We investigate numerically and experimentally the spatial collapse dynamics and polarization stability of radially and azimuthally polarized vortex beams in pure Kerr medium. These beams are unstable to azimuthal modulation instabilities and break up into distinct collapsing filaments. The polarization of the filaments is primarily linear with weak circular components at the filaments' boundari...

The present paper is concerned with the determination of frequency equation and sensitivity eigenfrequencies a fixed-free longitudinally vibrating rod transversally beam carrying tip mass by using several methods. First, exact equations such systems are established, then approximate formulas given for fundamental methods which contain equivalent system, Rayleigh quotient, Dunkerley’s formula co...

In this work, we are interested in tree-shaped networks of freely vibrating beams which geometrically exact (GEB) – the sense that large motions (deflections, rotations) accounted for addition to shearing and linked by rigid joints. For intrinsic GEB formulation, namely terms velocities internal forces/moments, derive transmission conditions show network is locally ...

Laser beam homogenizing and beam shaping are key enabling technologies for many applications today. Periodic microlens arrays are widely used to transform Gaussian or non-uniform beam profile into a uniform “flat-top”. Each microlens element samples the input beam and spreads it over a given angular distribution. Incoherent beams that are either temporally or spatially incoherent can produce ve...

A vibrating string, modelled by the wave equation, with an interior mass is considered. It is viewed as a linear delay system. A trajectory tracking problem is solved using a new type of controllability.