Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Nonlinear Sciences > Chaotic Dynamics

arXiv:nlin/0607010 (nlin)
[Submitted on 7 Jul 2006 (v1), last revised 14 Feb 2007 (this version, v2)]

Title:Fractal Properties of Anomalous Diffusion in Intermittent Maps

Authors:Nickolay Korabel, Rainer Klages, Aleksei V. Chechkin, Igor M. Sokolov, Vsevolod Yu. Gonchar
View PDF
Abstract: 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 time random walk theory well approximates the coarse behavior of this quantity in terms of a continuous function. This theory also reproduces a full suppression of the strength of diffusion, which occurs at the dynamical phase transition from one type of diffusive behavior to another. Similarly, the probability density function of this map exhibits a nontrivial fine structure while its coarse functional form is governed by a time fractional diffusion equation. A more detailed understanding of the irregular structure of the generalized diffusion coefficient is provided by an anomalous Taylor-Green-Kubo formula establishing a relation to de Rham-type fractal functions.
Comments: 15 pages, 11 figures, accepted for publication in PRE
Subjects: Chaotic Dynamics (nlin.CD); Statistical Mechanics (cond-mat.stat-mech)
Cite as: arXiv:nlin/0607010 [nlin.CD]
  (or arXiv:nlin/0607010v2 [nlin.CD] for this version)
  https://doi.org/10.48550/arXiv.nlin/0607010
Related DOI: https://doi.org/10.1103/PhysRevE.75.036213

Submission history

From: Korabel [view email]
[v1] Fri, 7 Jul 2006 22:32:38 UTC (179 KB)
[v2] Wed, 14 Feb 2007 21:00:47 UTC (193 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
nlin.CD
< prev   |   next >
new | recent | 2006-07

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)