Related papers: A variational perspective on cloaking by anomalous…
The regularized near-cloak via the transformation optics approach in the time-harmonic electromagnetic scattering is considered. This work extends the existing studies mainly in two aspects. First, it presents a near-cloak construction by…
In this note we establish existence and uniqueness of weak solutions of linear elliptic equation $\text{div}[\mathbf{A}(x) \nabla u] = \text{div}{\mathbf{F}(x)}$, where the matrix $\mathbf{A}$ is just measurable and its skew-symmetric part…
Numerous natural and technological phenomena are governed by resonances. In nanophotonics, resonances often result from the interaction of several optical elements. Controlling these resonances is an excellent opportunity to provide light…
In a series of paper, it has been shown that the distribution of polarisation position angles for visible light from quasars is not random in extremely large regions of the sky. As explained in a recent article, the measurement of vanishing…
This paper studies the behaviour of quadratic variations of a stochastic wave equation driven by a noise that is white in space and fractional in time. Complementing the analysis of quadratic variations in the space component carried out by…
From the spread of pollutants in the atmosphere to the transmission of nutrients across cell membranes, anomalous diffusion processes are ubiquitous in natural systems. The ability to understand and control the mechanisms guiding such…
We develop a theoretical framework, based on a multipole, quasi-static approach, for the prediction of the localized surface plasmon resonances in Fanoshells formed via geometrical symmetry-breaking in multilayer nanoshells consisting of a…
We discuss variational problems on two-dimensional domains with energy densities of linear growth and with radially symmetric data. The smoothness of generalized minimizers is established under rather weak ellipticity assumptions. Further…
Rendering objects invisible to impinging acoustic waves (cloaking) and creating acoustic illusions (holography) has been attempted using active and passive approaches. While passive methods are applicable only to narrow frequency bands,…
Nonlocal equations effectively preserve textures but exhibit weak regularization effects in image denoising, whereas local equations offer strong denoising capabilities yet fail to protect textures. To integrate the advantages of both…
Geostrophic jets propagating as Alfv\'en waves are shown to arise ina rapidly rotating spherical shell permeated by a magnetic field among the transient motions set up by an impulsive rotation of the inner core. These axially invariant…
Much of the qualitative nature of physical systems can be predicted from the way it scales with system size. Contrary to the continuum expectation, we observe a profound deviation from logarithmic scaling in the impedance of a…
In this paper we present in one-dimensional space a numerical solution of a partial differential equation of fractional order. This equation describes a process of anomalous diffusion. The process arises from the interactions within the…
We consider the semilinear wave equation in the radial case with conformal subcritical power nonlinearity. If we consider a blow-up point different from the origin, then we exhibit a new Lyapunov functional which is a perturbation of the…
Light injected into a spherical dielectric body may be confined very efficiently via the mechanism of total internal reflection. The frequencies that are most confined are called resonances. If the shape of the body deviates from the…
We study nonlinear resonance of coupled modes in nano-mechanical systems. To reveal the qualitative features of the dynamics, we consider the limiting cases, where the results can be obtained analytically. For 1:3 resonance, we find the…
We consider the standard relativistic geometrically thin and optically thick accretion disc around a distorted static black hole and a distorted naked singularity. The distortion is the result of the existence of a static axisymmetric…
Motivated by an apparent puzzle of the light-front vacua incompatible with the axial anomaly, we have considered the two-dimensional massless Schwinger model for an arbitrary interpolating angle of the quantization surface. By examining…
Recently a new type of Kramers-Fokker-Planck Equation has been proposed [R. Friedrich et al. Phys. Rev. Lett. {\bf 96}, 230601 (2006)] describing anomalous diffusion in external potentials. In the present paper the explicit cases of a…
We discuss a way to exploit the conformal mapping to study the response of a finite metallic element of arbitrary shape to an external electromagnetic field at finite frequencies. This provides a simple way to study different physics issues…