I obtained my PhD in 2017 from the University of Surrey under the supervision of Prof. Tom Bridges, titled Conservation Laws, Modulation and the Emergence of Universal Forms, which utilised Noether Theory to relate the critical points of conservation laws to the emergence of universal nonlinear, dispersive equations such as the Korteweg-de Vries equation and generalisations.
Following this, I worked with Dr Priya Subramanian and Profs. Andy Archer and Alastair Rucklidge on soft matter quasicrystals. Using ideas from pattern formation, we were able to gain insight not only into how polymeric systems self-organise into aperiodic orderings, but how one might start to tweak the chemistry of such molecules to either favour or hinder the formation of such never-repeating crystal structures.
I have worked here at Northumbria since 2020 as an applied mathematician across multiple disciplines - I still work in fluid dynamics, but can be found working on problems within magnetospheric plasmas/space weather, data sonification and soft matter physics.
My main research interest is nonlinear waves across physics, typically using a variety of multiple scales approaches to derive reduced, but still nonlinear, normal forms to describe their evolution in a more tractible and universal way.
My primary field of study is water waves, looking at how surface waves behave in the vicinity of various instabilities (such as the famous Benjamin-Feir instability) and to changing system parameters. Recent work focusses on how wave-mean flow interactions can alter properties of the surface wave, including causing spectral peak downshifting, the admittance of heteroclinic wave-wave connections and the description of the nonlinear stages of high-frequency instability bubbles.
I have recently started to research magnetospheric plasmas in a similar fashion, deriving nonlinear systems to understand the dynamics and statistics of Whistler-Mode Chorus waves. Wave-particle interactions are responsible for narrow-banded rising- or falling-tone behaviour, which mirrors how wave-mean flow interactions influence spectral properties of water waves, and so we are leveraging this parallel to reveal new insights into this family of waves which has included a novel explanation for the famous Band Gap seen in survey data.
Adam Toulson Wave-Particle Interactions in Whistler-Mode Chorus waves: Theory and Simulations of High Energisation Events Start Date: 01/10/2024
Mathematical Physics PhD October 31 2017
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