2025
Ammari H, Barandun S, Cao J, Davies B, Hiltunen EO, Liu P. (2025) The non-Hermitian skin effect with three-dimensional long-range coupling. To appear in Journal of the European Mathematical Society. [article | preprint | code]
Davies B, Thalhammer C. (2025) Convergence of supercell and superspace methods for computing spectra of quasiperiodic operators. Proceedings of the Royal Society A 481 (2319), 20240894. [article | preprint]
Ammari H, Barandun S, Davies B, Hiltunen EO, Uhlmann A. (2025) Universal estimates for the density of states for random block subwavelength resonator systems. Journal of Physics A 58, 415201. [article | preprint | code]
Alexopoulos K, Davies B, Hiltunen EO. (2025) Topological interface modes in systems with damping. SIAM Journal on Applied Mathematics 85 (4), 1500-1518. [article | preprint]
Wang Y, Davies B, Martí-Sabaté M. (2025) Edge modes in discrete lattices: phase transitions under the three-gap theorem. Proceedings of the Royal Society A 481 (2318), 20250019. [article | preprint]
Putley HJ, Davies B, Rodríguez-Fortuño FJ, Bykov AY, Zayats AV. (2025) Mixing skyrmions and merons in topological quasicrystals of the evanescent optical field. Optica 12 (5), 614-619. [article | preprint | talk]
Alexopoulos K, Davies B. (2025) Topologically protected modes in dispersive materials: the case of undamped systems. Multiscale Modeling and Simulation 23 (1), 611-639. [article | preprint]
Ammari H, Davies B, Hiltunen EO. (2025) Spectral convergence in large finite resonator arrays: the essential spectrum and band structure. Bulletin of the London Mathematical Society 57 (3), 730–747. [article | preprint]
Davies B, Barandun S, Hiltunen EO, Craster RV, Ammari H. (2025) Two-scale effective model for defect-induced localization transitions in non-Hermitian systems. Physical Review B 111 (3), 035109. [article | preprint | code]
Davies B et al. (39 contributing authors). (2025) Roadmap on metamaterial theory, modelling and design. Journal of Physics D 58, 203002. [article]
2024
Ammari H, Davies B, Hiltunen EO. (2024) Anderson localization in the subwavelength regime. Communications in Mathematical Physics 405, 1-20. [article | preprint | code]
Davies B, Morini L. (2024) Super band gaps and periodic approximants of generalised Fibonacci tilings. Proceedings of the Royal Society A, 480 (2285), 20230663. [article | preprint | code]
Ammari H, Barandun S, Davies B, Hiltunen EO, Liu P. (2024) Stability of the non-Hermitian skin effect in one dimension. SIAM Journal on Applied Mathematics 84 (4), 1697-1717. [article | preprint | code]
Hiltunen EO, Davies B. (2024) Coupled harmonics due to time-modulated point scatterers. Physical Review B 110 (18), 184102. [article | preprint]
Ammari H, Barandun S, Davies B, Hiltunen EO, Kosche T, Liu P. (2024) Exponentially localised interface eigenmodes in finite chains of resonators. Studies in Applied Mathematics 153 (4), e12765. [article | preprint | code]
Alexopoulos K, Davies B. (2024) The effect of singularities and damping on the spectra of photonic crystals. Journal of Mathematical Physics 65 (8), 081510. [article | preprint | code]
Ammari H, Davies B, Hiltunen EO. (2024) Functional analytic methods for discrete approximations of subwavelength resonator systems. Pure and Applied Analysis 6 (3), 873-939. [article | preprint]
Dunckley L, Davies B. (2024) Hierarchical band gaps in complex periodic systems. Comptes Rendus Mécanique 352, 143-157. [article | preprint]
Davies B, Lou Y. (2024) Landscape of wave focusing and localization at low frequencies. Studies in Applied Mathematics 152 (2), 760-777. [article | preprint | code]
Ammari H, Barandun S, Cao J, Davies B, Hiltunen EO. (2024) Mathematical foundations of the non-Hermitian skin effect. Archive for Rational Mechanics and Analysis 248, 33. [article | preprint | code]
2023
Davies B, Chaplain GJ, Starkey TA, Craster RV. (2023) Graded quasiperiodic metamaterials perform fractal rainbow trapping. Physical Review Letters, 131 (17), 177001. [article | preprint]
Ammari H, Davies B, Hiltunen EO. (2023) Convergence rates for defect modes in large finite resonator arrays. SIAM Journal on Mathematical Analysis, 55 (6), 7616-7634. [article | preprint]
Davies B, Fehertoi-Nagy L, Putley HJ. (2023) On the problem of comparing graded metamaterials. Proceedings of the Royal Society A 479 (2277), 20230537. [article | preprint | code]
