CiteULike: norris's library [788 articles]

Acoustic cloaking theory

Andrew Norris — 2008-05-13T13:22:28-00:00

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

An acoustic cloak is a compact region enclosing an object, such that sound incident from all directions passes through and around the cloak as though the object was not present. A theory of acoustic cloaking is developed using the transformation or change-of-variables method for mapping the cloaked region to a point with vanishing scattering strength. We show that the acoustical parameters in the cloak must be anisotropic: either the mass density or the mechanical stiffness or both. If the stiffness is isotropic, corresponding to a fluid with a single bulk modulus, then the inertial density must be infinite at the inner surface of the cloak. This requires an infinitely massive cloak. We show that perfect cloaking can be achieved with finite mass through the use of anisotropic stiffness. The generic class of anisotropic material required is known as a pentamode material (PM). If the transformation deformation gradient is symmetric then the PM parameters are explicit, otherwise its properties depend on a stress-like tensor that satisfies a static equilibrium equation. For a given transformation mapping, the material composition of the cloak is not uniquely defined, but the phase speed and wave velocity of the pseudo-acoustic waves in the cloak are unique. Examples are given from two and three dimensions.

Electromagnetic wave manipulation using layered systems

Huanyang Chen — 2008-05-13T13:19:42-00:00

(9 May 2008)

We show that the optical properties of an oblique layered system with two kinds of isotropic materials can be described using the concept of transformation media as long as the thickness of the layers is much smaller than the wavelength. Once the connection with transformation media is established, we then show that oblique layered system can serve as a universal element to build a variety of interesting functional optical components such as wave splitters, wave combiners, one-dimensional cloaking devices and reflectionless field rotators.

The impedance-matched reduced acoustic cloaking with realizable mass and its layered design

Huan-Yang Chen — 2008-05-13T13:18:20-00:00

(8 May 2008)

The authors present an impedance-matched reduced version of acoustic cloaking whose mass is in a reasonable range. A layered cloak design with isotropic material is also proposed for the reduced cloak. Numerical calculations from the transfer matrix methods show that the present layered cloak can reduce the scattering of an air cylinder substantially.

Statistical Mechanics of Polymer Stretching

Angela Rosa — 2008-05-12T13:27:41-00:00

(2003)

Theory of the new high-efficiency absorbing and nonscattering coatings

Bobrovnitski — 2007-11-15T09:49:50-00:00

Acoustical Physics, Vol. 53, No. 5. (September 2007), pp. 535-545.

Geometric picture of optical complementary media

Monzon — 2008-03-10T14:11:22-00:00

European Journal of Physics, Vol. 29, No. 3. (May 2008), pp. 431-437.

Experimental study on negative effective mass in a 1D mass–spring system

Shanshan Yao — 2008-04-15T18:11:53-00:00

New J. Phys., Vol. 10, No. 4. (April 2008), 043020.

On Norms of Force Functionals and Stress Representations

R Segev — 2008-05-06T13:47:11-00:00

Mathematics and Mechanics of Solids, Vol. 11, No. 3. (1 June 2006), pp. 229-250.

Forces in continuum mechanics are analyzed as 0-currents of geometric measure theory. The representation of forces by stresses is discussed and the flat norm of a force is expressed in terms of stress fields. An analogous treatment expresses the Sobolev norm of a force in terms of stress fields. In both cases, one obtains bounds on the stress fields that are in equilibrium with a given force. The analysis is universal in the sense that it is independent of any constitutive relation. 10.1177/1081286505040402

New Families of Exact Nonlinear Waves for the Neo-Hookean Finite Elastic Solid

James Hill — 2008-05-06T13:06:22-00:00

Mathematics and Mechanics of Solids, Vol. 9, No. 1. (1 February 2004), pp. 81-95.

For the perfectly elastic neo-Hookean material, two well known partial solutions are extended to produce new families of exact nonlinear waves. For plane strain deformations, new results are presented for longitudinal and shear waves, while for axially symmetric defornations incorporating torsion, new results are presented for longitudinal and torsional waves. The plane dynamic deformations also apply to the more general Mooney strain-energy function, while the solutions given for the axially symmetric dynamic deformations incorporating torsion can be similarly deternined for the Mooney material, except that the details are far more complicated and involve elliptic functions. Both families of solutions are illustrated graphically 10.1177/1081286503035200

On Conditions at an Interface between Two Materials in Three-Dimensional Space

L Wheeler — 2008-05-06T12:45:29-00:00

Mathematics and Mechanics of Solids, Vol. 4, No. 2. (1 June 1999), pp. 183-200.

