Related papers: Nearly cloaking the elastic wave fields
We analyse the elastic properties of a class of cylindrical cloaks deduced from linear geometric transforms ${\bf x} \to {\bf x}'$ in the framework of the Milton-Briane- Willis cloaking theory [New Journal of Physics 8, 248, 2006]. More…
Reducing electromagnetic scattering from an object has always been a task, inspiring efforts across disciplines such as materials science and electromagnetic theory. The pursuit of electromagnetic cloaking significantly advanced the field…
Application of transformation theory to underwater acoustics has been a challenging task because highly anisotropic density is unachievable in water. A possible strategy is to exploit anisotropic modulus rather than density, while has not…
We develop an optimization framework for the design of acoustic cloaks, with the aim of overcoming the limitations of usual transformation-based cloaks in terms of microstructure complexity and shape arbitrarity of the obstacle. This is…
We propose a cloak for coupled shear and pressure waves in solids. Its elastic properties are deduced from a geometric transform that retains the form of Navier equations. The spherical shell is made of an anisotropic and heterogeneous…
Hydrodynamic signatures at the Stokes regime, pertinent to motility of micro-swimmers, have a long-range nature. This implies that movements of an object in such a viscosity-dominated regime, can be felt tens of body-lengths away and…
The paper is concerned with an optimal control problem governed by the rate-independent system of quasi-static perfect elasto-plasticity. The objective is optimize the displacement field in the domain occupied by the body by means of…
Fundamental features of rotationally symmetric acoustic cloaks with anisotropic inertia are derived. Two universal relations are found to connect the radial and transverse phase speeds and the bulk modulus in the cloak. Perfect cloaking…
The coordinate transformation offers a remarkable way to design cloaks that can steer electromagnetic fields so as to prevent waves from penetrating into the {\em cloaked region} (denoted by $\Omega_0$, where the objects inside are…
The electromagnetic characteristics of plane-transformed invisibility cloaks are quantitatively studied in this paper. We take elliptical cylindrical cloak as the example, and use an elliptical cylindrical wave expansion method to obtain…
Invisibility cloaks for flexural waves have been mostly examined in the continuous-wave regime, while invisibility is likely to deteriorate for short pulses. Here, we propose the practical realization of a unidirectional invisibility cloak…
In this paper, we study approximate cloaking of active devices for the Helmholtz equation in the whole space of dimension 2 or 3 using the scheme introduced by Kohn, Shen, Vogelius, and Weinstein in \cite{KohnShenVogeliusWeinstein}. More…
This work concerns the cloaking due to anomalous localized resonance (CALR) in the quasi-static regime. We extend the related two-dimensional studies in [2,10] to the three-dimensional setting. CALR is shown not to take place for the…
Electromagnetic cloaks are devices that can be used to reduce the total scattering cross section of various objects. An ideal cloak removes all scattering from an object and thus makes this object "invisible" to the electromagnetic fields…
We establish a decoupling result for the $P$ and $S$ waves of linear, isotropic elasticity, in the setting of twice-differentiable Lam\'e parameters. Precisely, we show that the $P\leftrightarrow S$ components of the wave propagation…
Carpet cloaking is proposed to hide an object on a dielectric half-space from electromagnetic (EM) detection. A two-dimensional conformal transformation specified by an analytic function is utilized for the design. Only one nonsingular…
We develop a formalism for the calculation of the frequency band structure of a phononic crystal consisting of non-overlapping elastic spheres, characterized by Lam\'e coefficients which may be complex and frequency dependent, arranged…
We start by a review of the chronology of mathematical results on the Dirichlet-to-Neumann map which paved the way towards the physics of transformational acoustics. We then rederive the expression for the (anisotropic) density and bulk…
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…
Fiber-reinforced soft biological tissues are typically modeled as hyperelastic, anisotropic, and nearly incompressible materials. To enforce incompressibility a multiplicative split of the deformation gradient into a volumetric and an…