Model Selection and Parameter Estimation of One-Dimensional Gaussian Mixture ModelsXinyu Liu, Hai Zhang — Preprint, 2026.
Model Selection and Parameter Estimation of Multi-Dimensional Gaussian Mixture ModelsXinyu Liu, Hai Zhang — Preprint, 2026.
A Mathematical Theory of Computational Resolution Limit in One DimensionPing Liu, Hai Zhang — Applied and Computational Harmonic Analysis, 56, 402–446, 2022.
A Theory of Computational Resolution Limit for Line Spectral EstimationPing Liu, Hai Zhang — IEEE Transactions on Information Theory, 67(7), 2021.
A Mathematical Theory of Computational Resolution Limit in Multi-dimensional SpacesPing Liu, Hai Zhang — Inverse Problems, 37, 104001, 2021.
Theory of Topological Material
Spectral Topology and Edge Modes for One-Dimensional Non-Hermitian Photonic CrystalsJunshan Lin, Hai Zhang — Preprint.
Mathematical Theory for Photonic Hall Effect in Honeycomb Photonic CrystalsWei Li, Junshan Lin, Jiayu Qiu, Hai Zhang — Preprint, 2025.
Bulk-Edge Correspondence in Finite Photonic StructureJiayu Qiu, Hai Zhang — Preprint, arXiv:2501.15531, 2025.
A Mathematical Theory of Integer Quantum Hall Effect in PhotonicsJ. Qiu, H. Zhang — arXiv:2405.17200, 2024.
Interface Modes in Honeycomb Topological Photonic Structures with Broken Reflection SymmetryW. Li, J. Lin, J. Qiu, H. Zhang — arXiv:2405.03238, 2024.
Mathematical Theory for the Interface Mode in an Acoustic Waveguide Bifurcated from a Dirac PointJiayu Qiu, Junshan Lin, Peng Xie, Hai Zhang — Communications in Mathematical Sciences, 24(3), 749–796, 2026.
On the Bifurcation of a Dirac Point in a Photonic Waveguide without Band Gap OpeningJiayu Qiu, Hai Zhang — Journal of Functional Analysis, 291(1), 2026.
Mathematical Theory for Topological Photonic Materials in One DimensionJunshan Lin, Hai Zhang — Journal of Physics A: Mathematical and Theoretical, 55, 495203, 2022.
Bulk-Interface Correspondences for One Dimensional Topological Materials with Inversion SymmetryGuo Chuan Thiang, Hai Zhang — Proceedings of the Royal Society A, 479:20220675, 2023.
Dirac Points for the Honeycomb Lattice with Impenetrable ObstaclesWei Li, Junshan Lin, Hai Zhang — SIAM Journal on Applied Mathematics, 2023.
Theory of Metamaterial: A Case Study Using Resonant Bubbles
Double-negative Acoustic MetamaterialsHabib Ammari, Brian Fitzpatrick, Hyundae Lee, Sanghyeon Yu, Hai Zhang — Quarterly of Applied Mathematics, 77(4), 767–791, 2019.
Bloch Waves in Bubbly Crystal near the First Band Gap: A High-Frequency Homogenization Approachwith H. Ammari, H. Lee — SIAM Journal on Mathematical Analysis, 51(1), 45–59, 2019.
Subwavelength Phononic Bandgap Opening in Bubbly Mediawith H. Ammari, B. Fitzpatrick, H. Lee, S. Yu — Journal of Differential Equations, 263, 5610–5629, 2017.
A Mathematical and Numerical Framework for Bubble Meta-Screenswith H. Ammari, B. Fitzpatrick, D. Gontier, H. Lee — SIAM Journal on Applied Mathematics, 77(5), 1827–1850, 2017.
Minnaert Resonances for Acoustic Waves in Bubbly Mediawith H. Ammari, B. Fitzpatrick, D. Gontier, H. Lee — Annales de l'Institut Henri Poincaré: Analyse Nonlinéaire, 35, 1975–1998, 2018.
Plasmonic Sensing
Sensitivity of Resonance Frequency in the Detection of Thin Layer Using Nano-slit StructuresJunshan Lin, Sang-Hyun Oh, Hai Zhang — IMA Journal of Applied Mathematics, 86(1), 146–164, 2021.
