Physics – Physics and Society
Scientific paper
2006-10-19
Physics
Physics and Society
For related work see http://www.helbing.org
Scientific paper
10.1103/PhysRevLett.97.168001
We propose a many-particle-inspired theory for granular outflows from a hopper and for the escape dynamics through a bottleneck based on a continuity equation in polar coordinates. If the inflow is below the maximum outflow, we find an asymptotic stationary solution. If the inflow is above this value, we observe queue formation, which can be described by a shock wave equation. We also address the experimental observation of intermittent outflows, taking into account the lack of space in the merging zone by a minimum function and coordination problems by a stochastic variable. This results in avalanches of different sizes even if friction, force networks, inelastic collapse, or delay-induced stop-and-go waves are not assumed. Our intermittent flows result from a random alternation between particle propagation and gap propagation. Erratic flows in congested merging zones of vehicle traffic may be explained in a similar way.
Hansen Angela
Helbing Dirk
Jensen Mogens H.
Johansson Anders
Mathiesen Joachim
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