A simple diffusion model showing anomalous scaling
Abstract
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 )≠αm. A simple analytic treatment is given based on an effective diffusion that is dependent on 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.
- Publication:
-
Physics of Plasmas
- Pub Date:
- August 2008
- DOI:
- 10.1063/1.2969429
- Bibcode:
- 2008PhPl...15h2308R
- Keywords:
-
- 47.52.+j;
- 47.55.P-;
- Chaos in fluid dynamics;
- Buoyancy-driven flows;
- convection