On Cloaking, Anomalous Resonance, and Superlenses

  • Further comments on Mark Stockman's article "Criterion for Negative Refraction with Low Optical Losses from a Fundamental Principle of Causality (2020) , with A. Srivastava ArXiv Version .
  • A review of anomalous resonance, its associated cloaking, and superlensing (2020) , with R. C. McPhedran ArXiv Version .
  • Bounds on Herglotz functions and fundamental limits of broadband passive quasi-static cloaking (2017) , with M. Cassier ArXiv Version .
  • Sensitivity of anomalous localized resonance phenomena with respect to dissipation (2016) , with T. Meklachi, D. Onofrei, A. E. Thaler, and G. Funchess ArXiv Version .
  • Spectral theory of a Neumann-Poincare-type operator and analysis of cloaking due to anomalous localized resonance II (2014) , with H. Ammari, G. Ciraolo, H. Kang, and H. Lee ArXiv Version .
  • Anomalous localized resonance using a folded geometry in three dimensions (2013) , with H. Ammari, G. Ciraolo, H. Kang, and H. Lee ArXiv Version .
  • Spectral theory of a Neumann-Poincare-type operator and analysis of cloaking due to anomalous localized resonance (2013) , with H. Ammari, G. Ciraolo, H. Kang, and H. Lee ArXiv Version .
  • Mathematical analysis of the two dimensional active exterior cloaking in the quasistatic regime (2012) , with F. Guevara Vasquez and D. Onofrei ArXiv Version .
  • Exterior cloaking with active sources in two dimensional acoustics (2011) , with F. Guevara Vasquez and D. Onofrei ArXiv Version .
  • Broadband exterior cloaking (2009) , with F. Guevara Vasquez and D. Onofrei ArXiv Version .
  • Active exterior cloaking for the 2D Laplace and Helmholtz equations (2009) , with F. Guevara Vasquez and D. Onofrei ArXiv Version .
  • Cloaking by plasmonic resonance among systems of particles: cooperation or combat? (2009) , with R. C. McPhedran, N.-A. P. Nicorovici, and L.C.Botten.
  • Solutions in folded geometries, and associated cloaking due to anomalous resonance (2008) , with N.-A. P. Nicorovici, R. C. McPhedran, K. Cherednichenko, and Z. Jacob ArXiv Version .
  • Non-magnetic cloak with minimized scattering (2007) , with W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev ArXiv Version .
  • Quasistatic cloaking of two-dimensional polarizable discrete systems by anomalous resonance (2007) with N.A.Nicorovici, R.C.McPhedran, and L.C.Botten.
  • Opaque perfect lenses (2007) , with N.-A. P. Nicorovici and R. C. McPhedran ArXiv Version .
  • On cloaking for elasticity and physical equations with a transformation invariant form (2006) , with M. Briane and J. R. Willis.
  • Partial resonances of three-phase composites at long wavelengths (2006) , with N.-A. P. Nicorovici, R. C. McPhedran, and L. C. Botten ArXiv Version .
  • On the cloaking effects associated with anomalous localized resonance (2006) , with N.-A. P. Nicorovici
  • Optimizing the superlens: manipulating geometry to enhance the resolution (2005) , with V. A. Podolskiy and N. A. Kuhta .
  • A proof of superlensing in the quasistatic regime, and limitations of superlenses in this regime due to anomalous localized resonance (2005) , with N.-A. P. Nicorovici, R. C. McPhedran, and V. A. Podolskiy.

    • On the Hall Effect, and magnetotransport in composites

  • Theory of the Hall effect in three-dimensional metamaterials (2018) , with C. Kern, M. Kadic, and M. Wegener ArXiv Version .
  • Bounds on strong field magneto-transport in three-dimensional composites (2011) , with M. Briane ArXiv Version .
  • New bounds on strong field magneto-transport in multiphase columnar composites (2010) , with M. Briane. Hal.archives Version
  • An antisymmetric effective Hall matrix (2010) , with M. Briane Hal.archives Version .
  • Giant Hall effect in composites (2009) , with M. Briane. Hal.archives Version .
  • Homogenization of the three-dimensional Hall effect and change of sign of the {Hall}-coefficient (2009) , with M. Briane Hal.archives Version .
  • Homogenization of the two-dimensional Hall effect (2008) , with M. Briane and D. Manceau. Hal.archives Version .
  • Reversal of the Hall coefficient sign under homogenization (2007) , with M. Briane.

