Bounds on complex polarizabilities and a new perspective on scattering by a lossy inclusion

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Milton, Graeme W.;

Here we obtain explicit formulae for bounds on the complex electrical polarizability at a given frequency of an inclusion with known volume that follow directly from the quasistatic bounds of Bergman and Milton on the effective complex dielectric constant of a two-phase... View more
  • References (61)
    61 references, page 1 of 7

    [1] J.-L. Auriault, Acoustics of heterogeneous media: Macroscopic behavior by homogenization, Current Topics in Acoustics Research, 1 (1994), pp. 63-90.

    [2] J.-L. Auriault and G. Bonnet, Dynamique des composites elastiques periodiques, Archives of Mechanics = Archiwum Mechaniki Stosowanej, 37 (1985), pp. 269-284.

    [3] M. Avellaneda, Optimal bounds and microgeometries for elastic two-phase composites, SIAM Journal on Applied Mathematics, 47 (1987), pp. 1216-1228, doi:

    [4] D. J. Bergman, The dielectric constant of a composite material - A problem in classical physics, Physics Reports, 43 (1978), pp. 377-407, doi:, http://www.

    [5] D. J. Bergman, Exactly solvable microscopic geometries and rigorous bounds for the complex dielectric constant of a two-component composite material, Physical Review Letters, 44 (1980), pp. 1285- 1287, doi:, 1103/PhysRevLett.44.1285.

    [6] D. J. Bergman, Rigorous bounds for the complex dielectric constant of a two-component composite, Annals of Physics, 138 (1982), pp. 78-114, doi:

    [7] D. J. Bergman and D. Stroud, Theory of resonances in the electromagnetic scattering by macroscopic bodies, Physical Review B: Condensed Matter and Materials Physics, 22 (1980), pp. 3527- 3593, doi:, PhysRevB.22.3527.

    [8] T. Bückmann, M. Kadic, R. Schittny, and M. Wegener, Mechanical metamaterials with anisotropic and negative effective mass-density tensor made from one constituent material, Physica Status Solidi. B, Basic Solid State Physics, 252 (2015), pp. 1671-1674, doi:, http: //

    [9] Y. Capdeboscq and H. Kang, Improved Hashin-Shtrikman bounds for elastic moment tensors and an application, Applied Mathematics and Optimization, 57 (2008), pp. 263-288, doi: 007-9022-9,

    [10] A. Carini and O. Mattei, Variational formulations for the linear viscoelastic problem in the time domain, European Journal of Mechanics, A, Solids, 54 (2015), pp. 146-159, doi:, article/pii/S0997753815000510.

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