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

TL;DR

This paper revisits Maxwell's demon experiments with granular gas, revealing a transition from critical to sub-critical bifurcation at a tri-critical point and proposing a feedback-based setup to induce hyper-critical bifurcations for broader applications.

Contribution

It demonstrates the transition nature change in granular gas bifurcations and proposes a feedback control method to achieve hyper-critical bifurcations, challenging previous assertions.

Findings

Transition changes from critical to sub-critical at a tri-critical point.

Fluctuation amplitude is reinforced at the tri-critical point.

Proposes a feedback-based experimental setup for hyper-critical bifurcations.

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.