Related papers: Isolated resonances and nonlinear damping
Collisionless damping of electrical waves in plasma is investigated in the frame of the classical formulation of the problem. The new principle of regularization of the singular integral is used. The exact solution of the corresponding…
A one-dimensional metamaterial with parity-time (${\cal PT}$) symmetry that relies on balanced gain and loss is introduced, comprising of magnetically coupled split-ring resonators (SRRs). A particular topology that combines a non-trivial…
Irregular terrain has a pronounced effect on the propagation of seismic and acoustic wavefields but is not straightforwardly reconciled with structured finite-difference (FD) methods used to model such phenomena. Methods currently detailed…
The differential equations with piecewise constant argument (DEPCAs, for short) is a class of hybrid dynamical systems (combining continuous and discrete). In this paper, under the assumption that the nonlinear term is partially unbounded,…
We study the geometry and dynamics of both isolated and dynamical trapping horizons by considering the allowed variations of their foliating two-surfaces. This provides a common framework that may be used to consider both their possible…
In this paper, we develop a new deflation technique for refining or verifying the isolated singular zeros of polynomial systems. Starting from a polynomial system with an isolated singular zero, by computing the derivatives of the input…
Non-Hermitian systems characterized by suitable spatial distributions of gain and loss can exhibit "spectral singularities" in the form of zero-width resonances associated to real-frequency poles in the scattering operator. Here, we study…
We analyze the spectral properties and peculiar behavior of solutions of a damped wave equation on a finite interval with a singular damping of the form $\alpha/x$, $\alpha>0$. We establish the exponential stability of the semigroup for all…
Closed-loop positivity of feedback interconnections of positive monotone nonlinear systems is investigated. It is shown that an instantaneous gain condition on the open-loop systems which implies feedback well-posedness also guarantees…
Topological insulators possess protected boundary states which are robust against disorders and have immense implications in both fermionic and bosonic systems. Harnessing these topological effects in non-equilibrium scenarios is highly…
In high-contrast composites, if an inclusion is in close proximity to the matrix boundary, then the stress, which is represented by the gradient of a solution to the Lam\'{e} systems of linear elasticity, may exhibits the singularities with…
In the framework of semiclassical resonances, we make more precise the link between polynomial estimates of the extension of the resolvent and propagation of the singularities through the trapped set. This approach makes it possible to…
We propose nonlinear semi-discrete and discrete models for the elastic energy induced by a finite systems of edge dislocations in two dimensions. Within the dilute regime, we analyze the asymptotic behavior of the nonlinear elastic energy,…
We investigate qualitative properties of positive singular solutions of some elliptic systems in bounded and unbounded domains. We deduce symmetry and monotonicity properties via the moving plane procedure. Moreover, in the unbounded case,…
Approximate formulas are derived to describe energy loss in a harmonic oscillator that experiences three distinct damping mechanisms: constant-magnitude (Coulomb), velocity-proportional (Stokes), and velocity-squared (Newton), using…
In this paper, We develop the stratified de Rham theory on singular spaces using modern tools including derived geometry and stratified structures. This work unifies and extends the de Rham theory, Hodge theory, and deformation theory of…
Leveraging topological properties in the response of electromagnetic systems can greatly enhance their potential. Although the investigation of singularity-based electromagnetics and non-Hermitian electronics has considerably increased in…
We investigate the electronic structure induced by wedge-disclinations (conical singularities) in a honeycomb lattice model realizing Chern numbers $\gamma=\pm 1$. We establish a correspondence between the bound state of (i) an isolated…
A theoretical and experimental investigation is presented on the intermodal coupling between the flexural vibration modes of a single clamped-clamped beam. Nonlinear coupling allows an arbitrary flexural mode to be used as a self-detector…
We consider two-dimensional inviscid irrotational flow in a two layer fluid under the effects of gravity and surface tension. The upper fluid is bounded above by a rigid lid, and the lower fluid is bounded below by a rigid bottom. We use a…