Related papers: On the spectrum of a waveguide with periodic crack…
We numerically perform a spectral analysis of a quasi-periodically driven spin 1/2 system, the spectrum of which is Singular Continuous. We compute fractal dimensions of spectral measures and discuss their connections with the time…
A dispersion equation for the interface waves has been derived for the interface of two cubic crystals in the plane perpendicular to [001]. A reasonable hypothesis has been made about the total number of the acoustic modes. Due to this…
The spectrum of electromagnetic waves in periodic linear structures, such as periodic waveguides or chains of microelements i.e. spheres, cavities, exhibit the sequence of stop bands for propagating waves. Breaking the translational…
Nanomechanical and other mesoscopic vibrational systems typically have several nonlinearly coupled modes with different frequencies and with long lifetime. We consider the power spectrum of one of these modes. Thermal fluctuations of the…
The spectral problem of thin elastic shells in membrane approximation does not satisfy the classical properties of compactness and so there exists an essential spectrum. In the first part, we propose to determinate this spectrum and the…
A thin two-layered waveguide is considered. The governing equations for this waveguide is a matrix Klein--Gordon equation of dimension~2. A formal solution of this system in the form of a double integral can be obtained by using Fourier…
In this paper, the acoustic emission accompanying the formation of brittle cracks of finite length is investigated theoretically using the approach based on the application of Huygens' principle for elastic solids. In the framework of this…
Sufficient conditions for wave breaking are found for the short-pulse equation describing wave packets of few cycles on the ultra-short pulse scale. The analysis relies on the method of characteristics and conserved quantities of the…
When waves are propagated through a medium with scatters and these elements are positioned periodically, as in the crystal structures, multiple scattering leads to a phenomenon known as banded structures. This means that waves can propagate…
Motivated by phenomenological questions in quantum gravity, we consider the propagation of a scalar field on a random lattice. We describe a procedure to calculate the dispersion relation for the field by taking a limit of a periodic…
We study the spectral distribution of the threshold network model.The results contain an explicit description and its asymptotic behaviour.
The cosmic ray energy distributions contain spectral features, that is narrow energy regions where the slope of the spectrum changes rapidly. The identification and study of these features is of great importance to understand the…
This paper considers the propagation of TE-modes in photonic crystal waveguides. The waveguide is created by introducing a linear defect into a periodic background medium. Both the periodic background problem and the perturbed problem are…
We review various methods for the analysis of initial-value problems for integrable dispersive equations in the weak-dispersion or semiclassical regime. Some methods are sufficiently powerful to rigorously explain the generation of…
We study the dispersion relations in slow-light waveguide structures consisting of coupled microdisk resonators. A group theoretical analysis of the symmetry properties of the propagating modes reveals an interesting phenomenon: The…
The propagation properties of optical fields in linear and nonlinear parity-time symmetric microring coupled resonator optical waveguides are studied. The effects described include the existence of symmetry breaking thresholds, the…
We use a phenomenological Hamiltonian approach to derive a set of coupled mode equations that describe light propagation in waveguides that are periodically side-coupled to microcavities. The structure exhibits both Bragg gap and (polariton…
Mathematical settings in which heterogeneous structures affect electron transport through a tube-shaped quantum waveguide are studied, highlighting the interaction between heterogeneities and geometric parameters like curvature and torsion.…
We study a Helmholtz-type spectral problem in a two-dimensional medium consisting of a fully periodic background structure and a perturbation in form of a line defect. The defect is aligned along one of the coordinate axes, periodic in that…
We consider the quasi-static propagation of a Mode III crack along the interface in a bimaterial plane containing a finite array of small line defects (microcracks and rigid line inclusions). The microdefects are arranged to form a channel…