This article is concerned with expressing the kinematics of a bimaterial-bonded interface in terms of strains in the three-dimensional case. It is shown that the continuity of displacements can be replaced by the requirement that the change in principal curvatures, the mean geodesic torsion, and the interior strains be matched across the interface. The reduction of these conditions for a two-dimensional bonded interface is also discussed. 10.1177/108128659900400203

Pure Shears in the Mechanics of Materials

Andrzej Blinowski — 2008-05-06T12:38:15-00:00

Mathematics and Mechanics of Solids, Vol. 3, No. 4. (1 December 1998), pp. 471-503.

The pure shear tensors play a significant role in continuum mechanics. Recent authors' results concerning some remarkable properties of pure shear tensors and their sets are presented. A list of the properties defining pure shears is quoted. The properties of the whole set of all pure shears are described. An extraordinary role of the pure shears in the linear theory of elasticity is disclosed. A new approach, in terms of Kelvin moduli and pure shears as proper elastic states, to the description of the symmetries of elastic materials is proposed. Finally, it is shown that a two-parametric set of orthonormal bases of deviatoric space consisting solely of pure shears can be constructed. 10.1177/108128659800300406

Deformations of Nonlinear Elastic Solids in Unbounded Domains

KR Rajagopal — 2008-05-06T12:31:00-00:00

Mathematics and Mechanics of Solids, Vol. 1, No. 4. (1 December 1996), pp. 463-472.

A boundary layer approximation for nonlinearly elastic solids is advocated, with the full nonlinear equations assumed to hold in a narrow region adjacent to a boundary, whereas in the rest of the domain the equations of linearized elasticity are supposed to hold. 10.1177/108128659600100407

Eulerian Gaussian beams for high-frequency wave propagation

Shingyu Leung — 2008-05-01T18:17:41-00:00

MOUNTAIN WAVES AND GAUSSIAN BEAMS

Nicolay Tanushev — 2008-05-01T18:16:26-00:00

Surface induced phonon decay rates in thin film nano-structures

Douglas Photiadis — 2008-04-30T21:08:51-00:00

Journal of Physics: Conference Series 92 (2007)

CauchyBorn Rule and the Stability of Crystalline Solids: Static Problems

Weinan — 2008-04-22T15:35:12-00:00

Archive for Rational Mechanics and Analysis (February 2007), pp. 241-297.

We study the connection between atomistic and continuum models for the elastic deformation of crystalline solids at zero temperature. We prove, under certain sharp stability conditions, that the correct nonlinear elasticity model is given by the classical Cauchy-Born rule in the sense that elastically deformed states of the atomistic model are closely approximated by solutions of the continuum model with stored energy functionals obtained from the Cauchy-Born rule. The analysis is carried out for both simple and complex lattices, and for this purpose, we develop the necessary tools for performing asymptotic analysis on such lattices. Our results are sharp and they also suggest criteria for the onset of instabilities of crystalline solids.

On the Cauchy—Born Rule

JL Ericksen — 2008-04-22T14:57:15-00:00

Mathematics and Mechanics of Solids, Vol. 13, No. 3-4. (2008), pp. 199-220.

Michell trusses in the presence of microscale material randomness: limitation of optimality

2008-04-04T13:43:06-00:00

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 457, No. 2012. (July 2001), pp. 1787-1797.

The classical problem of a Michell (optimal) truss concerns a minimum-weight design of a planar truss that transmits a given load to a given rigid foundation with the requirement that the axial stresses in the bars of the truss stay within an allowable range &#1340 &#104 &#134 &#104 &#1340. The present study considers this problem when the truss is made of a material with random microstructure, that is, when &#1340 is a random field. The trusses tending to the optimal state can be determined through a net of characteristics generalized to a stochastic setting. While in the classical case of a homogeneous material this net gives the minimum weight as its spacing tends to zero, the presence of a random microstructure prevents the attainment of this state. Basically, the finer the net, the stronger the scatter of characteristics, which forces one to use more structural material to compensate for these fluctuations. In effect, there is a limitation to the attainment of the optimality of the Michell truss made of a hypothetical perfectly homogeneous material.

