Related papers: Simple Maps with Fractal Diffusion Coefficients
We analyse deterministic diffusion in a simple, one-dimensional setting consisting of a family of four parameter dependent, chaotic maps defined over the real line. When iterated under these maps, a probability density function spreads out…
Using a numerical library for arbitrary precision arithmetic I study the irregular dependence of the diffusion coefficient on the slope of a piecewise linear map defining a dynamical system. I find that the graph of the diffusion…
We analyze a simple model of deterministic diffusion. The model consists of a one-dimensional periodic array of scatterers in which point particles move from cell to cell as defined by a piecewise linear map. The microscopic chaotic…
For a piecewise linear version of the periodic map with anomalous diffusion, the evolution of statistical averages of a class of observables with respect to piecewise constant initial densities is investigated and generalized eigenfunctions…
An intermittent nonlinear map generating subdiffusion is investigated. Computer simulations show that the generalized diffusion coefficient of this map has a fractal, discontinuous dependence on control parameters. An amended continuous…
If a point particle moves chaotically through a periodic array of scatterers the associated transport coefficients are typically irregular functions under variation of control parameters. For a piecewise linear two-parameter map we analyze…
We show that the generalized diffusion coefficient of a subdiffusive intermittent map is a fractal function of control parameters. A modified continuous time random walk theory yields its coarse functional form and correctly describes a…
We model chaotic diffusion, in a symplectic 4D map by using the result of a theorem that was developed for stochastically perturbed integrable Hamiltonian systems. We explicitly consider a map defined by a free rotator (FR) coupled to a…
In this work, we investigate the presence of sub-diffusive behavior in the Chirikov-Taylor Standard Map. We show that the stickiness phenomena, present in the mixed phase space of the map setup, can be characterized as a Continuous Time…
Dynamical zeta functions provide a powerful method to analyze low dimensional dynamical systems when the underlying symbolic dynamics is under control. On the other hand even simple one dimensional maps can show an intricate structure of…
We analyse the chaotic motion and its shape dependence in a piecewise linear map using Fujisaka's characteristic function method. The map is a generalization of the one introduced by R. Artuso. Exact expressions for diffusion coefficient…
Rajagopalan and Sabir [nlin.CD/0104021 and Phys. Rev. E 63, 057201 (2001)] recently discussed deterministic diffusion in a piecewise linear map using an approach developed by Fujisaka et al. We first show that they rederived the random walk…
A paradigmatic nonhyperbolic dynamical system exhibiting deterministic diffusion is the smooth nonlinear climbing sine map. We find that this map generates fractal hierarchies of normal and anomalous diffusive regions as functions of the…
Consider a piecewise smooth expanding map of the interval possessing several invariant subintervals and the same number of ergodic absolutely continuous invariant probability measures (ACIMs). After this system is perturbed to make the…
We consider the time-dependent statistical distributions of diffusive processes in relaxation to a stationary state for simple, two dimensional chaotic models based upon random walks on a line. We show that the cumulative functions of the…
We investigate a contaminant transport in fractal media with randomly inhomogeneous diffusion barrier. The diffusion barrier is a low permeable matrix with extremely rare high permeability pathways (punctures). At times, less than a…
The nonlinear climbing sine map is a nonhyperbolic dynamical system exhibiting both normal and anomalous diffusion under variation of a control parameter. We show that on a suitable coarse scale this map generates an oscillating…
The power spectrum S of linear transects of the earth's topography is often observed to be a power-law function of wave number k with exponent close to -2: S(k) is proportional to k^-2. In addition, river networks are fractal trees that…
We study the connection between transport phenomenon and escape rate statistics in two-dimensional standard map. For the purpose of having an open phase space, we let the momentum co-ordinate vary freely and restrict only angle with…
We consider random networks whose dynamics is described by a rate equation, with transition rates $w_{nm}$ that form a symmetric matrix. The long time evolution of the system is characterized by a diffusion coefficient $D$. In one dimension…