model for cell boundary evolution in plastic deformation. We study the cell boundary size distribution and cell boundary misorientation distribution that experimentally have been found to have scaling forms…
Linear rate equations are used to describe the cascading decay of an initial heavy cluster into fragments. We consider moments of arbitrary orders of the mass multiplicity spectrum and derive scaling properties pertaining to their time…
The fluctuation scaling law has universally been observed in a wide variety of phenomena. For counting processes describing the number of events occurred during time intervals, it is expressed as a power function relationship between the…
Experimental data are presented on particle correlations and fluctuations in various high-energy multiparticle collisions, with special emphasis on evidence for scaling-law evolution in small phase-space domains. The notions of…
Most of various large-size complex systems in nature and society can be well described as complex networks (graphs) to better understand the evolutional mechanisms and dynamical functions behind themselves. Of some part follow scale-free…
An Engel series is a sum of reciprocals $\sum_{j\geq 1} 1/x_j$ of a non-decreasing sequence of positive integers $x_n$ with the property that $x_n$ divides $x_{n+1}$ for all $n\geq 1$. In previous work, we have shown that for any Engel…
The scaling behaviour of the diffraction intensity near the origin is investigated for (partially) ordered systems, with an emphasis on illustrative, rigorous results. This is an established method to detect and quantify the fluctuation…
Anomalous coarsening in far-from equilibrium one-dimensional systems is investigated by simulation and analytic techniques. The minimal hard core particle (exclusion) models contain mechanisms of aggregated particle diffusion, with rates…
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…
A scaling description is obtained for the $d$--dimensional random field Ising model from domains in a bar geometry. Wall roughening removes the marginality of the $d=2$ case, giving the $T=0$ correlation length $\xi \sim \exp\left(A…
We investigate fractional moments and expectations of power means of complex-valued random variables by using fractional calculus. We deal with both negative and positive orders of the fractional derivatives. The one-dimensional…
We review briefly the concepts underlying complex systems and probability distributions. The later are often taken as the first quantitative characteristics of complex systems, allowing one to detect the possible occurrence of regularities…
We extend a generic class of systems which have previously been shown to spontaneously develop scaling (power law) distributions of their elementary degrees of freedom. While the previous systems were linear and exploded exponentially for…