Imagine that a pollutant is released accidentally into the centre of a city with a rectangular grid plan, such as Manhattan, on a windy day. How does this pollutant spread across the city? Similar questions arise in a number of other contexts. How do chemicals spread across the blood system in porous media or in microfluidic channel devices?
In an article published in the prestigious Physical Review Letters journal, Alexandra Tzella, a lecturer at the School of Mathematics at the University of Birmingham and Jacques Vanneste from the University of Edinburgh, describe how to apply the sophisticated mathematical theory of large deviations, in order to obtain explicit results for the shape of the patch of the tracer long after its release.
The conclusions provide new insight into the way the geometry of the network complicates the way a tracer spreads out, both at the core (where the concentration is highest) and at the tails (where the concentration is lowest. An accurate approximation of their tails is particularly important in applications where low concentrations are critical, for example highly toxic chemicals or in the presence of amplifying chemical reactions. The technique itself is interesting as it is easily generalisable, to other network geometries for instance. The implications for urban pollution is a very real and exciting real world application.
You can read the full publication in the Physical Review Letters journal