Applied mathematics, by definition, concerns the application of mathematical techniques to a variety of diverse topics. Such applications, to fields not often associated with mathematics, often lead to fruitful interdisciplinary work. Applied mathematicians in Newcastle have frequently worked on such topics — recent examples include optical physiology and mitochondrial DNA replication — but interdisciplinary research is currently most active in mathematical modelling for archaeology and prehistory, and in radioastronomy.
The 'Neolithic revolution', involving the adoption of farming and pottery-making by previously hunter-gatherer societies, took place about 12,000 to 4,000 years ago in Europe. Many aspects of this process remain obscure or controversial. Quantitative interpretation of archaeological evidence and mathematical modelling of the processes involved can significantly improve our understanding of the nature of the Neolithic and, eventually, of human behaviour in prehistory. Our models are based on the equations of population dynamics (the reaction-diffusion equation), adapted to model prehistoric populations, and including environmental factors such as rivers and coastlines, soil types and climate changes.
This work is carried out in collaboration with seven groups throughout Europe, supported by an EU NEST Adventure grant.
Radio telescope observations are the main source of information on galactic magnetic fields and the cosmic ray particles that spiral around them. By working closely with radio astronomers in planning and carrying out new observations we can maintain a strong link between theoretical and experimental views of galactic magnetism and the fluid flows in interstellar space that interact with the magnetic fields.
Current projects involve data gathered at the Effelsberg 100m telescope (Germany), the Very Large Array (USA) and the Giant Metrewave Radio Telescope (India).