[HTML][HTML] Mathematical foundations of the non-Hermitian skin effect

H Ammari, S Barandun, J Cao, B Davies… - Archive for Rational …, 2024 - Springer
We study the skin effect in a one-dimensional system of finitely many subwavelength
resonators with a non-Hermitian imaginary gauge potential. Using Toeplitz matrix theory, we …

Functional analytic methods for discrete approximations of subwavelength resonator systems

H Ammari, B Davies, EO Hiltunen - arXiv preprint arXiv:2106.12301, 2021 - arxiv.org
We survey functional analytic methods for studying subwavelength resonator systems. In
particular, rigorous discrete approximations of Helmholtz scattering problems are derived in …

Exceptional Points in Parity--Time-Symmetric Subwavelength Metamaterials

H Ammari, B Davies, EO Hiltunen, H Lee, S Yu - SIAM Journal on …, 2022 - SIAM
When sources of energy gain and loss are introduced to a wave scattering system, the
underlying mathematical formulation will be non-Hermitian. This paves the way for the …

Convergence rates for defect modes in large finite resonator arrays

H Ammari, B Davies, EO Hiltunen - SIAM Journal on Mathematical Analysis, 2023 - SIAM
We show that defect modes in infinite systems of resonators have corresponding modes in
finite systems which converge as the size of the system increases. We study the generalized …

Spectral convergence in large finite resonator arrays: the essential spectrum and band structure

H Ammari, B Davies, EO Hiltunen - arXiv preprint arXiv:2305.16788, 2023 - arxiv.org
We show that resonant frequencies of a system of coupled resonators in a truncated periodic
lattice converge to the essential spectrum of corresponding infinite lattice. We use the …

Robustness of subwavelength devices: a case study of cochlea-inspired rainbow sensors

B Davies, L Herren - Proceedings of the Royal Society A, 2022 - royalsocietypublishing.org
We derive asymptotic formulae describing how the properties of subwavelength devices are
changed by the introduction of errors and imperfections. As a demonstrative example, we …

[HTML][HTML] Topological properties of a self-assembled electrical network via ab initio calculation

C Stephenson, D Lyon, A Hübler - Scientific reports, 2017 - nature.com
Interacting electrical conductors self-assemble to form tree like networks in the presence of
applied voltages or currents. Experiments have shown that the degree distribution of the …

Solutions of Laplace's equation with simple boundary conditions, and their applications for capacitors with multiple symmetries

M Morales, RA Diaz, WJ Herrera - Journal of electrostatics, 2015 - Elsevier
We find solutions of Laplace's equation with special boundary conditions, using a general
curvilinear system of coordinates. We call this purely geometrical solutions Basic Harmonic …

Landscape of wave focusing and localization at low frequencies

B Davies, Y Lou - Studies in Applied Mathematics, 2024 - Wiley Online Library
High‐contrast scattering problems are special among classical wave systems as they allow
for strong wave focusing and localization at low frequencies. We use an asymptotic …

Functional analytic methods for discrete approximations of subwavelength resonator systems

H Ammari, B Davies, E Orvehed Hiltunen - Pure and Applied Analysis, 2024 - msp.org
We survey functional analytic methods for studying subwavelength resonator systems. In
particular, rigorous discrete approximations of Helmholtz scattering problems are derived in …