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In this paper, we are concerned with the stabilization of linear port-Hamiltonian systems of arbitrary order $N \in \mathbb{N}$ on a bounded $1$-dimensional spatial domain $(a,b)$. In order to achieve stabilization, we couple the system to…
Born-Infeld nonlinear electrodynamics are considered. Main attention is given to existence of singular point at static field configuration that M.Born and L.Infeld are considered as a model of electron. It is shown that such singularities…
Resolvers, like all electromagnetic devices, are constantly under investigation, both operationally and structurally. In this regard, proposing a modeling methodology that can save significant time without compromising accuracy is a big…
We introduce a scalar reduction method for forced or coupled systems with nonlinearities in both heterogeneity and coupling strength. Heterogeneity is formulated as a relatively weak but nonlinear alteration of the vector field(s). The…
A system of singular integral equations with monotone and concave nonlinearity in the subcritical case is investigated. The specified system and its scalar analog have direct applications in various areas of physics and biology. In…
We develop a model to calculate nonlinear polarization in a nondegenerate four-wave mixing in diamond configuration which includes the effects of hyperfine structure and Doppler broadening. We verify the model against the experiment with…
We consider a non-linear, one-dimensional wave equation system with finite-dimensional stochastic driving terms and with weak dissipation. A stationary process that solves the system is used to model steady-state non-equilibrium heat flow…
Based on the conventional energy band theory, an approach is presented to describe the electronic structure of crystalline insulators in the presence of a finite homogeneous electric field. The expression of polarization is derived which…
On-chip optical nonreciprocal devices are vital components for integrated photonic systems and scalable quantum information processing. Nonlinear optical isolators and circulators have attracted considerable attention because of their…
We report an experimental and theoretical investigation of a system whose dynamics is dominated by an intricate interplay between three key concepts of modern physics: topology, nonlinearity, and spontaneous symmetry breaking. The…
We study the stability of coupled impedance passive regular linear systems under power-preserving interconnections. We present new conditions for strong, exponential, and non-uniform stability of the closed-loop system. We apply the…
We study electric polarization and nonlinear optical effects in spin systems with broken inversion symmetry. We apply strong coupling expansion to the underlying electronic Hamiltonians, and systematically derive expressions for electric…
In this article, we present a stabilization feedback law with integral action for conservative abstract linear systems subjected to actuator nonlinearity. Based on the designed control law, we first prove the well-posedness and global…
We consider nonlinear effects in scattering of light by a periodic structure supporting optical bound states in the continuum. In the spectral vicinity of the bound states the scattered electromagnetic field is resonantly enhanced…
We consider the non-equilibrium dynamics of a molecular level interacting with local phonon modes in the case of a strong polaronic shift which prevents a perturbative treatment of the problem. Instead, we find that in an adiabatic regime…
An oscillatory system can have clockwise and anticlockwise senses of rotation. We propose a general rule how to obtain counter-rotating oscillators from the definition of a dynamical system and then investigate synchronization. A type of…
We derive a novel two-component generalization of the nonlinear variational wave equation as a model for the director field of a nematic liquid crystal with a variable order parameter. The two-component nonlinear variational wave equation…
We propose a comprehensive model describing the Kerr nonlinear dynamics of an electric field in a cylindrical microresonator with an effective radius variation, coupled to a radiation source. The proposed system of equations for coupled…
In this paper, we describe a numerical continuation method that enables harmonic analysis of nonlinear periodic oscillators. This method is formulated as a boundary value problem that can be readily implemented by resorting to a standard…
We study a family of nonholonomic mechanical systems. These systems consist of harmonic oscillators coupled through nonholonomic constraints. In particular, the family includes the so called contact oscillator, which has been used as a test…