Global Uniqueness for a Two-Dimensional Inverse Boundary Value Problem

Adrian Nachman — 2008-04-02T14:12:59-00:00

The Annals of Mathematics, Vol. 143, No. 1. (jan 1996), pp. 71-96.

We show that the coefficient $\γ(x)$ of the elliptic equation $\∇ \⋅ (\γ \∇ u) = 0$ in a two-dimensional domain is uniquely determined by the corresponding Dirichlet-to-Neumann map on the boundary, and give a reconstruction procedure. For the equation $\Σ \∂_i (\γ^ij \∂_j u) = 0$, two matrix-valued functions $\γ_1$ and $\γ_2$ yield the same Dirichlet-to-Neumann map if and only if there is a diffeomorphism of the domain which fixes the boundary and transforms $\γ_1$ into $\γ_2$.

Cylindrically anisotropic, radially inhomogeneous elastic materials

2008-03-27T13:49:30-00:00

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 457, No. 2007. (March 2001), pp. 671-693.

In cylindrically anisotropic, radially inhomogeneous materials, e.g. tree trunks, the elastic constants referred to a cylindrical coordinate system depend on the radius but not the angle. The elasticity of these media is developed in analogy to layered media in terms of eigenfunction expansions. Green's functions for hollow and full cylinders under various boundary conditions are constructed.

A Sextic Formalism for Three-Dimensional Elastodynamics of Cylindrically Anisotropic Radially Inhomogeneous Materials

AL Shuvalov — 2008-03-27T13:29:10-00:00

Proceedings: Mathematical, Physical and Engineering Sciences, Vol. 459, No. 2035. (2003), pp. 1611-1639.

High refractive-index sonic material based on periodic subwavelength structure

Feiyan Cai — 2008-03-24T21:18:59-00:00

Applied Physics Letters, Vol. 91, No. 20. (2007)

View this record in Web of Science

Metamaterial with Simultaneously Negative Bulk Modulus and Mass Density

Yiqun Ding — 2008-03-24T21:17:37-00:00

Physical Review Letters, Vol. 99, No. 9. (2007)

We report a metamaterial which simultaneously possesses a negative bulk modulus and mass density. This metamaterial is a zinc blende structure consisting of one fcc array of bubble-contained-water spheres (BWSs) and another relatively shifted fcc array of rubber-coated-gold spheres (RGSs) in epoxy matrix. The negative bulk modulus and mass density are simultaneously derived from the coexistent monopolar resonances from the embedded BWSs and dipolar resonances from the embedded RGSs. The Poisson ratio of the metamaterial also turns negative near the resonance frequency.

Energy minimization for self-organized structure formation and actuation

Guggi Kofod — 2008-03-23T14:19:53-00:00

Applied Physics Letters, Vol. 90, No. 8. (2007)

View this record in Web of Science

A survey on symplectic and multi-symplectic algorithms

Linghua Kong — 2008-03-21T12:55:17-00:00

Applied Mathematics and Computation, Vol. 186, No. 1. (1 March 2007), pp. 670-684.

We simply review symplectic and multi-symplectic algorithms in the paper. These algorithms have many superiorities to general non-symplectic algorithms, such as: they have long time behavior; they can preserve the symplectic geometry structure of the Hamiltonian system exactly; and they can simulate original physical phenomena well. Some commonly used methods to construct symplectic and multi-symplectic schemes are simply surveyed. Numerical examples are also enumerated to illustrate their performances.

Formal Structure of Electromagnetics: General Covariance and Electromagnetics

EJ Post — 2008-03-18T14:37:23-00:00

(17 September 1997)

<div>High-level, explicit treatment of the principle of general covariance as applied to electromagnetics examines the natural invariance of the Maxwell equations, general properties of the medium, nonuniformity, anisotropy and general coordinates in three-space, reciprocity and nonreciprocity, and matter-free space with a gravitational field. 1962 edition.<br></div>

Refraction and geometry in Maxwell's equations

AJ Ward — 2008-03-17T13:42:32-00:00

Journal of Modern Optics, Vol. 43, No. 4. (1996), pp. 773-793.

Computational studies of Maxwell's equations in complex geometries encountered in photonic band structure calculations run into difficulties when several length scales occur, such as the wavelength of light in free space and the skin depth in metal. These problems are remedied by using an adaptive co-ordinate system which expands or contracts length scales as necessary. Here we show that moving to a general co-ordinate transformation is equivalent to renormalizing &b.epsi; and &b.mu;. This is an huge simplification because now we need only write one computer code in a Cartesian system, and we can use this same code to handle any co-ordinate system by adjusting the &b.epsi; and &b.mu; we feed into the calculation.

