Front Propagation from Radiative Sources

Abstract

Fronts are regions of transition from one state to another in a medium. They are present in many areas of science and applied mathematics, and modelling them and their evolution is often an effective way of treating the underlying phenomena responsible for them. In this paper, we propose a new approach to modelling front propagation, which characterises the evolution of structures surrounding radiative sources. This approach is generic and has a wide range of applications, particularly when dealing with the propagation of phase or state transitions in media surrounding radiation emitting objects. As an illustration, we show an application in modelling the propagation of ionisation fronts around early stars during the cosmological Epoch of Reionisation (EoR) and show that the results are consistent with those of existing equations but provide much richer sources of information.