Stirring a two-dimensional viscous fluid with rods is often an effective wayto mix. The topological features of periodic rod motions give a lower bound onthe topological entropy of the induced flow map, since material lines must`catch' on the rods. But how good is this lower bound? We present examples fromnumerical simulations and speculate on what affects the 'gap' between the lowerbound and the measured topological entropy. The key is the sign of the rodmotion's action on first homology of the orientation double cover of thepunctured disk.
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