Cloaking of Matter Waves

Shuang Zhang — 2008-03-16T16:42:49-00:00

(15 Jan 2008)

Invariant transformation for quantum mechanical systems is proposed. A cloaking of matter wave can be realized at given energy by designing the potential and effective mass of the matter waves in the cloaking region. The general conditions required for such a cloaking are determined and confirmed by both the wave and particle (classical) approaches. We show that it may be possible to construct such a cloaking system for cold atoms using optical lattices.

Anisotropic mass density by two-dimensional acoustic metamaterials

Daniel Torrent — 2008-03-12T18:54:31-00:00

New J. Phys., Vol. 10, No. 2. (2008), pp. 023004-1-023004-26.

Guided elastic waves and perfectly matched layers

Elizabeth Skelton — 2008-03-12T13:56:15-00:00

Wave Motion, Vol. 44, No. 7-8. (August 2007), pp. 573-592.

Elastic waveguides support propagating modes that have two possible features, negative group velocities and long wavelengths that, for some frequencies, degrade the accuracy or otherwise poison existing numerical schemes that utilise perfectly matched layers (PMLs) to mimic infinite domains. We illustrate why negative group velocities and long waves are potentially an issue and describe how these problems are overcome. Detailed numerical simulations confirm the accuracy of the modified scheme and provide both theoretical and pragmatic estimates for the parameters within the PML model, in particular for the damping function. We also contrast and compare different implementations of the PML model using spectral and finite difference methods.

Modeling of wave dispersion along cylindrical structures using the spectral method

Florian Karpfinger — 2008-03-12T13:38:58-00:00

JASA

Extreme Lame Compliance in Anisotropic Crystals

Cliff Guo — 2008-03-11T16:46:52-00:00

Mathematics and Mechanics of Solids (11 March 2008), 1081286507080807.

For a crystalline material, Poisson�s ratio depends upon two orthogonal directions, one corresponding to the applied uniaxial stress and another for the resulting transverse strain. Interest in directions that yield a negative value leads to a consideration of extreme values and associated directions. Another indicator of a negative Poisson�s ratio is the Lame compliance, defined as the transverse strain response to a unit uniaxial stress. Where this quantity is positive, Poisson�s ratio is negative and it is natural to associate a near mnimum value of the ratio with a maximum of the Lame compliance. Moreover, the stationary directions associated with the compliance bear a clearer relationship to the crystallographic directions than those of the ratio. Indeed, many of these directions are not dependent upon the elastic constants within a given crystal symmetry class. In the case of alpha-cristobalite, the maximum value of the Lame compliance is associated with such invariant stationary points. In the present work, we describe the invariant stationary directions and touch on a few of the simplest material-dependent stationary points. 10.1177/1081286507080807

Engineering Space for Light via Transformation Optics

Alexander Kildishev — 2008-03-10T12:35:32-00:00

(1 Nov 2007)

Conceptual studies and numerical simulations are performed for imaging devices that transform a near-field pattern into magnified far-zone images and are based on high-order spatial transformation in cylindrical domains. A lens translating a near-field pattern from an almost circular input boundary onto a magnified far-field image at a flat output boundary is considered. The lens is made of a metamaterial with anisotropic permittivity and permeability both depending on a single 'scaling' parameter of the transformation. Open designs of the lens with a truncated body ('3/4-body' and '1/4-body' lenses) are suggested and analyzed. It is shown that the ideal full-lens and the '3/4-body' lens produce identical images. Numerical simulations of '1/4-body' designs indicate that further truncation of the lens could limit its per-formance. A light concentrator, "focusing" far-zone fields into a nanometer-scale area, is also considered.

A Dynamical Effective Medium Theory for Elastic Metamaterials

Ying Wu — 2008-03-10T12:35:06-00:00

(8 Jul 2007)

We develop a dynamical effective medium theory to accurately predict the unusual properties of elastic metamaterials in two dimensions near the resonant frequencies. The theory shows that the effective bulk modulus, shear modulus, and mass density can be made negative by choosing proper resonant scatterers, leading to 8 possible types of wave propagation. The theory not only provides a convenient tool to search for various metamaterials with desired properties, but also gives a unified physical picture of these properties. Here we demonstrate two examples. One possesses large band gaps at low frequencies. The other exhibits two regions of negative refraction: one for both longitudinal and transverse waves and the other for longitudinal waves only.

