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 quasistatic 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 NeumannPoincaretype 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 NeumannPoincaretype 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 .

Nonmagnetic cloak with minimized
scattering (2007)
, with W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev
ArXiv Version .

Quasistatic cloaking of twodimensional
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 threephase
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
threedimensional metamaterials (2018) , with C. Kern, M. Kadic, and M. Wegener
ArXiv Version .

Bounds on strong field magnetotransport in threedimensional composites (2011)
, with M. Briane
ArXiv Version .

New bounds on strong field magnetotransport 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 threedimensional Hall effect and
change of sign of the {Hall}coefficient (2009)
, with M. Briane
Hal.archives Version .

Homogenization of the twodimensional 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 3dprinted materials:
a complete solution to the weak Gclosure problem for
3dprinted materials (2018)
, with M. CamarEddine
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 2dimensional
and 3dimensional printed materials (2017)
, with M. Briane and D. Harutyunyan
ArXiv Version .

New examples of threedimensional
dilational materials (2015)
,
ArXiv Version .

Rigorous bounds on the effective moduli of composites and
inhomogeneous bodies with negativestiffness phases (2014)
, with D. Kochmann
ArXiv Version .

On threedimensional 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 .
Spacetime 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 superresolution 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 twodimensional
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
thininterphase composites (2013)
, with B. Alali
ArXiv Version .

An effective medium theory for multiphase matrixbased
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
visvis the HashinShtrikman bounds in twophase matrixbased composites. II The
generalized selfconsistent scheme (2010)
, with Y. Benveniste

The effective medium approximation
and the average field approximation vis\'avis the
HashinShtrikman bounds in twophase
matrixbased composites. I The selfconsistent scheme in matrixbased
composites (2010)
, with Y. Benveniste

Nonlocal interactions in the homogenization closure of
thermoelectric functionals (2005)
, with M. CamarEddine.

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 quasiconvexity (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
quasiconvexity (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 timeharmonic
waves in a dissipative medium and associated variational
principles of HashinShtrikman 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 notension
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 multiterminal electrical,
acoustic and elastodynamic networks at a given
frequency (2008)
, with P. Seppecher
ArXiv Version .
On seismic isolators

A biomimetic slidingâ€“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 2phase 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 twophase materials that directly reveals
information about the internal geometry (2022)
, with O. Mattei and M. Putinar
ArXiv Version .

Criteria for guaranteed breakdown
in twophase 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 twodimensional complex conductivity (2014)
, with H. Kang, K. Kim, H. Lee, and X. Li
ArXiv Version .

Bounds on the volume fraction of the twophase 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 2phase, 2dimensional
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 twophase 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 twodimensional body from electrical boundary
measurements: the translation method (2012)
, with H. Kang and E. Kim
ArXiv Version .
On the PolyaSzego and Eshelby conjectures, and inclusions
with uniform fields inside them

Inclusions of General Shapes Having Constant Field Inside the Core and NonElliptical 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 PolyaSzego
conjecture and the weak Eshelby conjecture (2008)
, with H. Kang
ArXiv Version .

On conjectures of PolyaSzego 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 timeharmonic 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 .