Open Access
Volume 57, Number 2, March-April 2023
Page(s) 491 - 543
Published online 23 March 2023
  1. G. Allaire, Homogenization of the Stokes flow in a connected porous medium. Asymptotic Anal. 2 (1989) 203–222. [Google Scholar]
  2. Y. Almog, Averaging of dilute random media: a rigorous proof of the Clausius-Mossotti formula. Arch. Ration. Mech. Anal. 207 (2013) 785–812. [Google Scholar]
  3. Y. Almog, The Clausius-Mossotti formula for dilute random media of perfectly conducting inclusions. SIAM J. Math. Anal. 49 (2017) 2885–2919. [Google Scholar]
  4. H. Ammari and B. Davies, Mimicking the active cochlea with a fluid-coupled array of subwavelength Hopf resonators. Proc. R. Soc. A 476 (2020) 20190870. [Google Scholar]
  5. H. Ammari and H. Zhang, Super-resolution in high-contrast media. Proc. R. Soc. A Math. Phys. Eng. Sci. 471 (2015) 20140946. [Google Scholar]
  6. H. Ammari and H. Zhang, Effective medium theory for acoustic waves in bubbly fluids near Minnaert resonant frequency. SIAM J. Math. Anal. 49 (2017) 3252–3276. [Google Scholar]
  7. H. Ammari, H. Kang and H. Lee, Layer Potential Techniques in Spectral Analysis. Vol. 153. American Mathematical Society, Providence, Rhode Island (2009). [Google Scholar]
  8. H. Ammari, G. Ciraolo, H. Kang, H. Lee and G.W. Milton, Spectral theory of a Neumann–Poincaré-type operator and analysis of cloaking due to anomalous localized resonance. Arch. Ration. Mech. Anal. 208 (2013) 667–692. [Google Scholar]
  9. H. Ammari, B. Fitzpatrick, D. Gontier, H. Lee and H. Zhang, A mathematical and numerical framework for bubble meta-screens. SIAM J. Appl. Math. 77 (2017) 1827–1850. [Google Scholar]
  10. H. Ammari, B. Fitzpatrick, D. Gontier, H. Lee and H. Zhang, Sub-wavelength focusing of acoustic waves in bubbly media. Proc. R. Soc. A Math. Phys. Eng. Sci. 473 (2017) 20170469. [Google Scholar]
  11. H. Ammari, B. Fitzpatrick, D. Gontier, H. Lee and H. Zhang, Minnaert resonances for acoustic waves in bubbly media. Annales de l’Institut Henri Poincaré (C) Analyse Non Linéaire 35 (2018) 1975–1998. [CrossRef] [MathSciNet] [Google Scholar]
  12. H. Ammari, B. Fitzpatrick, H. Kang, M. Ruiz, S. Yu and H. Zhang, Mathematical and Computational Methods in Photonics and Phononics. Vol. 235 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, Rhode Island (2018). [Google Scholar]
  13. H. Ammari, D.P. Challa, A.P. Choudhury and M. Sini, The point-interaction approximation for the fields generated by contrasted bubbles at arbitrary fixed frequencies. J. Differ. Equ. 267 (2019) 2104–2191. [CrossRef] [Google Scholar]
  14. H. Ammari, B. Fitzpatrick, H. Lee, S. Yu and H. Zhang, Double-negative acoustic metamaterials. Q. Appl. Math. 77 (2019) 767–791. [Google Scholar]
  15. H. Ammari, D.P. Challa, A.P. Choudhury and M. Sini, The equivalent media generated by bubbles of high contrasts: volumetric metamaterials and metasurfaces. Multiscale Model. Simul. 18 (2020) 240–293. [Google Scholar]
  16. H. Ammari, B. Davies, E.O. Hiltunen, H. Lee and S. Yu, High-order exceptional points and enhanced sensing in subwavelength resonator arrays. Stud. Appl. Math. 146 (2020) 440–462. [Google Scholar]
