Spatial distribution of heating rates and superoscillation in the plane transverse to the propagation during the transition from sausage to kink. Left: a density plot of superoscillations versus heating rates where this latter is seen to reach a maximum for superoscillation factors of around 3. Right: a map of the transverse plane with heating rates in colour and superoscillation factors in contours (values of 2, 3, 5 and 10 times the global frequency shown). Two superoscillatory lobes appear around the position of the dislocation, but only one of them is associated with high heating rates. This asymmetry is due to the interaction between the f and g parts of the expression for the heating; see text.