Fig. 9: Effervescence is ubiquitous.
From: Effervescence in a binary mixture with nonlinear non-reciprocal interactions
a Snapshots of the fields ϕ1,2 at two separate times showing travelling waves moving in the direction of the black arrow. Fluctuations transverse to the travelling wave propagate along the red arrow. b The dynamics follows from the restoration of reciprocity in fluctuating spatial domains, as evident in the snapshots of the non-reciprocal coupling α. In the darker regions α is close to zero meaning that free-energy-driven interactions dominate inside these regions promoting phase-separation. Larger α leads to chasing dynamics. The constraint of rational invariance in the composition plane is lifted for these simulations, a feature visible in the formation of the reciprocal granules and droplets preferentially at certain phases of the travelling wave. c α is a fluctuating field whose probability distribution P evolves to a stationary distribution independent of its parametrization. Drawing parameters randomly from a Gaussian with variance 4 and mean zero, we find on an average a universal form for P(α) for steady-states that show effervescence. P has significant weight at negative values, and it is bimodal with peaks at positive and negative values. d, e Effervescence is ubiquitous - it is the dominant steady-state when non-linear non-reciprocal interactions are allowed as seen in the statistics of observed steady states with varying reciprocal interaction coefficient χ.
