Abstract
Recent experiments show that both natural and artificial microswimmers in narrow channel-like geometries will self-organise to form steady, directed flows. This suggests that networks of flowing active matter could function as novel autonomous microfluidic devices. However, little is known about how information propagates through these far-from-equilibrium systems. Through a mathematical analogy with spin-ice vertex models, we investigate here the input–output characteristics of generic incompressible active flow networks (AFNs). Our analysis shows that information transport through an AFN is inherently different from conventional pressure or voltage driven networks. Active flows on hexagonal arrays preserve input information over longer distances than their passive counterparts and are highly sensitive to bulk topological defects, whose presence can be inferred from marginal input–output distributions alone. This sensitivity further allows controlled permutations on parallel inputs, revealing an unexpected link between active matter and group theory that can guide new microfluidic mixing strategies facilitated by active matter and aid the design of generic autonomous information transport networks.
Highlights
In a network without inputs or outputs, the space of integer-valued incompressible flows is spanned by a cycle basis B1 = {Ca}, 1 a |E|−|V |+1
Each flow is guaranteed to be unique up to orientation because B1 is a basis for cycles on the closed graph, so we need only sample the 2|B| sets of coefficients {bi} to cover the entire space
The replica temperatures within a run were roughly tuned to give a 30–50% swap acceptance rate, which we found reasonable for our purposes [3]
Summary
The sets B1, B2, I were constructed using Mathematica. We used different algorithmic approaches depending on the type of graph considered. A minimal weight basis, consisting of the shortest possible cycles, has few overlaps between elements and so is preferable here to reduce rejected state changes in Monte Carlo sampling.) The input–output paths I were constructed by taking (one of) the shortest path(s) between each input–output pair. In this case the basis B2 was not necessary as these graphs were always considered with all inputs and outputs activated, leaving no free outputs for flows to switch between; if it were needed, shortest paths between output pairs would again be a simple scheme. Output–output connections B2 remained intact from the planar hexagonal network
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