Related papers: Transformation elastodynamics and active exterior …
Beginning with a straightforward formulation of electromagnetic cloaking that reduces to a boundary value problem involving a single Maxwell first-order differential equation, explicit formulae for the relative permittivity-permeability…
By an idealized quantum mechanical model, we formally describe the dispersion of nonretarded electromagnetic waves that express charge density oscillations near a fixed plane in three spatial dimensions (3D) at zero temperature. Our goal is…
Using a sum rule, we derive new bounds on Herglotz functions that generalize those given in (Gustafson and Sj\"oberg 2010) and (Bernland, Luger and Gustafson 2011). These bounds apply to a wide class of linear passive systems such as…
Transformation equations for physical quantities that characterize plane electromagnetic wave propagation in transparent optical media are presented. The Doppler effect, and measurements performed by an observer moving with the wave are…
Many organisms have an elastic skeleton that consists of a closed shell of epithelial cells that is filled with fluid, and can actively regulate both elastic forces in the shell and hydrostatic pressure inside it. In this work we introduce…
The fully covariant formulation of transformation optics is used to find the configuration of a cloaking device operating in an expanding universe modelled by a Friedmann-Lema\^itre-Robertson-Walker spacetime. This spacetime cloak is used…
For geometric systems of real principal type, we define a subprincipal symbol and derive a transport equation for polarizations which, in the scalar case, is a well-known equation of Duistermaat and H\"ormander. We apply the transport…
A multiscale asymptotic homogenization method for periodic microstructured materials in presence of thermoelasticity with periodic spatially dependent one relaxation time is introduced. The asymptotic expansions of the micro-displacement…
In this work we present the mathematical model and simulations of a particular wave energy converter, the so-called oscillating water column. In this device, waves governed by the one-dimensional nonlinear shallow water equations arrive…
Cloaking effects have now been identified in almost every field of physics. In all cases, substrate-carved metamaterials make the reshaping of the concealed volume impossible. In fluids, recognizing that d'Alembert's paradox describes in…
This paper explores the concept of near-cloaking in the context of time-dependent heat propagation. We show that after the lapse of a certain threshold time instance, the boundary measurements for the homogeneous heat equation are close to…
The aim of this article is to study the attenuation of transient low-frequency waves in 2D lattices in both plane and antiplane problems. The main idea of this article is that analytical solutions to problems of mechanics of discrete…
A one-dimensional wave propagation through elastically asymmetric media is investigated. A class of metamaterials possessing an arbitrary elastic asymmetry is proposed. This asymmetry results in different wave speeds of tensile and…
We study numerically how multiple deformable capsules squeeze into a constriction. This situation is largely encountered in microfluidic chips designed to manipulate living cells, which are soft entities. We use fully three-dimensional…
In this paper, we develop a general mathematical framework for perfect and approximate hydrodynamic cloaking and shielding of electro-osmotic flow, which is governed by a coupled PDE system via the field-effect electro-osmosis. We first…
A new phenomenological model of turbulent fluctuations is constructed by considering the Lagrangian dynamics of 4 points (the tetrad). The closure of the equations of motion is achieved by postulating an anisotropic, i.e. tetrad shape…
This paper is concerned with the analysis of time-harmonic electromagnetic scattering from plasmonic inclusions in the finite frequency regime beyond the quasi-static approximation. The electric permittivity and magnetic permeability in the…
Calculating by analytical theory the deformation of finite-sized elastic bodies in response to internally applied forces is a challenge. Here, we derive explicit analytical expressions for the amplitudes of modes of surface deformation of a…
A novel variational formulation of layer potentials and boundary integral operators generalizes their classical construction by Green's functions, which are not explicitly available for Helmholtz problems with variable coefficients.…
Existing theoretical results for attenuation of surface waves propagating on water of random fluctuating depth are shown to over predict the rate of decay due to the way in which ensemble averaging is performed. A revised approach is…