[HTML][HTML] Mathematical foundations of the non-Hermitian skin effect
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 …
resonators with a non-Hermitian imaginary gauge potential. Using Toeplitz matrix theory, we …
Functional analytic methods for discrete approximations of subwavelength resonator systems
We survey functional analytic methods for studying subwavelength resonator systems. In
particular, rigorous discrete approximations of Helmholtz scattering problems are derived in …
particular, rigorous discrete approximations of Helmholtz scattering problems are derived in …
Exceptional Points in Parity--Time-Symmetric Subwavelength Metamaterials
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 …
underlying mathematical formulation will be non-Hermitian. This paves the way for the …
Convergence rates for defect modes in large finite resonator arrays
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 …
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
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 …
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 …
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 …
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 …
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 …
for strong wave focusing and localization at low frequencies. We use an asymptotic …
Functional analytic methods for discrete approximations of subwavelength resonator systems
We survey functional analytic methods for studying subwavelength resonator systems. In
particular, rigorous discrete approximations of Helmholtz scattering problems are derived in …
particular, rigorous discrete approximations of Helmholtz scattering problems are derived in …