Associate Professor

Biography

Prof. Zhang is an Assistant Professor at HKUST. Before the current position, he was a postdoc at DMA, ENS, Paris.

Research Interests

Applied Math, Inverse Problems, Wave Propagation, Imaging, Super-resolution.

Teaching

• MATH5285  Applied Analysis

Selected Publications

  Article

1. A rigorous theory on electromagnetic diffraction by a planar aperture in a perfectly conducting screen
   • Author(s): Liang, Ying; Zhang, Hai
   • Source: Journal of Mathematical Physics, v. 65, (7), July 2024, article number 072902
   • Year: 2024


2. IFF: A Superresolution Algorithm for Multiple Measurements
   • Author(s): Fei, Zetao; Zhang, Hai
   • Source: SIAM Journal on Imaging Sciences, v. 16, (4), December 2023, p. 2175-2201
   • Year: 2023


3. Dirac Points for the Honeycomb Lattice with Impenetrable Obstacles
   • Author(s): Li, Wei; Lin, Junshan; Zhang, Hai
   • Source: SIAM Journal on Applied Mathematics, v. 83, (4), August 2023, p. 1546-1571
   • Year: 2023


4. Mathematical Theory for Electromagnetic Scattering Resonances and Field Enhancement in a Subwavelength Annular Gap
   • Author(s): Junshan, Lin; Wangtao, Lu; Zhang, Hai
   • Source: Multiscale Modeling and Simulation, v. 21, (3), September 2023, p. 1012-1052
   • Year: 2023


5. Bulk-interface correspondences for one-dimensional topological materials with inversion symmetry
   • Author(s): Thiang, Guo Chuan; Zhang, Hai
   • Source: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, v. 479, (2270), February 2023, article number 20220675
   • Year: 2023


6. A mathematical theory of the computational resolution limit in one dimension
   • Author(s): Liu, Ping; Zhang, Hai
   • Source: Applied and Computational Harmonic Analysis, v. 56, January 2022, p. 402-446
   • Year: 2022


7. Mathematical theory for topological photonic materials in one dimension
   • Author(s): Lin, Junshan; Zhang, Hai
   • Source: Journal of Physics A: Mathematical and Theoretical, v. 55, (49), December 2022, article number 495203
   • Year: 2022


8. Sensitivity of resonance frequency in the detection of thin layer using nano-slit structures
   • Author(s): Lin, Junshan; Oh, Sang-Hyun; Zhang, Hai
   • Source: IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications), v. 86, (1), February 2021, p. 146-164
   • Year: 2021


9. A mathematical theory of computational resolution limit in multi-dimensional spaces
   • Author(s): Liu, Ping; Zhang, Hai
   • Source: Inverse Problems, v. 37, (10), October 2021, article number 104001
   • Year: 2021


10. A Theory of Computational Resolution Limit for Line Spectral Estimation
    • Author(s): Liu, Ping; Zhang, Hai
    • Source: IEEE Transactions on Information Theory, v. 67, (7), July 2021, p. 4812-4827
    • Year: 2021


11. A Mathematical theory for fano resonance in a periodic array of narrow slits
    • Author(s): Lin, Junshan; Shipman, Stephen P.; Zhang, Hai
    • Source: SIAM Journal on Applied Mathematics, v. 80, (5), September 2020, p. 2045-2070
    • Year: 2020


12. Superresolution Imaging via Subwavelength Hole Resonances
    • Author(s): Lin, Junshan; Zhang, Hai
    • Source: Physical Review Applied, v. 14, (3), 3 September 2020, article number 034066
    • Year: 2020


13. Fano resonance in metallic grating via strongly coupled subwavelength resonators
    • Author(s): Lin, Junshan; Zhang, Hai
    • Source: European Journal of Applied Mathematics, v. 32, (2), 30 June 2020, p. 370-394
    • Year: 2020


14. Photonic Band Gap Phenomenon in a Metal–Dielectric Periodic Structure
    • Author(s): Santosa, Fadil; Zhang, Hai
    • Source: Research in Mathematical Sciences, v. 7, (3), September 2020, article number 15
    • Year: 2020


15. Characterization of the Essential Spectrum of the Neumann-poincaré Operator in 2D Domains With Corner via Weyl Sequences
    • Author(s): Bonnetier, Eric; Zhang, Hai
    • Source: Revista Matematica Iberoamericana, v. 35, (3), 2019, p. 925-948
    • Year: 2019


16. The plasmonic resonances of a bowtie antenna
    • Author(s): Bonnetier, Eric; Triki, Faouzi; Dapogny, Charles; Zhang, Hai
    • Source: Analysis in Theory and Applications, v. 35, (1), April 2019, p. 85-116
    • Year: 2019