    • On the possible elastic, mechanical, and elastodynamic properties of metamaterials and composites

  • Planar polycrystals with extremal bulk and shear moduli (2021) ArXiv Version .
  • Stiff competition (2018)
  • Near optimal pentamodes as a tool for guiding stress while minimizing compliance in 3d-printed materials: a complete solution to the weak G-closure problem for 3d-printed materials (2018) , with M. Camar-Eddine ArXiv Version .
  • Towards a complete characterization of the effective elasticity tensors of mixtures of an elastic phase and an almost rigid phase (2017) , with M. Briane and D. Harutyunyan ArXiv Version .
  • On the possible effective elasticity tensors of 2-dimensional and 3-dimensional printed materials (2017) , with M. Briane and D. Harutyunyan ArXiv Version .
  • New examples of three-dimensional dilational materials (2015) , ArXiv Version .
  • Rigorous bounds on the effective moduli of composites and inhomogeneous bodies with negative-stiffness phases (2014) , with D. Kochmann ArXiv Version .
  • On three-dimensional dilational elastic metamaterials (2014) , with T. Buckmann, R. Schittny, M. Thiel, M. Kadic, and M. Wegener ArXiv Version .
  • Adaptable nonlinear bimode metamaterials with rigid bars, pivots, and actuators (2013) , ArXiv Version .
  • Complete characterization of the macroscopic deformations of periodic unimode metamaterials of rigid bars and pivots (2013) , ArXiv Version .
  • A metamaterial having a frequency dependent elasticity tensor and a zero effective mass density (2012) , with P. Seppecher ArXiv Version .
  • New metamaterials with macroscopic behavior outside that of continuum elastodynamics (2007) , ArXiv Version .
  • On modifications of Newton's second law and linear continuum elastodynamics (2007) , with J. R. Willis.
  • The total creep of viscoelastic composites under hydrostatic or antiplane loading (2005) with V. Vinogradov.

    • Bounds on the complex conductivity of composites

  • Tight Bounds on the Effective Complex Permittivity of Isotropic Composites and Related Problems (2020) , with C. Kern and O. Miller ArXiv Version .

    • Space-time interfaces, microstructures and hyperbolic metamaterials

  • An energy conserving mechanism for temporal metasurfaces (2022) , with K. Deshmukh ArXiv Version .
  • Frontal waves and transmissions for temporal laminates and imperfect chiral interfaces (2022) , with A.B. Movchan, N.V. Movchan, I.S. Jones, and H.M Nguyen ArXiv Version .
  • Field Patterns: A new type of wave with infinitely degenerate band structure (2017) , with O. Mattei ArXiv Version .
  • Field patterns without blow up (2017) , with O. Mattei ArXiv Version .
  • Field Patterns: A New Mathematical Object (2017) , with O. Mattei ArXiv Version .
  • The searchlight effect in hyperbolic materials (2013) , with R. C. McPhedran and A. Sihvola ArXiv Version .

    • Review of the subject of metamaterials

  • 3D metamaterials (2019) , with M.Kadic, M. van Hecke, and M.Wegener Leiden Repository Version .

    • Open problems

  • Some open problems in the theory of composites (2021) ArXiv Version .

    • On FFT algorithms and other numerical results for composites

  • Convergence of iterative methods based on Neumann series for composite materials: theory and practice (2018) , with H. Moulinec and P. Suquet ArXiv Version .
  • Spectral super-resolution in metamaterial composites (2011) , with J. Helsing and R. C. McPhedran ArXiv Version .
  • An accelerated FFT algorithm for thermoelastic and nonlinear composites (2008) , with V. Vinogradov.