  17. H. Ammari, B. Davies, E.O. Hiltunen and S. Yu, Topologically protected edge modes in one-dimensional chains of subwavelength resonators. J. Math. Appl. 144 (2020) 17–49. [Google Scholar]
  18. H. Ammari, E.O. Hiltunen and S. Yu, A high-frequency homogenization approach near the dirac points in bubbly honeycomb crystals. Arch. Ration. Mech. Anal. 238 (2020) 1559–1583. [CrossRef] [MathSciNet] [Google Scholar]
  19. H. Ammari, P. Millien and A.L. Vanel, Modal expansion for plasmonic resonators in the time domain. Preprint arXiv:2003.09200 (2020). [Google Scholar]
  20. H. Ammari, B. Davies, E.O. Hiltunen, H. Lee and S. Yu, Wave interaction with subwavelength resonators, in Applied Mathematical Problems in Geophysics. Springer, Cham (2022) 23–83. [CrossRef] [Google Scholar]
  21. O.F. Bandtlow, Estimates for norms of resolvents and an application to the perturbation of spectra. Math. Nachr. 267 (2004) 3–11. [Google Scholar]
  22. G. Bouchitté and D. Felbacq, Homogenization near resonances and artificial magnetism from dielectrics. C. R. Math. 339 (2004) 377–382. [CrossRef] [MathSciNet] [Google Scholar]
  23. G. Bouchitté and R. Petit, Homogenization techniques as applied in the electromagnetic theory of gratings. Electromagnetics 5 (1985) 17–36. [CrossRef] [Google Scholar]
  24. G. Bouchitté, C. Bourel and D. Felbacq, Homogenization near resonances and artificial magnetism in three dimensional dielectric metamaterials. Arch. Ration. Mech. Anal. 225 (2017) 1233–1277. [Google Scholar]
  25. T. Brunet, O. Poncelet, C. Aristégui, J. Leng and O. Mondain-Monval, Soft 3D acoustic metamaterials. J. Acoust. Soc. Am. 138 (2015) 1733–1733. [CrossRef] [Google Scholar]
  26. D.P. Challa and M. Sini, On the justification of the Foldy-Lax approximation for the acoustic scattering by small rigid bodies of arbitrary shapes. Multiscale Model. Simul. 12 (2014) 55–108. [Google Scholar]
  27. D.P. Challa, A. Mantile and M. Sini, Characterization of the acoustic fields scattered by a cluster of small holes. Asymptotic Anal. 118 (2020) 235–268. [CrossRef] [MathSciNet] [Google Scholar]
  28. Y. Chen, H. Liu, M. Reilly, H. Bae and M. Yu, Enhanced acoustic sensing through wave compression and pressure amplification in anisotropic metamaterials. Nat. Commun. 5 (2014) 1–9. [Google Scholar]
  29. K.D. Cherednichenko, Y.Y. Ershova and A.V. Kiselev, Effective behaviour of critical-contrast PDEs: micro-resonances, frequency conversion, and time dispersive properties. I. Commun. Math. Phys. 375 (2020) 1833–1884. [Google Scholar]
  30. K.D. Cherednichenko, Y.Y. Ershova, A.V. Kiselev and S.N. Naboko, Unified approach to critical-contrast homogenisation with explicit links to time-dispersive media. Trans. Moscow Math. Soc. 80 (2020) 251–294. [Google Scholar]
  31. V. Chiado Piat and M. Codegone, Scattering problems in a domain with small holes. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas (RACSAM) 97 (2003) 447. [Google Scholar]
  32. D. Cioranescu and F. Murat, A strange term coming from nowhere, in Topics in the Mathematical Modelling of Composite Materials. Vol. 31 of Progr. Nonlinear Differential Equations Appl. Birkhäuser Boston, Boston, MA (1997) 45–93. [Google Scholar]
  33. D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory. Vol. 93 of Applied Mathematical Sciences, Springer, Cham (2019). [CrossRef] [Google Scholar]
