Critical exponents in zero dimensions
Statistical Mechanics
2015-06-05 v1 Chaotic Dynamics
Fluid Dynamics
Abstract
In the vicinity of the onset of an instability, we investigate the effect of colored multiplicative noise on the scaling of the moments of the unstable mode amplitude. We introduce a family of zero dimensional models for which we can calculate the exact value of the critical exponents for all the moments. The results are obtained through asymptotic expansions that use the distance to onset as a small parameter. The examined family displays a variety of behaviors of the critical exponents that includes anomalous exponents: exponents that differ from the deterministic (mean-field) prediction, and multiscaling: non-linear dependence of the exponents on the order of the moment.
Cite
@article{arxiv.1207.4355,
title = {Critical exponents in zero dimensions},
author = {Alexandros Alexakis and François Pétrélis},
journal= {arXiv preprint arXiv:1207.4355},
year = {2015}
}