Reconstructing Fine Details of Small Objects by Using Plasmonic Spectroscopic Data. Part II: The Strong Interaction Regimewith Habib Ammari, Matias Ruiz, Sanghyeon Yu — SIAM Journal on Imaging Sciences, 11(3), 1931–1953, 2018.
Reconstructing Fine Details of Small Objects by Using Plasmonic Spectroscopic Datawith Habib Ammari, Matias Ruiz, Sanghyeon Yu — SIAM Journal on Imaging Sciences, 11, 1–23, 2018.
Shape Reconstruction of Nanoparticles from Their Associated Plasmonic Resonanceswith H. Ammari, M. Putinar, M. Ruiz, S. Yu — Journal de Mathématiques Pures et Appliquées, 122, 23–48, 2019.
Plasmonic Resonances
Photonic Bandgap Phenomenon in a Metal-Dielectric Periodic Structurewith Fadil Santosa — Research in the Mathematical Sciences, 7(3), 2020.
Mathematical Analysis of Surface Plasmon Resonance by a Nano-gap in the Plasmonic Metalwith Junshan Lin — SIAM Journal on Mathematical Analysis, 51(6), 4448–4489, 2019.
An Integral Equation Method for Numerical Computation of Plasmonic Resonances in a Narrow Metallic Slitwith J. Lin — Journal of Computational Physics, 385, 75–105, 2019.
Field Expansions for Systems of Strongly Coupled Plasmonic NanoparticlesHabib Ammari, Matias Ruiz, Sanghyeon Yu, Hai Zhang — SIAM Journal on Numerical Analysis, 56(4), 2029–2044, 2018.
The Plasmonic Resonances of a Bowtie Antennawith Eric Bonnetier, Charles Dapogny, Faouzi Triki — Analysis in Theory and Applications, 35(1), 85–116, 2019.
Characterization of the Essential Spectrum of the Neumann–Poincaré Operator in 2D Domains with Corner via Weyl Sequenceswith E. Bonnetier — Revista Matemática Iberoamericana, 35(3), 925–948, 2019.
Mathematical and Numerical Framework for Metasurfaces Using Thin Layers of Periodically Distributed Plasmonic Nanoparticleswith H. Ammari, M. Ruiz, W. Wu, S. Yu — Proceedings of the Royal Society A, 472:20160445, 2017.
Mathematical Analysis of Plasmonic Resonances for Nanoparticles: The Full Maxwell Equationswith H. Ammari, M. Ruiz, S. Yu — Journal of Differential Equations, 261, 3615–3669, 2016.
Mathematical Analysis of Plasmonic Nanoparticles: The Scalar Casewith Habib Ammari, Pierre Millien, Matias Ruiz — Archive for Rational Mechanics and Analysis, 224, 597–658, 2017.
Theory of Anomalous Scattering (Extraordinary Optical Transmission)
Resonances through Subwavelength Holes: Theory, Computation, and ApplicationsJunshan Lin, Hai Zhang — Physics Reports, 1170, 1–34, 2026.
Mathematical Theory for Electromagnetic Scattering Resonances and Field Enhancement in a Subwavelength Annular GapJunshan Lin, Wangtao Lu, Hai Zhang — SIAM Journal on Multiscale Modeling and Simulation, 2023.
Scattering by a Periodic Array of Subwavelength Slits II: Surface Bound State, Total Transmission and Field Enhancement in Homogenization Regimeswith J. Lin — SIAM Journal on Multiscale Modeling and Simulation, 16(2), 954–990, 2018.
Scattering by a Periodic Array of Subwavelength Slits I: Field Enhancement in the Diffraction Regimewith J. Lin — SIAM Journal on Multiscale Modeling and Simulation, 16(2), 922–953, 2018.
Scattering and Field Enhancement of a Perfect Conducting Narrow Slitwith J. Lin — SIAM Journal on Applied Mathematics, 77(3), 951–976, 2017.
Fano Resonance for a Periodic Array of Perfectly Conducting Narrow Slitswith Junshan Lin, Stephen P. Shipman — SIAM Journal on Applied Mathematics, 80(5), 2045–2070, 2020.
Fano Resonance in Metallic Grating via Strongly Coupled Subwavelength ResonatorsJunshan Lin, Hai Zhang — European Journal of Applied Mathematics, 2020.
Theory of Super-Resolution and Super-Focusing in Resonant Media
Sub-wavelength Focusing of Acoustic Waves in Bubbly Mediawith H. Ammari, B. Fitzpatrick, D. Gontier, H. Lee — Proceedings of the Royal Society A, 473:20170469, 2017.