17. An Integral Equation Method for Numerical Computation of Scattering Resonances in a Narrow Metallic Slit
    • Author(s): Lin, Junshan; Zhang, Hai
    • Source: Journal of Computational Physics, v. 385, May 2019, p. 75-105
    • Year: 2019


18. Double-negative acoustic metamaterials
    • Author(s): Ammari, Habib; Fitzpatrick, Brian; Lee, Hyundae; Yu, Sanghyeon; Zhang, Hai
    • Source: Quarterly of Applied Mathematics, v. 77, (4), December 2019, p. 767-791
    • Year: 2019


19. Bloch Waves in Bubbly Crystal Near the First Band Gap: A High-frequency Homogenization Approach
    • Author(s): Ammari, Habib; Lee, Hyundae; Zhang, Hai
    • Source: SIAM Journal on Mathematical Analysis, v. 51, (1), January 2019, p. 45-59
    • Year: 2019


20. Mathematical Analysis of Surface Plasmon Resonance by a Nano-Gap in the Plasmonic Metal
    • Author(s): Lin, Junshan; Zhang, Hai
    • Source: SIAM Journal on Mathematical Analysis, v. 51, (6), 2019, p. 4448-4489
    • Year: 2019


21. Shape reconstruction of nanoparticles from their associated plasmonic resonances
    • Author(s): Ammari, Habib; Putinar, Mihai; Ruiz, Matias; Yu, Sanghyeon; Zhang, Hai
    • Source: Journal des Mathematiques Pures et Appliquees, v.122, February 2019, p. 23-48
    • Year: 2019


22. Scattering by a Periodic Array of Subwavelength Slits II: Surface Bound States, Total Transmission, and Field Enhancement in Homogenization Regimes
    • Author(s): Lin, Junshan; Zhang, Hai
    • Source: Multiscale Modeling & Simulation, v. 16, (2), 2018, p. 954-990
    • Year: 2018


23. Scattering by a Periodic Array of Subwavelength Slits I: Field Enhancement in the Diffraction Regime
    • Author(s): Zhang, Hai; Lin, Junshan
    • Source: Multiscale Modeling & Simulation, v. 16, (2), May 2018, p. 922-953
    • Year: 2018


24. Reconstructing Fine Details of Small Objects by Using Plasmonic Spectroscopic Data
    • Author(s): Amman, Habib; Ruiz, Matias; Yu, Sanghyeon; Zhang, Hai
    • Source: SIAM Journal on Imaging Sciences, v. 11, (1), January 2018, p. 1-23
    • Year: 2018


25. Field Expansions for Systems of Strongly Coupled Plasmonic Nanoparticles
    • Author(s): Ammari, Habib; Ruiz, Matias; Yu, Sanghyeon; Zhang, Hai
    • Source: SIAM Journal on Numerical Analysis, v. 56, (4), July 2018, p. 2029-2044
    • Year: 2018


26. Reconstructing Fine Details of Small Objects by Using Plasmonic Spectroscopic Data. Part II: The Strong Interaction Regime
    • Author(s): Ammari, Habib; Ruiz, Matias; Yu, Sanghyeon; Zhang, Hai
    • Source: SIAM Journal on Imaging Sciences, v. 11, (3), 2018, p. 1931-1953
    • Year: 2018


27. Minnaert Resonances for Acoustic Waves in Bubbly Media
    • Author(s): Ammari, Habib; Fitzpatrick, Brian; Gontier, David; Lee, Hyundae; Zhang, Hai
    • Source: Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, v. 35, (7), November 2018, p. 1975-1998
    • Year: 2018


28. Mathematical Analysis of Plasmonic Nanoparticles: The Scalar Case
    • Author(s): Ammari, Habib; Millien, Pierre; Ruiz, Matias; Zhang, Hai
    • Source: Archive for Rational Mechanics and Analysis, v. 224, (2), May 2017, p. 597-658
    • Year: 2017


29. Stability for the Lens Rigidity Problem
    • Author(s): Bao, Gang; Zhang, Hai
    • Source: Archive For Rational Mechanics and Analysis, 225, 3, September 2017, p. 1127-1160
    • Year: 2017


30. Scattering and Field Enhancement of a Perfect Conducting Narrow Slit
    • Author(s): Lin, Junshan; Zhang, Hai
    • Source: SIAM Journal on Applied Mathematics, v. 77, (3), 2017, p. 951-976
    • Year: 2017


