Cyclic Maxwell Demon in granular gas using 2 kinds of spheres with different masses

TL;DR

This paper investigates a granular gas system with two particle species of different masses, revealing cyclic segregation orbits and bifurcation phenomena influenced by vibration amplitude, contributing new insights into Maxwell's demon behavior in granular matter.

Contribution

It demonstrates the existence of cyclic orbits and bifurcation behavior in a granular gas mixture with different particle masses, highlighting the role of energy transfer rules.

Findings

Cyclic segregation orbits are observed at certain vibration amplitudes.

Steady state convergence occurs via spiral trajectories.

Bifurcation thresholds depend on vibration amplitude and parameters.

Abstract

The problem of Maxwell's demon in granular gas is revisited in the case of a mixture of two particle species. The phase space is found to be 2d. Existence of cyclic orbits, with periodic segregation, is demonstrated by investigating the case of 2 kinds of particles with identical parameters but different masses. At large excitation equi-partition shall be obtained, but convergence towards the steady state is found in spiral. The spiral convergence is imposed due to the rule of kinetic-energy transfer between the two species. It results that the most probable scenario is that the steady state breaks into cyclic orbit at lower amplitude of vibration below a bifurcation threshold. The nature of the bifurcation is not known; it can be critical, subcritical, hypercritical or can exhibit a tri-critical point as varying the control parameters. No conclusion is obtained at very low vibration amplitude: it is guessed two scenarii under further cooling which generates Maxwell's demon and segregation..