Effective Medium Theory for Acoustic Waves in Bubbly Fluids near Minnaert Resonant Frequencywith H. Ammari — SIAM Journal on Mathematical Analysis, 49(4), 3252–3276, 2017.
Super-Resolution in High Contrast Mediawith Habib Ammari — Proceedings of the Royal Society A, 471, 2015.
A Mathematical Theory of Super-Resolution by Using a System of Sub-wavelength Helmholtz Resonatorswith Habib Ammari — Communications in Mathematical Physics, 337(1), 2015.
Super-Resolution Techniques / Algorithms in Imaging
Towards a Theory of Stable Super-Resolution: Model-Based Formulation and Stability AnalysisZetao Fei, Hai Zhang — Inverse Problems and Imaging, 2026.
Mathematical Analysis of Resonances for an Array of Subwavelength Annular Holes and Its Application in Super-Resolution ImagingJiaxin Zhou, Junshan Lin, Wangtao Lu, Hai Zhang — SIAM Journal on Applied Mathematics, 85(4), 1785–1809, 2025.
SCAN-MUSIC: An Efficient Super-Resolution Algorithm for Single Snapshot Wide-Band Line Spectral EstimationZetao Fei, Hai Zhang — Numerical Algorithms, 101, 2069–2100, 2026.
IFF: A Super-Resolution Algorithm for Multiple MeasurementsZetao Fei, Hai Zhang — SIAM Journal on Imaging Sciences, 16(4), 2175–2201, 2023.
A Measurement Decoupling Based Efficient Algorithm for Super-Resolving Point Sources with a Multi-Cluster StructurePing Liu, Hai Zhang — submitted, arXiv:2204.00469v1.
Sensitivity of Resonance Frequency in the Detection of Thin Layer Using Nano-slit StructuresJunshan Lin, Sang-Hyun Oh, Hai Zhang — IMA Journal of Applied Mathematics, 86(1), 146–164, 2021.
A Super-Resolution Imaging Approach via Subwavelength Hole ResonancesJunshan Lin, Hai Zhang — Physical Review Applied, 14(3), 034066, 2020.
Inverse Problems (Uniqueness and Stability)
Stability for the Lens Rigidity Problemwith Gang Bao — Archive for Rational Mechanics and Analysis, 225(3), 1127–1160, 2017.
Stability Analysis for Magnetic Resonance Elastographywith Habib Ammari, Alden Waters — Journal of Mathematical Analysis and Applications, 430, 919–931, 2015.
Sensitivity Analysis of an Inverse Problem for the Wave Equation with Causticswith Gang Bao — Journal of the American Mathematical Society, 27, 953–981, 2014.
Unique Determination of Periodic Polyhedral Structures by Scattered Electromagnetic Fields II: The Resonance Casewith Gang Bao, Jun Zou — Transactions of the AMS, 366(3), 1333–1361, 2014.
Unique Determination of Periodic Polyhedral Structures by Scattered Electromagnetic Fieldswith Gang Bao, Jun Zou — Transactions of the AMS, 363, 4527–4551, 2011.
Recovery of Polyhedral Obstacles by a Single Far Field Measurementwith Hongyu Liu, Jun Zou — Journal of Mathematical Physics, 50, 2009.
Miscellaneous
Multiple Particle Tracking via Velocity Filtering (MPT-vVF): A Spatiotemporal Filtering Framework for Robust Tracking of Organelles in Living CellsXinyu Liu, Zetao Fei, Ka Hei Ho, Chun Pui Wu, Jiamin Zeng, Yandong Yin, Hai Zhang, Hyokeun Park — Preprint, 2026.
Optimal Design of Broadband Absorbers with Multiple Plasmonic Nanoparticles via Reduced Basis MethodYu Gao, Kai Zhang, Hai Zhang — SIAM Journal on Multiscale Modeling & Simulation, 24(3), 913–945, 2026.
A Convergent Multiscale Gaussian Beam Parametrix for Wave Equationswith Gang Bao, Jianliang Qian, Lexing Ying — Communications in Partial Differential Equations, 38, 2013.
A Rigorous Theory on Electromagnetic Diffraction by a Planar Aperture in a Perfectly Conducting ScreenYing Liang, Hai Zhang — Journal of Mathematical Physics, 65(7), 072902, 2024.