Stability boundary characterization of nonlinear autonomous dynamical systems in the presence of saddle-node equilibrium points

A dynamical characterization of the stability boundary for a fairly large class of nonlinear autonomous dynamical systems is developed in this paper. This characterization generalizes the existing results by allowing the existence of saddle-node equilibrium points on the stability boundary. The stability boundary of an asymptotically stable equilibrium point is shown to consist of the stable manifolds of the hyperbolic equilibrium points on the stability boundary and the stable, stable center and center manifolds of the saddle-node equilibrium points on the stability boundary.

Influence of nanoparticle size on the nonlinear optical properties of magnetite ferrofluids

The nonlinear index of refraction (n(2)) and the two-photon absorption coefficient (beta) of water-based ferrofluids made of magnetite nanocrystals of different sizes and with different coatings have been measured through the Z-scan technique, with ultrashort (femtoseconds) laser pulses. Their third-order susceptibility is calculated from the values of n(2) and beta. The influence of different particles' coatings and sizes on these nonlinear optical properties are investigated. The values of n(2) and beta depend more significantly on the nanoparticles' size than on the particular coating. We observe a decrease of beta as the nanoparticles' diameters decrease, although the optical gap is found to be the same for all samples. The results are interpreted considering modifications in the electronic orbital shape due to the particles' nanosize effect.

Solitons in nonlinear Schrödinger equations.

Using a mathematical approach accessible to graduate students of physics and engineering, we show how solitons are solutions of nonlinear Schrödinger equations. Are also given references about the history of solitons in general, their fundamental properties and how they have found applications in optics and fiber-optic communications.

Nonlinear optical characterizations of dibenzoylmethane in solution

This work reports on the two-photon absorption (2PA) cross-section and first hyperpolarizability of dibenzoylmethane solutions using femtosecond Z-scan and hyper-Rayleigh scattering techniques. The 2PA spectrum, spanning the wavelength range from 460 to 740 nm, presents a band centered at 510 nm, with a cross-section value estimated as 37 GM at this wavelength. Owing to the molecular symmetry, this band is not observed in the linear absorption spectrum. The sum-over-state approach was adopted to evaluate various spectroscopic parameters. Experimental and theoretical values of the first hyperpolarizability values were estimated in ethanol and DMSO solutions.