Related papers: Diffraction Problem and Amplitudes-Phases Dispersi…
We show that the wide-spread concept of optical eigen modes in lossless waveguide structures, which assumes the separation on propagating and evanescent modes, fails in the case of metal-dielectric structures, including photonic crystals.…
Motivated by new technologies for designing and tailoring metamaterials, we seek properties for certain classes of nonlinear optical materials that allow room for a reversibly controlled opacity-to-transparency phase transition through the…
The problem of the equilibrium state of the charged many-particle system above dielectric surface is formulated.We consider the case of the presence of the external attractive pressing field and the case of its absence. The equilibrium…
We describe the structure of the time-harmonic electromagnetic field of a vertical Hertzian electric dipole source radiating over an infinite, translation invariant two-dimensional electron system. Our model for the electron flow takes into…
Electrophoresis is a motion of charged dispersed particles relative to a fluid in a uniform electric field. The effect is widely used to separate macromolecules, to assemble colloidal structures, to transport particles in nano- and…
We consider a sub-wavelength periodic layered medium whose slabs are filled by arbitrary linear metamaterials and standard nonlinear Kerr media and we show that the homogenized medium behaves as a Kerr medium whose parameters can assume…
We study the propagation of light beams through optical media with competing nonlocal nonlinearities. We demonstrate that the nonlocality of competing focusing and defocusing nonlinearities gives rise to self-organization and stationary…
A mathematical model for the discrete nonlinear fragmentation (collision-induced breakage) equation with diffusion is studied. The existence of global weak solutions is established in arbitrary spatial dimensions without assuming a strictly…
We analyze the optical resonances of a dielectric sphere whose surface has been slightly deformed in an arbitrary way. Setting up a perturbation series up to second order, we derive both the frequency shifts and modified linewidths. Our…
Nonlinear dynamics of the free surface of finite depth non-conducting fluid with high dielectric constant subjected to a strong horizontal electric field is considered. Using the conformal transformation of the region occupied by the fluid…
We prove the existence of solutions to a non-linear, non-local, degenerate equation which was previously derived as the formal hydrodynamic limit of an active Brownian particle system, where the particles are endowed with a position and an…
We study the asymptotic behaviour of a system of nonlinear reaction--diffusion--advection equations in a domain consisting of two bulk regions connected via microscopic channels distributed within a thin membrane. Both the width of the…
Diffraction is a fundamental property of light propagation. Owing to this phenomenon,light diffracts out in all directions when it passes through a subwavelength slit.This imposes a fundamental limit on the transverse size of a light beam…
Near-critical behavior of the free surface of an ideally conducting liquid in an external electric field is considered. Based on an analysis of three-wave processes using the method of integral estimations, sufficient criteria for hard…
In the present work fournontrivial stages of electrokinetic instability are identified by direct numerical simulation (DNS) of the full Nernst-Planck-Poisson-Stokes (NPPS) system: i) The stage of the influence of the initial conditions…
Diffraction of multi-level atoms by an evanescent wave reflective diffraction grating is modeled by numerically solving the time-dependent Schr\"{o}dinger equation. We are able to explain the diffraction observed in experiments with…
The origin of self-organized criticality in a model without conservation law (Olami, Feder, and Christensen, Phys. Rev. Lett. {\bf 68}, 1244 (1992)) is studied. The homogeneous system with periodic boundary condition is found to be periodic…
In this paper we study nonlinear Helmholtz equations with sign-changing diffusion coefficients on bounded domains. The existence of an orthonormal basis of eigenfunctions is established making use of weak T-coercivity theory. All…
The weakly nonlinear dynamics of the free surface of a dielectric liquid in an electric field directed tangentially to the unperturbed boundary is investigated numerically. Within the framework of the strong field model, when the effects of…
Magnetoelectric materials have the interesting property of exhibiting polarization induced by a magnetic field or magnetization induced by an electric field. As a consequence, a multitude of effects can be produced by means of controllable…