This paper investigates various aspects of the links between exporting and productivity for a large sample of firms in the United Kingdom. We find evidence to support the proposition that sunk costs are important. Self selection takes place, with larger and more productive firms entering export markets, and firms have to become more productive in order to enter. Industry characteristics also af...

The harmonic map heat flow is a model for nematic liquid crystals and also has origins in geometry. We present an analysis of the asymptotic behaviour of singularities arising in this flow for a special class of solutions which generalises a known (radially symmetric) reduction. Specifically, the rate at which blowup occurs is investigated in settings with certain symmetries using the method of...