  34. S.A. Cummer, J. Christensen and A. Alù, Controlling sound with acoustic metamaterials. Nat. Rev. Mater. 1 (2016) 1–13. [Google Scholar]
  35. F. Feppon, High order homogenization of the Poisson equation in a perforated periodic domain. To appear in the Radon Series on Computational and Applied Mathematics (2020). [Google Scholar]
  36. F. Feppon, High order homogenization of the Stokes system in a periodic porous medium. SIAM J. Math. Anal. 53 (2021) 2890–2924. [Google Scholar]
  37. F. Feppon and H. Ammari, Analysis of a Monte-Carlo Nystrom method. SIAM J. Numer. Anal. 60 (2022) 1226–1250. [Google Scholar]
  38. F. Feppon and H. Ammari, Modal decompositions and point scatterer approximations near the Minnaert resonance frequencies. Stud. Appl. Math. 149 (2022) 164–229. [Google Scholar]
  39. R. Figari, E. Orlandi and S. Teta, The Laplacian in regions with many small obstacles: fluctuations around the limit operator. J. Stat. Phys. 41 (1985) 465–487. [Google Scholar]
  40. R. Figari, G. Papanicolaou and J. Rubinstein, Remarks on the point interaction approximation. Hydrodyn. Behav. Interacting Part. Syst. 9 (1987) 45–55. [CrossRef] [Google Scholar]
  41. L.L. Foldy, The multiple scattering of waves. I. General theory of isotropic scattering by randomly distributed scatterers. Phys. Rev. 67 (1945) 107. [Google Scholar]
  42. D. Gerard-Varet, A simple justification of effective models for conducting or fluid media with dilute spherical inclusions. Asymptotic Anal. 128 (2022) 31–53. [CrossRef] [MathSciNet] [Google Scholar]
  43. A. Giunti, R. Höfer and J.J. Velázquez, Homogenization for the Poisson equation in randomly perforated domains under minimal assumptions on the size of the holes. Commun. Part. Differ. Equ. 43 (2018) 1377–1412. [CrossRef] [Google Scholar]
  44. A. Giunti, C. Gu and J.-C. Mourrat, Quantitative homogenization of interacting particle systems. Ann. Probab. 50 (2022) 1885–1946. [CrossRef] [MathSciNet] [Google Scholar]
  45. X. Hu, K.M. Ho, C.T. Chan and J. Zi, Homogenization of acoustic metamaterials of Helmholtz resonators in fluid. Phys. Rev. B – Condens. Matter Mater. Phys. 77 (2008) 2–5. [Google Scholar]
  46. M. Kadic, G.W. Milton, M. van Hecke and M. Wegener, 3D metamaterials. Nat. Rev. Phys. 1 (2019) 198–210. [Google Scholar]
  47. N. Kaina, F. Lemoult, M. Fink and G. Lerosey, Negative refractive index and acoustic superlens from multiple scattering in single negative metamaterials. Nature 525 (2015) 77–81. [Google Scholar]
  48. S. Kanagawa, Y. Mochizuki and H. Tanaka, Limit theorems for the minimum interpoint distance between any pair of iid random points in ℝd. Ann. Inst. Stat. Math. 44 (1992) 121–131. [CrossRef] [Google Scholar]
  49. R.V. Kohn, J. Lu, B. Schweizer and M.I. Weinstein, A variational perspective on cloaking by anomalous localized resonance. Commun. Math. Phys. 328 (2014) 1–27. [CrossRef] [Google Scholar]
  50. R. Kress, Linear Integral Equations. Vol. 82. Springer New York (2014). [Google Scholar]
  51. A. Lamacz and B. Schweizer, Effective acoustic properties of a meta-material consisting of small Helmholtz resonators. Preprint arXiv:1603.05395 10 (2016). [Google Scholar]
