Dr Daniel Ratliff

Assistant Professor

Department: Mathematics, Physics and Electrical Engineering

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.

Email Daniel

Research Themes and Scholarly Interests

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.

Key Publications

Please visit the Pure Research Information Portal for further information
Characteristic times for radiation belt drift phase mixing, Lejosne, S., Albert, J., Ratliff, D. 24 Jun 2024, In: Frontiers in Astronomy and Space Sciences
The challenge to understand the zoo of particle transport regimes during resonant wave-particle interactions for given survey-mode wave spectra, Allanson, O., Ma, D., Osmane, A., Albert, J., Bortnik, J., Watt, C., Chapman, S., Joseph, S., Ratliff, D., Meredith, N., Elsden, T., Neukirch, T., Hartley, D., Black, R., Watkins, N., Elvidge, S. 13 Mar 2024, In: Frontiers in Astronomy and Space Sciences
Two methods to analyse radial diffusion ensembles: the peril of space- and time- dependent diffusion, Bentley, S., Stout, J., Thompson, R., Ratliff, D., Watt, C. 4 Sep 2024
Two methods to analyze radial diffusion ensembles: The perils of space- and time-dependent diffusion, Bentley, S., Stout, J., Thompson, R., Ratliff, D., Watt, C. Nov 2024, In: Physics of Plasmas
The nonlinear evolution of whistler-mode chorus: modulation instability as the source of tones, Ratliff, D., Allanson, O. 12 Dec 2023, In: Journal of Plasma Physics
Genuine nonlinearity and its connection to the modified Korteweg–de Vries equation in phase dynamics, Ratliff, D. 6 Jan 2022, In: Nonlinearity
Kink–antikink stripe interactions in the two-dimensional sine–Gordon equation, Carretero-González, R., Cisneros-Ake, L., Decker, R., Koutsokostas, G., Frantzeskakis, D., Kevrekidis, P., Ratliff, D. 1 Jun 2022, In: Communications in Nonlinear Science and Numerical Simulation
Reappraisal of Whitham's 1967 theory for wave–meanflow interaction in shallow water, Bridges, T., Ratliff, D. 1 Nov 2022, In: Wave Motion
Density Distribution in Soft Matter Crystals and Quasicrystals, Subramanian, P., Ratliff, D., Rucklidge, A., Archer, A. 26 May 2021, In: Physical Review Letters
Nonlinear Theory for Coalescing Characteristics in Multiphase Whitham Modulation Theory, Bridges, T., Ratliff, D. Feb 2021, In: Journal of Nonlinear Science