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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…
The contribution of the polarization associated with the noncollinear parts of spins in the dielectric permeability tensor of multiferroic materials is considered. As the equilibrium state, we consider the systems of parallel spins, so we…
We consider a two-component scalar dark matter model in this work, where the scalars are stabilized by extra $Z_2 \times Z'_2$ symmetry. To guarantee the stability of the vacuum, we consider the copositive criteria and different choices of…
Spatial field correlation functions represent a key quantity for the description of mesoscopic phenomena in disordered media and the optical characterization of complex materials. Yet many aspects related to the vector nature of light waves…
Motivated by bouncing motion of an inelastic particle on a vibrating board, a simple two-dimensional map is constructed and its behavior is studied numerically. In addition to the typical route to chaos through a periodic doubling…
The dynamics of the domains is studied in a two-dimensional model of the microphase separation of diblock copolymers in the vicinity of the transition. A criterion for the validity of the mean field theory is derived. It is shown that at…
An analysis of the matrix models representing the polarimetric properties of light and material media is carried out by using the concept of the coherency matrix, which leads to the identification and definition of their corresponding…
We introduce a model of a passive optical cavity based on a novel variety of the two-dimensional Lugiato-Lefever equation, with a localized pump carrying intrinsic vorticity S, and the cubic or cubic-quintic nonlinearity. Up to S = 5,…
We consider the electromagnetic field in a cavity with a periodically oscillating perfectly reflecting boundary and show that the mathematical theory of circle maps leads to several physical predictions. Notably, well-known results in the…
Radio polarimetry is a three-dimensional statistical problem. The three-dimensional aspect of the problem arises from the Stokes parameters Q, U, and V, which completely describe the polarization of electromagnetic radiation and…
Orbits in the principal planes of triaxial potentials are known to be prone to unstable motion normal to those planes, so that three dimensional investigations of those orbits are needed even though they are two dimensional. We present here…
In this article we initiate the study of 1+ 2 dimensional wave maps on a curved spacetime in the low regularity setting. Our main result asserts that in this context the wave maps equation is locally well-posed at almost critical…
We show that singularities form after the interaction of three transversal semilinear conormal waves. Our results hold for space dimensions two and higher, and for arbitrary smooth nonlinearity. The case of two space dimensions in which the…
We show that isotropic component of circular polarization of stochastic gravitational wave background can be explored by breaking two dimensional configuration of multiple laser interferometers for correlation analysis. By appropriately…
Using polarization measurements in remote sensing and optical studies allows retrieving more information. We consider relationship between the reflection coefficients of plane and rough surfaces for linearly polarized waves. Certain…
We experimentally achieve selective wave filtering and polarization control in a three-dimensional elastic frame embedding local resonators. By connecting multi-resonating elements to a frame structure, a complete low-frequency,…
We discuss the parametric oscillatory instability in a Fabry-Perot cavity of the Einstein Telescope. Unstable combinations of elastic and optical modes for two possible configurations of gravitational wave third-generation detector are…
Consider the time-domain multiple cavity scattering problem, which arises in diverse scientific areas and has significant industrial and military applications. The multiple cavity embedded in an infinite ground plane, is filled with…
The Lugiato-Lefever equation is a cubic nonlinear Schr\"odinger equation, including damping, detuning and driving, which arises as a model in nonlinear optics. We study the existence of stationary waves which are found as solutions of a…
The propagation of unstable interfaces is at the origin of remarkable patterns that are observed in various areas of science as chemical reactions, phase transitions, growth of bacterial colonies. Since a scalar equation generates usually…