Bryn Davies is a mathematician whose work establishes mathematical solutions for fundamental physical problems. He is an applied analyst and typically studies models based on partial differential equations, using approaches based on a variety of asymptotic analysis, homogenisation, dynamical systems and ideas from spectral theory. He also collaborates regularly with experimental and industrial colleagues. He studies problems from across wave physics, quantum mechanics, metamaterial science and continuum mechanics. He has, for example, developed theory for applications including topological waveguides, high-contrast nano-particulate materials, energy harvesting, quasicrystalline metamaterials, non-reciprocal wave phenomena and bio-inspired sensing.

Bryn leads the Theory, Modelling and AI-Design special interest group (SIG) of the UK Metamaterials NetworkPlus.

Before moving to Warwick, Bryn was a Marie Skłodowska-Curie Fellow in the Department of Mathematics at Imperial College London, where he was part of Prof. Richard Craster's 'Waves' research group. Prior to that, he was based at ETH Zurich where he completed a doctorate under the supervision of Prof. Dr. Habib Ammari. He was previously a student at the University of Oxford, where he completed projects on exponential asymptotics and snaking bifurcations under the supervision of Dr. Philippe Trinh.

Doctoral students

• Konstantinos Alexopoulos - based at ETH Zurich in Habib Ammari's group, Konstantinos works on developing asymptotic methods for characterising waves in dispersive media. We have, so far, published articles in PDEs & Applications, Math. Meth. Appl. Sci. and J. Math. Phys..

Masters students

• Clemens Thalhammer - working on spectral properties of quasicrystalline differential operators (work published in Proc. R. Soc. A).

• Liyang Wang - working on developing asymptotic methods for predicting localisation in random lattices.

Undergraduate students

• Yu Xiao - a Mary Lister McCammon Summer Research Fellow working on spectral theoretic methods for predicting the statistics of non-linear dynamical systems.

• Thomas Stobart - a summer research student funded by an EPSRC Vacation Bursary working on latent symmetries in wave systems.

• Yinglai Wang - a summer research student working on modulated metamaterials related to the three-gap theorem.

• Hafsa Al Saadi - a summer research student working on topological methods for predicting wave localisation in random lattices.

• Krish Nigam - a  summer research student working on spectra of Fibonacci-generated systems.

Masters students

• Yiqi Lou (2022-2023) - MSc thesis on using the generalised capacitance matrix to develop landscape methods fro predicting wave focusing and localisation at low frequencies in high-contrast systems (work published in Stud. Appl. Math.).

• Karlo Bujas (2022-2023) - MSc thesis on topological methods for predicting localisation in random lattices.

• Diandian Chen (2022-2023) - MSc thesis on using variants of the "cluster potential" to propose landscape functions for predicting localisation in discrete random systems.

• Nina Dekoninck Bruhin (2021-2022) - MSc thesis on the role of random projections in robust signal processing (work published in SIAM J. Imaging Sci.). Nina moved on to Cambridge to start a PhD.

• Laura Herren (2020-2021) - MSc thesis on the robustness properties of cochlea-inspired metamaterials (work published in Proc. R. Soc. A). Laura moved on to a graduate program at Yale.

Undergraduate students

• Lucas Dunckley (2023) - a summer research student who worked on group theoretic approaches to predicting spectral features of complex periodic systems (work published in Comp. Rend. Mécanique).

• Daniel Barnett (2023) - a summer research student funded by a bursary from Dstl, Daniel worked on Fourier methods for modelling thermal metamaterials.

• Ross Ah-Weng (2023) - a summer research student who studied gallery modes in two-dimensional quasicrystals.

• Yafei He (2023) - a Mary Lister McCammon Summer Research Fellow who worked on characterising symmetries of the generalised capacitance matrix.

• Chang Su (2023) - a summer research student who worked on symmetry-induced edge modes in two-dimensional quasicrystals.

• Lili Fehertoi-Nagy (2022) - a summer research student who used two-scale asymptotic methods ("high-frequency homogenisation") to compare the relative performance of graded metamaterials (work published in Proc. R. Soc. A). Lili moved on to Part III Maths in Cambridge, before starting a PhD in Cambridge.

•  Jingyi Ma (2022) - a summer research student who studied edge modes in arrays of metacylinders.

• Gaspard Mudry (2021) - BSc thesis on musical instrument classification using gammatone transforms.

• Nils Wachsmuth (2020) - BSc thesis on using the statistical coefficients of "natural sounds" as the basis for classification (applied to the problem of musical instrument classification).