A number of PhD studentships are funded by the Engineering and Physical Sciences Research Council (EPSRC) Doctoral Training Partnership with Exeter to commence in September 2017. The projects are funded on a competitive basis. Usually the projects that receive the best applicants will be awarded the funding. The studentships will provide funding for a stipend which, is currently £14,296 per annum for 2016-2017, research costs and UK/EU tuition fees at Research Council UK rates for 42 months (3.5 years) for full-time students, pro rata for part-time students.
The link to the list of projects is here (note that the list is long, applied maths & dynamics projects are mixed with others):
A 3-year position as a Postdoctoral Research Fellow is available in the research group (working with Jan Sieber:
Also, internationally, several tenure track/permanent positions are open:
McGill (tenure track, info from Tony Humphries):
DTU Lyngby (permanent, info from Frank Schilder):