Teaching linear algebra routines for computing eigenvalues of a matrix can be well motivated to students using interesting examples. We propose in this paper to use vibrating plates for two reasons: first there are interesting applications, from which we chose the Chladni figures representing sand ornaments which form on a vibrating plate, and the Tacoma bridge, one of the most spectacular brid...

It is shown that optical vortex beams can be generated from a non-vortex fundamental beam by an optical frequency conversion process taking place within a twisted nonlinear photonic crystal. This is done without any first-order (linear) refractive optics. Through such a proposed structure, all-optical switching of vortices with different helicities is made possible, as well as the simultaneous ...

The present article contains a brief description of several methods for solving non-linear tasks used when calculating the strength, stability and oscillation of construction structures. The investigated structures are: beams, thin-wall reinforced shells, including shells with fractures in the middle of the surface. Calculations are carried out with consideration of physical and geometrical non...

— We consider a network of vibrating elastic strings and Euler-Bernoulli beams. Using a generalized Poisson formula and some Tauberian theorem, we give a Weyl formula with optimal remainder estimate. As a consequence we prove some observability and stabilization results. Résumé (Formule de Weyl avec reste optimal de quelques réseaux élastiques et applications) Nous considérons un réseau de cord...

One of the principal objectives of vibration isolation technology is to isolate sensitive equipment from a vibrating structure or to isolate the structure from an uncertain exogenous disturbance source. In this paper, a dynamic observer-based active isolator is proposed that guarantees closed-loop asymptotic stability and disturbance decoupling between the vibrating structure and isolated struc...

– We present experimental observations of hexagonal patterns in strongly anisotropic non-linear optical media. Close to threshold rolls are observed. As the non-linearity is increased a transition from rolls to hexagons, leading finally to a pure hexagonal state, is observed. A mean-field model, in agreement with experiments, shows that the anisotropy locks the far-field orientation of the hexa...

The electric field intensity of the compressed ultrarelativistic electron beams is approaching GV/m levels, which is sufficient to cause observable tunneling effect in the low band gap materials. In this article the tunneling ionization rate is estimated for the experimentally available electron beam parameters, and a proposed proof of principle experiment is outlined. Tunneling effect has expo...