Related papers: A variational perspective on cloaking by anomalous…
Aspects of the theory of characteristic modes, based on their variational formulation, are presented and an explicit form of a related functional, involving only currents in a spatial domain, is derived. The new formulation leads to deeper…
We experimentally study anomalous diffusion of ultra-cold atoms in a one dimensional polarization optical lattice. The atomic spatial distribution is recorded at different times and its dynamics and shape are analyzed. We find that the…
We study a porous medium equation with nonlocal diffusion effects given by an inverse fractional Laplacian operator. More precisely, $$ u_t=\nabla\cdot(u\nabla (-\Delta)^{-s}u), \quad \ 0<s<1. $$ The problem is posed in $\{x\in\ren, t\in…
Local positional disorder in soft, anharmonic materials has emerged as a central factor in shaping their electronic, vibrational, optical, and transport properties. Viewed mainly as a source of performance degradation, recent theoretical…
We consider the effect of spatial correlations on sources of polarized electromagnetic radiation. The sources, assumed to be monochromatic, are constructed out of dipoles aligned along a line such that their orientation is correlated with…
In this work the polarizability of a subwavelength core-shell sphere is considered, where the shell exhibits a radially inhomogeneous permittivity profile. A mathematical treatment of the elec- trostatic polarizability is formulated in…
The paper presents the study of waves in a structured geometrically chiral solid. A special attention is given to the analysis of the Bloch-Floquet waves in a doubly periodic high-contrast lattice containing tilted resonators. Dirac-like…
This paper is concerned with inverse crack scattering problems for time-harmonic acoustic waves. We prove that a piecewise linear crack with the sound-soft boundary condition in two dimensions can be uniquely determined by the far-field…
This paper derives the Fokker-Planck (FP) equation for a particle moving in potential by a randomly modulated dipole. The FP equation describes the anomalous diffusion observed in the companion paper [1] and breaks the conservation of the…
An uncommon double-ray scenario of light resonant scattering by a periodic metasurface is proposed to provide strong non-specular reflection. The metasurface is constracted as an array of silicon nanodisks placed on thin silica-on-metal…
Exploring the relationship between geometry and the resonant frequencies of a shape is of interest to pure and applied mathematicians. These resonant frequencies are related to the spectrum of the Laplacian, a partial differential operator.…
We study a nonlocal version of the total variation-based model with $L^1-$fidelity for image denoising, where the regularizing term is replaced with the fractional $s$-total variation. We discuss regularity of the level sets and uniqueness…
The Lyman alpha (LyA) line of neutral hydrogen plays a central role in observations of star-forming galaxies. However, resonant scattering makes it difficult to directly interpret LyA signatures. Monte Carlo radiative transfer (MCRT)…
This work is concerned with the propagation of electromagnetic waves in isotropic chiral media and with the effects produced by a plane boundary between two such media. In analogy with the phenomena of reflection and refraction of plane…
The dynamic response of a coated inclusion is considered in the context of active cloaking. The active cloak is achieved for a coated inclusion in the presence of membrane and flexural waves. In this paper, we investigate the design of an…
We consider a homogenization problem for the diffusion equation $-\operatorname{div}\left(a_{\varepsilon} \nabla u_{\varepsilon} \right) = f$ when the coefficient $a_{\varepsilon}$ is a non-local perturbation of a periodic coefficient. The…
The phenomenon of anomalous localized resonance (ALR) is observed at the interface between materials with positive and negative material parameters and is characterized by the fact that, when a given source is placed near the interface, the…
A previously developed approach for the numerical treatment of two particles that are confined in a finite optical-lattice potential and interact via an arbitrary isotropic interaction potential has been extended to incorporate an…
We present a review of recent works devoted to the variation of the fine structure constant alpha, strong interaction and fundamental masses. There are some hints for the variation in quasar absorption spectra, Big Bang nucleosynthesis, and…
The paper addresses an important issue of cloaking transformations for fourth-order partial differential equations representing flexural waves in thin elastic plates. It is shown that, in contrast with the Helmholtz equation, the general…