Figure 2
Characteristics of the trained mixer. (a) Time series of the flow parameter, \(\theta _{n}(t)\), for the n-th episode: \(n=2000\), 3000, and 4000. The vertical axis is \(\theta _{n}(t)/\pi \) and the horizontal dot lines represent \(k/4~(k \in \mathbb {Z})\). Inset: the mix-variance, \(\Phi (t=1)\), in the case of the flow parameter with the constant angular frequency, \(\theta (t)= \omega t\). The horizontal dashed-dotted line indicates the value of the mix-variance by the trained mixer. (b) Time evolution of the velocity vector field by the trained mixer. The blue line and the red point represent the material line and one of the fixed points, respectively: \(t=0,~0.1,~0.2,~0.3,~0.36,~0.46,~0.54\), and 0.68. (c) Probability density functions of the mix-variance, \(\Phi (t=1)\), by the completely randomized mixer and the partially randomized mixers I and II from top to bottom panels. (d) Scalar fields, \(c(x,t=1)\), at the end of the mixing process by the trained mixer (left) and the completely randomized mixer (right).
