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Basic assumptions of the model. Example of circuit :. Circuits consist of nodes, channels, pumps and bubble-sources Channels are 1-dimensional, nodes are 0-dimensional, as in a planar graph Bubbles are point charges of resistance, added to the constant resistance of the channel they occupy
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Basic assumptions of the model Example of circuit : • Circuits consist of nodes, channels, pumps and bubble-sources • Channels are 1-dimensional, nodes are 0-dimensional, as in a planar graph • Bubbles are point charges of resistance, added to the constant resistance of the channel they occupy • Bubbles flow at the superficial speed of flow • Flow is driven by a pressure drop applied to the inlet and outlet of the system
In search of a stationary flow – two channel loop Input Outlet The stationary flow is not unique - different patterns can be repeated !!
What happens for f other than fsync ? The Fourier transform of n(t) for two different cases :
Regular and chaotic bands for an asymmetric loop (L1/L2 = 1.002)
Within the regular band pattern resists perturbations (Frame distance in the movie is equal to the average period of the pattern)
A network with three possible paths • Three possible trajectories: • RB RC RE • RB RD RE • RA
Summary • A simple loop exhibits non-trivial behavior such as regular/chaotic bands • A unique stationary state does not exist (memorizing patterns) • Some systems exhibit spontaneous oscillations of large amplitudes • Systems with large number of bubbles are equivalent as long as the flux of resistance (z = f r ) is kept constant • Possibly there exist a continuous limit r 0 with constantz • Such a limit represents waves of flowing resistance density, instead of discrete bubbles