Related papers: Approximate Isotropic Cloak for the Maxwell equati…
We propose a class of line-transformed cylindrical cloaks which have easily-realizable constitutive parameters. The scattering properties of such cloaks have been investigated numerically for both transverse-electric (TE) and…
In this paper, we establish approximate cloaking for the heat equation via transformation optics. We show that the degree of visibility is of the order $\epsilon$ in three dimensions and $|\ln\epsilon|^{-1}$ in two dimensions, where…
This paper presents a homogenization framework for elastomeric metamaterials exhibiting long-range correlated fluctuation fields. Based on full-scale numerical simulations on a class of such materials, an ansatz is proposed that allows to…
The concept of cloaking -- hiding objects from external detection -- has seen wide success in linear systems. Yet, translating these advancements to nonlinear mechanical systems remains an open challenge. Here, we present a new approach to…
This paper is concerned with the invisibility cloaking in acoustic wave scattering from a new perspective. We are especially interested in achieving the invisibility cloaking by completely regular and isotropic mediums. It is shown that an…
We present a formalism for light optics starting with the Maxwell equations and casting them into an exact matrix form taking into account the spatial and temporal variations of the permittivity and permeability. This $8 \times 8$ matrix…
We study the regularity and finite element approximation of the axisymmetric Stokes problem on a polygonal domain $\Omega$. In particular, taking into account the singular coefficients in the equation and non-smoothness of the domain, we…
There are great demands to design functional devices with isotropic materials, however the transformation method usually leads to anisotropic material parameters difficult to be realized in practice. In this letter, we derive the isotropic…
The robustness of XRD methods for the determination of the lattice parameters of crystals is well established. These methods have been extended to helical atomic structures using twisted x-rays \cite{friesecke_twisted_2016}. Building on an…
We present an active cloaking method for the parabolic heat (and mass or light diffusion) equation that can hide both objects and sources. By active we mean that it relies on designing monopole and dipole heat source distributions on the…
We present a method for constructing global analytical expressions that approximate a function over its entire range. These approximations not only mirror the original function as accurately as desired, but are purposefully created to…
We study the approximation of maps into complex manifolds along with interpolation on certain compact subsets of the plane. Results are also obtained regarding approximation and interpolation of sections of holomorphic submersions.
We present a novel shape-approximating anisotropic re-meshing algorithm as a geometric generalization of the adaptive moving mesh method. Conventional moving mesh methods reduce the interpolation error of a mesh that discretizes a given…
The deformation method of transformation optics has been demonstrated to be a useful tool, especially in designing arbitrary and nonsingular transformation materials. Recently, there are emerging demands for isotropic material parameters,…
A new type of cloak is discussed: one that gives all cloaked objects the appearance of a flat conducting sheet. It has the advantage that none of the parameters of the cloak is singular and can in fact be made isotropic. It makes broadband…
Mechanical cloaks are materials engineered to manipulate the elastic response around objects to make them indistinguishable from their homogeneous surroundings. Typically, methods based on material-parameter transformations are used to…
Invisibility cloak capable of hiding an object can be achieved by properly manipulating electromagnetic field. Such a remarkable ability has been shown in transformation and ray optics. Alternatively, it may be realistic to create a spatial…
We propose a general method to circumvent the singularity of arbitrary 2D cloaks, which arises from infinitely large values of material parameters at inner boundaries. The presented method is based on the deformation view of the…
We present a reconstruction algorithm for recovering both "magnetic-hard" and "magnetic-soft" obstacles in a background domain with known isotropic medium from the boundary impedance map. We use in our algorithm complex geometric optics…
In this paper, we develop a general mathematical framework for the electro-osmosis problem to design simultaneous microscale electric and hydrodynamic cloaking in a Hele-Shaw configuration. A novel approach to achieving simultaneously…