    • Homogenization and approximations for effective moduli of composites, and connections with Stieltjes functions

  • A theory of composites perspective on matrix valued Stieltjes functions (2023) with M. Putinar ArXiv Version .
  • Approximating the effective tensor as a function of the component tensors in two-dimensional composites of two anisotropic phases (2018) ArXiv Version .
  • High frequency homogenization for travelling waves in periodic media (2016) , with D. Harutyunyan and R. Craster ArXiv Version .
  • Effective conductivities of thin-interphase composites (2013) , with B. Alali ArXiv Version .
  • An effective medium theory for multi-phase matrix-based dielectric composites with randomly oriented ellipsoidal inclusions (2011) , with Y. Benveniste.
  • Realizability of metamaterials with prescribed electric permittivity and magnetic permeability tensors (2010) , ArXiv Version .
  • The effective medium approximation and the average field approximation vis-vis the Hashin-Shtrikman bounds in two-phase matrix-based composites. II The generalized self-consistent scheme (2010) , with Y. Benveniste
  • The effective medium approximation and the average field approximation vis-\'a-vis the Hashin-Shtrikman bounds in two-phase matrix-based composites. I The self-consistent scheme in matrix-based composites (2010) , with Y. Benveniste
  • Non-local interactions in the homogenization closure of thermoelectric functionals (2005) , with M. Camar-Eddine.
  • On optimizing the properties of hierarchical laminates using Pontryagin's maximum principle (2005) .

    • On realizability of fields in composites and bodies

  • Isotropic realizability of current fields in R^3 (2015) , with M. Briane Hal.archives Version .
  • Which electric fields are realizable in conducting materials? (2014) , with M. Briane and A. Treibergs ArXiv Version .

    • On quasiconvexity, Q*-convenvexity, boundary field equalities and inequalities

  • Exact relations for Green's functions in linear PDE and boundary field equalities: a generalization of conservation laws (2019), with D. Onofrei ArXiv Version .
  • A new route to finding bounds on the spectrum of many physical operators (2018), ArXiv Version .
  • Towards characterization of all 3 x 3 extremal quasiconvex quadratic forms (2017) , with D. Harutyunyan ArXiv Version .
  • On the relation between extremal elasticity tensors with orthotropic symmetry and extremal polynomials (2017) , with D. Harutyunyan ArXiv Version .
  • Addendum to ``Sharp inequalities which generalize the divergence theorem: an extension of the notion of quasi-convexity (2015) , ArXiv Version .
  • Explicit examples of extremal quasiconvex quadratic forms that are not polyconvex (2015) , with D. Harutyunyan ArXiv Version .
  • Sharp inequalities which generalize the divergence theorem: an extension of the notion of quasi-convexity (2013) , ArXiv Version .

    • On Analytic Materials

  • Analytic Materials (2016) , ArXiv Version .

    • On Variational Principles for Wave Equations in Lossy Media

  • Bounds on complex polarizabilities and a new perspective on scattering by a lossy inclusion (2017) ArXiv Version .
  • Minimum variational principles for time-harmonic waves in a dissipative medium and associated variational principles of Hashin-Shtrikman type (2010) , with J. Willis ArXiv Version .
  • Minimization variational principles for acoustics, elastodynamics, and electromagnetism in lossy inhomogeneous bodies at fixed frequency (2008) , with P. Seppecher and G. Bouchitte ArXiv Version .

    • On Networks and Discrete Models

  • The obstacle problem in no-tension structures and cable nets (2023) , with A. Amendola, O. Mattei, and P. Seppecher ArXiv Version .
  • Limit analysis of strut nets (2022) , with A. Amendola, A. Fortunato, F. Fraternali, O. Mattei, and P. Seppecher ArXiv Version .
  • On the forces that cable webs under tension can support and how to design cable webs to channel stresses (2019) , with G. Bouchitte, O. Mattei, and P. Seppecher. ArXiv Version .
  • The set of forces that ideal trusses, or wire webs, under tension can support (2017) ArXiv Version .
  • Complete characterization and synthesis of the response function of elastodynamic networks (2011) , with F. Guevara Vasquez and D. Onofrei ArXiv Version .
  • Hybrid electromagnetic circuits (2010) , with P. Seppecher ArXiv Version .
  • Electromagnetic circuits (2010) , with P. Seppecher ArXiv Version .
  • Realizable response matrices of multi-terminal electrical, acoustic and elastodynamic networks at a given frequency (2008) , with P. Seppecher ArXiv Version .

    • On seismic isolators

  • A biomimetic sliding–stretching approach to seismic isolation (2021) , with F. Fraternali, N. Singh, A. Amendola, and G. Benzoni.

