A Simple Diffusion Model Showing
G. Rowlands1 and J. C.
University of Warwick, Coventry CV4 7AL, England
University of Wisconsin, Madison, Wisconsin 53706, USA
Received 25 April 2008; accepted 21 July 2008; published
13 August 2008
A number of iterated maps and one flow, which show chaotic behavior,
have been studied numerically and their time evolution expressed in
terms of higher-order moments Mm(t) All the cases show anomalous
behavior with Mm(t)
~ tg(m) with g(m) <> am.
A simple analytic
treatment isgiven based on an effective diffusion that is dependent
both space and time. This leads to a form for g(m)/m = a − b/m,
which is in good agreement with numerical results. This behavior is
attributed to the presence of convective motion superimposed on the
background diffusion, and hence this behavior is expected in a wide
variety of maps and flows.
Rowlands and J. C. Sprott,
Physics of Plasmas 15,
082308-1 - 082308-7
The complete paper is available
in PDF format.
Return to Sprott's Books and Publications.
Fig. 1. Intermittency in the Chirikov map for K
Fig. 2. Anomalous scaling in the Chirikov map as a function of K.
Fig. 3. Simple and anomalous scaling in the Chirikov map as a
Fig. 4. Normalized PDF for the Chirikov map after 1000 iterations.
Fig. 5. The Weiss map for k
Fig. 6. Scaling of moments in the Weiss map as a function of m
Fig. 7. Scaling of moments in the labyrinth model as a function of
Fig. 8. Normalized PDFs for the Chirikov map at two different