Craster RV, Davies B. (2023) Asymptotic characterisation of localised defect modes: Su-Schrieffer-Heeger and related models. Multiscale Modeling and Simulation 21 (3), 827-848. [article | preprint | code]
Alexopoulos K, Davies B. (2023) A mathematical design strategy for highly dispersive resonator systems. Mathematical Methods in the Applied Sciences 46 (14), 15883-15908. [article | preprint]
Putley HJ, Guenneau S, Craster RV, Davies B, Poulton CG. (2023) Effective properties of periodic plate-array metacylinders. Physical Review B 108 (21), 214105. [article | code]
Chaplain GJ, Gliozzi AS, Davies B, Urban D, Descrovi E, Bosia F, Craster RV. (2023) Tunable topological edge modes in Su-Schrieffer-Heeger arrays. Applied Physics Letters 122 (22), 221703. [article | preprint]
Ammari H, Davies B. (2023) Asymptotic links between signal processing, acoustic metamaterials and biology. SIAM Journal on Imaging Sciences 16 (1), 64-88. [article | preprint | code]
Ammari H, Davies B. (2023) Metamaterial Analysis and Design: A Mathematical Treatment of Cochlea-inspired Sensors. De Gruyter Series in Applied and Numerical Mathematics, volume 9, De Gruyter. [book]
Davies B. (2023) Using functional analysis to design the materials of the future. LMS Newsletter 505. [article]
2022
Ammari H, Davies B, Hiltunen EO. (2022) Robust edge modes in dislocated systems of subwavelength resonators. Journal of the London Mathematical Society 106 (3), 2075-2135. [article | preprint]
Davies B, Herren L. (2022) Robustness of subwavelength devices: a case study of cochlea-inspired rainbow sensors. Proceedings of the Royal Society A 478 (2262), 20210765. [article | preprint | code]
Davies B, Craster RV. (2022) Symmetry-induced quasicrystalline waveguides. Wave Motion 115, 103068. [article | preprint | code]
Bruhin ND, Davies B. (2022) Bioinspired random projections for robust, sparse classification. SIAM Journal on Imaging Sciences 15 (4), 1833-1850. [article | preprint | code]
Ammari H, Davies B, Lee H, Hiltunen EO, Yu S. (2022) Exceptional points in parity–time-symmetric subwavelength metamaterials. SIAM Journal on Mathematical Analysis 54 (6), 6223-6253. [article | preprint]
Alexopoulos K, Davies B. (2022) Asymptotic analysis of subwavelength halide perovskite resonators. Partial Differential Equations and Applications 3 (44), 1-28. [article | preprint]
Bell A, Davies B, Ammari H. (2022) Bernhard Riemann, the ear, and an atom of consciousness. Foundations of Science 27 (3), 855-873. [article]
Ammari H, Davies B, Lee H, Hiltunen EO, Yu S. (2022) Wave interaction with subwavelength resonators. M. Chiappini, V. Vespri (eds.), Applied Mathematical Problems in Geophysics, C.I.M.E. Foundation Subseries, 2308, 23-83, Springer. [article | preprint | code]
2021
Ammari H, Davies B, Lee H, Hiltunen EO, Yu S. (2021) Bound states in the continuum and Fano resonances in subwavelength resonator arrays. Journal of Mathematical Physics 62, 101506. [article | preprint]
Ammari H, Davies B, Lee H, Hiltunen EO, Yu S. (2021) High-order exceptional points and enhanced sensing in subwavelength resonator arrays. Studies in Applied Mathematics 146 (2), 440-462. [article | preprint | code]
2020
Ammari H, Davies B, Hiltunen EO, Yu S. (2020) Topologically protected edge modes in one-dimensional chains of subwavelength resonators. Journal de Mathématiques Pures et Appliquées 144, 17–49. [article | preprint]
Ammari H, Davies B. (2020) Mimicking the active cochlea with a fluid-coupled array of subwavelength Hopf resonators. Proceedings of the Royal Society A 476 (2234), 20190870. [article | preprint | code]
Ammari H, Davies B, Yu S. (2020) Close-to-touching acoustic subwavelength resonators: eigenfrequency separation and gradient blow-up. Multiscale Modeling and Simulation 18 (3), 1299–1317. [article | preprint]
Recently submitted pre-prints
Davies B, Morini L. (2025) Hofstadter butterflies in phononic structures: commensurate spectra, wave localization and metal-insulator transitions. [preprint | code]
Davies B, Xiao AY. (2024) Spectral theoretic characterisation of Markov chain convergence. [preprint]
Davies B. (2024) Van Hove singularities in the density of states of a chaotic dynamical system. [preprint | code]