  52. M. Lanoy, R. Pierrat, F. Lemoult, M. Fink, V. Leroy and A. Tourin, Subwavelength focusing in bubbly media using broadband time reversal. Phys. Rev. B 91 (2015) 224202. [Google Scholar]
  53. G. Ma and P. Sheng, Acoustic metamaterials: from local resonances to broad horizons. Sci. Adv. 2 (2016) e1501595. [Google Scholar]
  54. J.J. Marigo and A. Maurel, Two-scale homogenization to determine effective parameters of thin metallic-structured films. Proc. R. Soc. A Mathe. Phys. Eng. Sci. 472 (2016) 20160068. [Google Scholar]
  55. W.C.H. McLean, Strongly Elliptic Systems and Boundary Integral Equations. Vol. 86. Cambridge University Press (2000). [Google Scholar]
  56. A.M. Merzlikin and R.S. Puzko, Homogenization of Maxwell’s equations in a layered system beyond the static approximation. Sci. Rep. 10 (2020) 1–10. [Google Scholar]
  57. M. Minnaert, XVI, On musical air-bubbles and the sounds of running water. London Edinburgh Dublin Philos. Mag. J. Sci. 16 (1933) 235–248. [Google Scholar]
  58. J.-C. Nédélec, Acoustic and Electromagnetic Equations: Integral Representations for Harmonic Problems. Vol. 144. Springer Science & Business Media (2013). [Google Scholar]
  59. Y. Noguchi and T. Yamada, Topology optimization of acoustic metasurfaces by using a two-scale homogenization method. Appl. Math. Modell. 98 (2021) 465–497. [CrossRef] [Google Scholar]
  60. T. Onoyama, M. Sibuya and H. Tanaka, Limit distribution of the minimum distance between independent and identically distributed d-dimensional random variables, in Statistical Extremes and Applications. Springer (1984) 549–562. [Google Scholar]
  61. B. Orazbayev and R. Fleury, Quantitative robustness analysis of topological edge modes in C6 and valley-Hall metamaterial waveguides. Nanophotonics 8 (2019) 1433–1441. [Google Scholar]
  62. G.C. Papanicolaou and Diffusion in random media, in Surveys in Applied Mathematics. Springer (1995) 205–253. [Google Scholar]
  63. J.B. Pendry, Negative refraction makes a perfect lens. Phys. Rev. Lett. 85 (2000) 3966–3969. [PubMed] [Google Scholar]
  64. K. Pham, J.F. Mercier, D. Fuster, J.J. Marigo and A. Maurel, Scattering of acoustic waves by a nonlinear resonant bubbly screen. J. Fluid Mech. 906 (2021) A19. [CrossRef] [Google Scholar]
  65. J. Rauch, Lecture #3. Scattering by many tiny obstacles, in Partial Differential Equations and Related Topics. Springer, Berlin, Heidelberg (1975) 380–389. [Google Scholar]
  66. J. Rauch and M. Taylor, Potential and scattering theory on wildly perturbed domains. J. Funct. Anal. 18 (1975) 27–59. [CrossRef] [Google Scholar]
  67. B. Schweizer, The low-frequency spectrum of small Helmholtz resonators. Proc. R. Soc. A: Math. Phys. Eng. Sci. 471 (2015) 20140339. [Google Scholar]
  68. B. Schweizer, Resonance meets homogenization. Jahresbericht der Deutschen Mathematiker-Vereinigung 119 (2017) 31–51. [CrossRef] [MathSciNet] [Google Scholar]
  69. M. Touboul, K. Pham, A. Maurel, J.J. Marigo, B. Lombard and C. Bellis, Effective resonant model and simulations in the time-domain of wave scattering from a periodic row of highly-contrasted inclusions. J. Elast. 142 (2020) 53–82. [CrossRef] [Google Scholar]

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