How one can make the bifurcation of Maxwell’s demon in Granular Gas   Hyper-Critical

P. Evesque, Lab MSSMat,  UMR 8579 CNRS, Ecole Centrale Paris, 92295 Châtenay-Malabry, France, pierre.evesque@ecp.fr

Abstract: Experimental data from Maxwell's demon experiments on granular gas are revisited. It is shown that the transition nature changes from critical to sub-critical via a tri-critical point when frequency of vibration is increased continuously. So (i) the transition is not hyper-critical as asserted previously, but (ii)  the fluctuations amplitude is spontaneously reinforced at the tri-critical point compared to the one at other frequencies. So, (iii) this analysis still contradicts a recent study which asserts that the bifurcation is always critical, and that  fluctuations shall depend on the number of grains only. Beside, (iv) it is proposed a way to build an experiment, based on some modification of the "Maxwell's demon in granular gas" set up, which undergoes a hyper-critical bifurcation, with the use of some controlled feed-back of the flows. This last idea can be generalised and used in other domains where bifurcation theory applies, i.e. physics, chemistry, population dynamics, economy,…, to improve regulation , but generating  hyper- fluctuations. Finally it is shown that the dynamical  result is sensitive to the very-details of the regulation.

Pacs # : 5.40 ; 45.70 ; 62.20 ; 83.70.Fn

poudres & grains 16 (1), 1-13 (Février 2007)