1 / 18

Basic assumptions of the model

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

dustinl
Télécharger la présentation

Basic assumptions of the model

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 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

  2. Stationary flow – single channel

  3. Stationary flow – single channel

  4. Approaching the stationary flow – single channel

  5. Approaching the stationary flow – single channel

  6. In search of a stationary flow – two channel loop Input Outlet The stationary flow is not unique - different patterns can be repeated !!

  7. What happens for f other than fsync ?

  8. What happens for f other than fsync ? The Fourier transform of n(t) for two different cases :

  9. Regular and chaotic bands for an asymmetric loop (L1/L2 = 1.002)

  10. Regular and chaotic band (magnified fragment)

  11. Within the regular band pattern resists perturbations (Frame distance in the movie is equal to the average period of the pattern)

  12. A network with three possible paths • Three possible trajectories: • RB RC  RE • RB RD  RE • RA

  13. 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

More Related