    • On bounding the size inclusion in a body, or fields in that inclusion, or the volume fraction in a composite

  • Determining the volume fraction in 2-phase composites and bodies using time varying applied fields (submitted) , with O. Mattei and M. Putinar ArXiv Version .
  • An extremal problem arising in the dynamics of two-phase materials that directly reveals information about the internal geometry (2022) , with O. Mattei and M. Putinar ArXiv Version .
  • Criteria for guaranteed breakdown in two-phase inhomogeneous bodies (2017) , with P. Bardsley, M. S. Primrose, M. Zhao, J. Boyle, N. Briggs, and Z. Koch ArXiv Version .
  • Bounds on the volume of an inclusion in a body from a complex conductivity measurement (2015) , with A. Thaler ArXiv Version .
  • Exact determination of the volume of an inclusion in a body having constant shear modulus (2014) , with A. Thaler ArXiv Version .
  • Bounds on the size of an inclusion using the translation method for two-dimensional complex conductivity (2014) , with H. Kang, K. Kim, H. Lee, and X. Li ArXiv Version .
  • Bounds on the volume fraction of the two-phase shallow shell using one measurement (2014) , with H. Kang and J.-N. Wang ArXiv Version .
  • Bounds on the volume fractions of two materials in a three dimensional body from boundary measurements by the translation method (2013) , with H. Kang ArXiv Version .
  • Bounds on the volume fraction of 2-phase, 2-dimensional elastic bodies and on (stress, strain) pairs in composites (2012) , with L. H. Nguyen ArXiv Version .
  • Universal bounds on the electrical and elastic response of two-phase bodies and their application to bounding the volume fraction from boundary measurements (2012) , ArXiv Version .
  • Sharp bounds on the volume fractions of two materials in a two-dimensional body from electrical boundary measurements: the translation method (2012) , with H. Kang and E. Kim ArXiv Version .

    • On the Polya-Szego and Eshelby conjectures, and inclusions with uniform fields inside them

  • Inclusions of General Shapes Having Constant Field Inside the Core and Non-Elliptical Neutral Coated Inclusions With Anisotropic Conductivity (2020) , with M. Lim ArXiv Version .
  • Progress on the strong Eshelby's conjecture and extremal structures for the elastic moment tensor (2010) , with H. Ammari, Y. Capdeboscq, H. Kang, H. Lee, and H. Zribi ArXiv Version .
  • Inclusion pairs satisfying Eshelby's uniformity property (2008) , with H. Kang and E. Kim.
  • Solutions to the Polya-Szego conjecture and the weak Eshelby conjecture (2008) , with H. Kang ArXiv Version .
  • On conjectures of Polya-Szego and Eshelby (2006) , with H. Kang.

    • On a unifying perspective on linear equations in science

  • A unifying perspective on linear continuum equations prevalent in science. Part I: Canonical forms for static, steady, and quasistatic equations (2020) ArXiv Version .
  • A unifying perspective on linear continuum equations prevalent in science. Part II: Canonical forms for time-harmonic equations (2020) ArXiv Version .
  • A unifying perspective on linear continuum equations prevalent in science. Part III: Canonical forms for dynamic equations with moduli that may, or may not, vary with time (2020) ArXiv Version .
  • A unifying perspective on linear continuum equations prevalent in science. Part IV: Canonical forms for equations involving higher order gradients (2020) ArXiv Version .
  • A unifying perspective on linear continuum equations prevalent in science. Part V: Resolvents; bounds on their spectrum; and their Stieltjes integral representations (2020) ArXiv Version .
  • A unifying perspective on linear continuum equations prevalent in science. Part VI: Rapidly converging series expansions for their solution (2020) ArXiv Version .
  • A unifying perspective on linear continuum equations prevalent in science. Part VII: Boundary value and scattering problems (2021) ArXiv Version .

    • On climbing ropes

  • On ideal dynamic climbing ropes (2016) , with D. Harutyunyan, T. J. Dick, and J. Boyer ArXiv Version .

    • On dark matter and dark energy in the universe

  • A possible explanation of dark matter and dark energy involving a vector torsion field (2022) , ArXiv Version .