31. Subwavelength Phononic Bandgap Opening in Bubbly Media
    • Author(s): Ammari, Habib; Fitzpatrick, Brian; Lee, Hyundae; Yu, Sanghyeon; Zhang, Hai
    • Source: Journal of Differential Equations, v. 263, (9), November 2017, p. 5610-5629
    • Year: 2017


32. Sub-wavelength Focusing of Acoustic Waves in Bubbly Media
    • Author(s): Ammari, Habib; Fitzpatrick, Brian; Gontier, David; Lee, Hyundae; Zhang, Hai
    • Source: PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, v.473, (2208), December 2017, article number 20170469
    • Year: 2017


33. A Mathematical and Numerical Framework for Bubble Meta-screens
    • Author(s): Ammari, Habib; Fitzpatrick, Brian; Gontier, David; Lee, Hyundae; Zhang, Hai
    • Source: SIAM Journal on Applied Mathematics, v. 77, (5), October 2017, p. 1827-1850
    • Year: 2017


34. Effective Medium Theory for Acoustic Waves in Bubbly Fluids Near Minnaert Resonant Frequency
    • Author(s): Ammari, Habib; Zhang, Hai
    • Source: SIAM Journal on Mathematical Analysis, v.49, (4), August 2017, p. 3252-3276
    • Year: 2017


35. Mathematical and Numerical Framework for Metasurfaces Using Thin Layers of Periodically Distributed Plasmonic Nanoparticles
    • Author(s): Ammari, Habib; Ruiz, Matias; Wu, Wei; Yu, Sanghyeon; Zhang, Hai
    • Source: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, v. 472, (2193), September 2016, article number 20160445
    • Year: 2016


36. Mathematical Analysis of Plasmonic Resonances for Nanoparticles: The Full Maxwell Equations
    • Author(s): Ammari, Habib; Ruiz, Matias; Yu, Sanghyeon; Zhang, Hai
    • Source: Journal of Differential Equations, v. 261, (6), September 2016, p. 3615-3669
    • Year: 2016


37. Stability analysis for Magnetic Resonance Elastography
    • Author(s): Habib, Ammari; Alden, Waters; Zhang, Hai
    • Source: Journal of Mathematical Analysis and Applications, v. 430, (2), October 2015, p. 919-931
    • Year: 2015


38. Super-resolution in High-contrast Media
    • Author(s): Habib, Ammari; Zhang, Hai
    • Source: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, v. 471, (2178), June 2015, article number 20140946
    • Year: 2015


39. A Mathematical Theory of Super-Resolution by Using a System of Sub-Wavelength Helmholtz Resonators
    • Author(s): Habib, Ammari; Zhang, Hai
    • Source: Communications in Mathematical Physics, v. 337, (1), July 2015, p. 379-428
    • Year: 2015


40. Unique Determination of Periodic Polyhedral Structures by Scattered Electromagnetic Fields II: the Resonance Case
    • Author(s): Gang, Bao; Jun, Zou; Zhang, Hai
    • Source: ransactions of the American Mathematical Society, v. 336, (3), MAR 2014, p. 1333-1361
    • Year: 2014


41. Sensitive Analysis of an Inverse Problem for the Wave Equation with Caustics
    • Author(s): Gang, Bao; Zhang, Hai
    • Source: Journal of the American Mathematical Society, v. 27, (4), October 2014, p. 953-981
    • Year: 2014


42. A Convergent Multiscale Gaussian Beam Parametrix for Wave Equations
    • Author(s): Gang, Bao; Qian, Jianliang; Ying, Lexing; Zhang, Hai
    • Source: Communications in Partial Differential Equations, v. 38, (1), January 2013, p. 92-134
    • Year: 2013


43. Unique determination of periodic polyhedral structures by scattered electromagnetic fields
    • Author(s): Gang, Bao; Zhang, Hai; Jun, Zou
    • Source: Transactions of the American Mathematical Society, v. 363, (9), 2011, p. 4527-4551
    • Year: 2011


44. Recovery of polyhedral obstacles by a single far-field measurement
    • Author(s): Liu, Hongyu; Jun, Zou; Zhang, Hai
    • Source: Journal of Mathematical Physics, v, 50, (12), 2009, p. 123506
    • Year: 2009

  Book

1. Mathematical and Computational Methods in Photonics and Phononics
   • Author(s): Ammari, Habib; Fitzpatrick, Brian; Kang, Hyeonbae; Ruiz, Matias; Yu, Sanghyeon; Zhang, Hai
   • Year: 2018

  Conference paper

1. Imaging, Multi-Scale and High Contrast PDE
   • Author(s): Zhang, Hai
   • Year: 2014


2. Stability/sensitivity of Recovering Velocity Fields from Boundary Measurements
   • Author(s): Zhang, Hai
   • Year: 2013