Electromagnetic cloaking in the visible frequency range

II Smolyaninov — 2008-03-10T12:34:50-00:00

(10 Dec 2007)

Electromagnetic metamaterials provide unprecedented freedom and flexibility to introduce new devices, which control electromagnetic wave propagation in very unusual ways. Very recently theoretical design of an "invisibility cloak" has been suggested, which has been realized at microwave frequencies in a two-dimensional cylindrical geometry. In this communication we report on the experimental realization of the dielectric permittivity distribution required for non-magnetic cloaking in the visible frequency range.

Controlling the Emission of Electromagnetic Sources by Coordinate transformation

Yu Luo — 2008-03-10T12:31:21-00:00

(21 Dec 2007)

The coordinate transformation on the space that contains electromagnetic sources is studied. We find that, not only the permittivity and permeability tensors of the media, but also the sources inside the media will take another form in order to behave equivalently as the original case. It is demonstrated that, a source of arbitrary shape and position in the free space can be replaced by an appropriately designed metamaterial coating with current distributed on the inner surface and would not be detected by outer observers, because the emission of the source can be controlled at will in this way. As examples, we show how to design conformal antennas by covering the sources with transformation media. The method proposed in this letter provides a completely new approach to develop novel active EM devices.

Untapped: The Scramble for Africa's Oil

John Ghazvinian — 2008-03-05T16:23:07-00:00

(09 April 2007)

<div><div>Although Africa has long been known to be rich in oil, extracting it hadn’t seemed worth the effort and risk until recently. But with the price of Middle Eastern crude oil skyrocketing and advancing technology making reserves easier to tap, the region has become the scene of a competition between major powers that recalls the nineteenth-century scramble for colonization there. Already the United States imports more of its oil from Africa than from Saudi Arabia, and China, too, looks to the continent for its energy security. <br><br>What does this giddy new oil boom mean—for America, for the world, for Africans themselves? To find out, John Ghazvinian traveled through twelve African countries—from Sudan to Congo to Angola—talking to warlords, industry executives, bandits, activists, priests, missionaries, oil-rig workers, scientists, and ordinary people whose lives have been transformed—not necessarily for the better—by the riches beneath their feet. The result is a high-octane narrative that reveals the challenges, obstacles, reasons for despair, and reasons for hope emerging from the world’s newest energy hot spot.<br><br></div></div>

Analysis of the PML equations in general convex geometry

Matti Lassas — 2008-03-04T16:25:34-00:00

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Vol. 131, No. 05. (2007), pp. 1183-1207.

In this work, we study a mesh termination scheme in acoustic scattering, known as the perfectly matched layer (PML) method. The main result of the paper is the following. Assume that the scatterer is contained in a bounded and strictly convex artificial domain. We surround this domain by a PML of constant thickness. On the peripheral boundary of this layer, a homogenous Dirichlet condition is imposed. We show in this paper that the resulting boundary-value problem for the scattered field is uniquely solvable for all wavenumbers and the solution within the artificial domain converges exponentially fast toward the full-space scattering solution when the layer thickness is increased. The proof is based on the idea of interpreting the PML medium as a complex stretching of the coordinates in R<sup><em>n</em></sup> and on the use of complexified layer potential techniques.

Electromagnetic wormholes and virtual magnetic monopoles

Allan Greenleaf — 2007-05-08T00:28:54-00:00

Comm. Math. Phys. (20 Mar 2008)

We describe new configurations of electromagnetic (EM) material parameters, the electric permittivity $ε$ and magnetic permeability $μ$, that allow one to construct from metamaterials objects that function as invisible tunnels. These allow EM wave propagation between two points, but the tunnels and the regions they enclose are not detectable to EM observations. Such devices function as wormholes with respect to Maxwell's equations and effectively change the topology of space vis-a-vis EM wave propagation. We suggest several applications, including devices behaving as virtual magnetic monopoles.

On nonuniqueness for Calderon's inverse problem

Allan Greenleaf — 2008-03-04T16:01:37-00:00

Math. Res. Lett., Vol. 10 (1 Jul 2003), pp. 685-693.

We construct anisotropic conductivities with the same Dirichlet-to-Neumann map as a homogeneous isotropic conductivity. These conductivities are singular close to a surface inside the body.

