About the Stabilization of a Nonlinear Perturbed Difference Equation

This paper investigates the local asymptotic stabilization of a very general class of instable autonomous nonlinear difference equations which are subject to perturbed dynamics which can have a different order than that of the nominal difference equation. In the general case, the controller consists of two combined parts, namely, the feedback nominal controller which stabilizes the nominal (i.e., perturbation-free) difference equation plus an incremental controller which completes the stabilization in the presence of perturbed or unmodeled dynamics in the uncontrolled difference equation. A stabilization variant consists of using a single controller to stabilize both the nominal difference equation and also the perturbed one under a small-type characterization of the perturbed dynamics. The study is based on Banach fixed point principle, and it is also valid with slight modification for the stabilization of unstable oscillatory solutions.

Metamaterialen simulazioa FDTD metodoaren bidez

Azken urteetan metamaterialek izugarrizko arreta eragin dute. Material artifizial horiek hainbat aplikazio ezberdin izateko diseinatzen dira eta horretarako, ikerkuntza haien propietate elektromagnetikoak ulertzean zentratu da. Lan honen helburua, hortaz, metamaterialen jokabide elektromagnetikoa ulertzea da. Horretarako, FDTD (Finite Difference Time Domain) metodoa erabiliko dugu Maxwell-en ekuazioak ebazteko. Oinarria ulertzeko, lehenik, uhin elektromagnetikoen hedapena aztertuko dugu ingurune sinpleagoetan eta ingurune desberdinen arteko muga-azalen jokabidea simulatuko dugu. Hori egin eta gero, amaitzeko, uhin elektromagnetikoen hedapena aztertuko dugu errefrakzio-indize negatiboko materialetan (metamaterialetan).

Crank-Nicholson method for rate equations in powder random lasers

3rd International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE 2014)