laboratoire de physique statistique
 
 
laboratoire de physique statistique

Publications

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2012 


Alexandros ALEXAKIS 


2
P U B L I C A T I O N S



 
2012
Anomalous Exponents at the Onset of an Instability - Petrelis, F. and Alexakis, A.
PHYSICAL REVIEW LETTERS 108 (2012) 
LPS


Abstract : Critical exponents are calculated exactly at the onset of an instability, by using asymptotic expansion techniques. When the unstable mode is subject to multiplicative noise whose spectrum at zero frequency vanishes, we show that the critical behavior can be anomalous; i.e., the mode amplitude X scales with departure from onset mu as < X > proportional to mu(beta) with an exponent beta different from its deterministic value. This behavior is observed in a direct numerical simulation of the dynamo instability, and our results provide a possible explanation for recent experimental observations.
Critical Exponents in Zero Dimensions - Alexakis, A. and Petrelis, F.
JOURNAL OF STATISTICAL PHYSICS 149738-753 (2012) 
LPS


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 beta (m) 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.