Anisotropic conductivities that cannot be detected by EIT.

A Greenleaf — 2008-03-04T15:59:22-00:00

Physiol Meas, Vol. 24, No. 2. (May 2003), pp. 413-419.

We construct anisotropic conductivities in dimension 3 that give rise to the same voltage and current measurements at the boundary of a body as a homogeneous isotropic conductivity. These conductivities are non-zero, but degenerate close to a surface inside the body.

Acoustic metamaterials for sound focusing and confinement

Sébastien Guenneau — 2007-11-07T20:44:54-00:00

New J. Phys., Vol. 9, No. 11. (November 2007), 399.

Improvement of cylindrical cloaking with the SHS lining

A Greenleaf — 2008-02-11T17:27:28-00:00

Opt. Express, Vol. 15, No. 20. (1 October 2007), pp. 12717-12734.

We analyze the effectiveness of cloaking an infinite cylinder from observations by electromagnetic waves in three dimensions. We show that, as truncated approximations of the ideal permittivity and permeability material parameters tend towards the singular ideal cloaking values, the D and B fields blow up near the cloaking surface. Since the metamaterials used to implement cloaking are based on effective medium theory, the resulting large variation in D and B poses a challenge to the suitability of the field-averaged characterization of ε and μ. We also consider cloaking with and without the SHS (soft-and-hard surface) lining. We demonstrate numerically that cloaking is significantly improved by the SHS lining, with both the far field of the scattered wave significantly reduced and the blow up of D and B prevented.

Electromagnetic analysis of cylindrical invisibility cloaks and the mirage effect

Frédéric Zolla — 2008-02-11T16:16:10-00:00

Opt. Lett., Vol. 32, No. 9. (1 May 2007), pp. 1069-1071.

We present a finite-element analysis of a diffraction problem involving a coated cylinder enabling the electromagnetic cloaking of a lossy object with sharp wedges located within its core. The coating consists of a heterogeneous anisotropic material deduced from a geometrical transformation as first proposed by Pendry [Science 312, 1780 (2006)]. We analyze the electromagnetic response of the cloak in the presence of an electric line source in p polarization and a loop of magnetic current in s polarization. We find that the electromagnetic field radiated by such a source located a fraction of a wavelength from the cloak is perturbed by less than 1%. When the source lies in the coating, it seems to radiate from a shifted location.

Full-Wave Invisibility of Active Devices at All Frequencies

Allan Greenleaf — 2008-02-11T16:09:58-00:00

Communications in Mathematical Physics, Vol. 275, No. 3. (4 November 2007), pp. 749-789.

Abstract There has recently been considerable interest in the possibility, both theoretical and practical, of invisibility (or “cloaking”) from observation by electromagnetic (EM) waves. Here, we prove invisibility with respect to solutions of the Helmholtz and Maxwell’s equations, for several constructions of cloaking devices. The basic idea, as in the papers [GLU2, GLU3, Le, PSS1], is to use a singular transformation that pushes isotropic electromagnetic parameters forward into singular, anisotropic ones. We define the notion of finite energy solutions of the Helmholtz and Maxwell’s equations for such singular electromagnetic parameters, and study the behavior of the solutions on the entire domain, including the cloaked region and its boundary. We show that, neglecting dispersion, the construction of [GLU3, PSS1] cloaks passive objects, i.e., those without internal currents, at all frequencies k. Due to the singularity of the metric, one needs to work with weak solutions. Analyzing the behavior of such solutions inside the cloaked region, we show that, depending on the chosen construction, there appear new “hidden” boundary conditions at the surface separating the cloaked and uncloaked regions. We also consider the effect on invisibility of active devices inside the cloaked region, interpreted as collections of sources and sinks or internal currents. When these conditions are overdetermined, as happens for Maxwell’s equations, generic internal currents prevent the existence of finite energy solutions and invisibility is compromised. We give two basic constructions for cloaking a region D contained in a domain $$Ω⊂\mathbb R^n, n≥ 3$$ , from detection by measurements made at $$∂Ω$$ of Cauchy data of waves on Ω. These constructions, the single and double coatings, correspond to surrounding either just the outer boundary $$∂ D^+$$ of the cloaked region, or both $$∂ D^+$$ and $$∂ D^-$$ , with metamaterials whose EM material parameters (index of refraction or electric permittivity and magnetic permeability) are conformal to a singular Riemannian metric on Ω. For the single coating construction, invisibility holds for the Helmholtz equation, but fails for Maxwell’s equations with generic internal currents. However, invisibility can be restored by modifying the single coating construction, by either inserting a physical surface at $$∂ D^-$$ or using the double coating. When cloaking an infinite cylinder, invisibility results for Maxwell’s equations are valid if the coating material is lined on $$∂ D^-$$ with a surface satisfying the soft and hard surface (SHS) boundary condition, but in general not without such a lining, even for passive objects.

