Proc. Natl Acad. Sci. USA (2013)


At first sight, the London Underground ('the Tube') and interacting polymers don't have a lot in common. Yet Chi Ho Yeung and colleagues apply some of the theoretical machinery developed for describing intertwined polymer structures to optimize the Tube's operation.

The Tube obviously represents a network — stations (nodes) connected by rails (segments). A polymer is a chain of monomers, so an arrangement of many polymers can be seen as a set of nodes connected by segments. Yeung et al. considered polymers with fixed ends: the path between a polymer's endpoints is variable, but segments have to connect through neighbouring nodes, and one polymer cannot go through a node more than once. The authors introduced an energy function that can either penalize or encourage polymer overlap.

Translating this to the Tube, polymers correspond to passenger source–destination pairs, and overlap to traffic congestion. When concentration is penalized, the algorithm distributes traffic uniformly. The authors processed actual Tube data to propose optimal network usage and suggest differential pricing. Solutions that favour congestion may be relevant when the network is required to operate a reduced service — for example, during a strike.