Comment on "Scattering Theory Derivation of a 3D Acoustic Cloaking Shell"

Allan Greenleaf — 2008-02-11T16:04:03-00:00

(21 Jan 2008)

In a recent Letter, Cummer et al. give a description of material parameters for acoustic wave propagation giving rise to a 3D spherical cloak, and verify the cloaking phenomenon on the level of scattering coefficients. A similar configuration has been given by Chen and Chan. In this Comment, we show that these theoretical constructions follow directly from our earlier work <a href="http://arxiv.org/abs/math/0611185">this http URL</a> on full wave analysis of cloaking for the Helmholtz equation with respect to Riemannian metrics. Furthermore, the analysis there covers the case of acoustically radiating objects being enclosed in the cloaked region.

Cloaking via change of variables in electric impedance tomography

RV Kohn — 2008-02-09T17:39:24-00:00

Inverse Problems, Vol. 24, No. 1. (2008), 015016.

A recent paper by Pendry et al (2006 Science 312 1780-2) used the coordinate invariance of Maxwell's equations to show how a region of space can be 'cloaked'--in other words, made inaccessible to electromagnetic sensing--by surrounding it with a suitable (anisotropic and heterogenous) dielectric shield. Essentially the same observation was made several years earlier by Greenleaf et al (2003 Math. Res. Lett. 10 685-93, 2003 Physiol. Meas. 24 413-9) in the closely related setting of electric impedance tomography. These papers, though brilliant, have two shortcomings: (a) the cloaks they consider are rather singular; and (b) the analysis by Greenleaf, Lassas and Uhlmann does not apply in space dimension n = 2. The present paper provides a fresh treatment that remedies these shortcomings in the context of electric impedance tomography. In particular, we show how a regular near-cloak can be obtained using a nonsingular change of variables, and we prove that the change-of-variable-based scheme achieves perfect cloaking in any dimension n [?] 2.

Elastic wave transparency of a solid sphere coated with metamaterials

Xiaoming Zhou — 2008-02-09T16:51:42-00:00

Physical Review B (Condensed Matter and Materials Physics), Vol. 77, No. 2. (2008)

The elastic wave transparency phenomenon of a solid sphere coated with metamaterials is investigated in a solid host medium having nonzero shear modulus. The first three scattering coefficients of the coated sphere are derived in the Rayleigh limit and expressed in terms of the effective parameters of the coated sphere assemblage. It is found that the effective bulk modulus, mass density, and shear modulus of the coated sphere system dominate the zeroth, first, and second order scattering effects, respectively. Quasistatic transparency conditions are obtained by setting these scattering coefficients to be zero. It is also shown that the obtained transparency conditions are the same as those derived from the neutral inclusion concept. Obtained results from full-wave analyses show that the given conditions can well predict the transparency induced by metamaterials even in the regime far beyond the Rayleigh limit.

Analysis of Cummer–Schurig acoustic cloaking

Liang-Wu Cai — 2007-12-20T10:56:27-00:00

New J. Phys., Vol. 9, No. 12. (December 2007), 450.

Which Elasticity Tensors are Realizable?

Graeme Milton — 2008-02-09T16:31:43-00:00

Journal of Engineering Materials and Technology, Vol. 117, No. 4. (1995), pp. 483-493.

It is shown that any given positive definite fourth order tensor satisfying the usual symmetries of elasticity tensors can be realized as the effective elasticity tensor of a two-phase composite comprised of a sufficiently compliant isotropic phase and a sufficiently rigid isotropic phase configured in an suitable microstructure. The building blocks for constructing this composite are what we call extremal materials. These are composites of the two phases which are extremely stiff to a set of arbitrary given stresses and, at the same time, are extremely compliant to any orthogonal stress. An appropriately chosen subset of the extremal materials are layered together to form the composite with elasticity tensor matching the given tensor.