EIGENVALUES of FIBONACCI STOCHASTIC ADDING MACHINE

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Band edge states of the < n >=0 gap of Fibonacci photonic lattices

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Predictor-Corrector Primal-Dual Interior Point Method for Solving Economic Dispatch Problems: A Postoptimization Analysis

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On the spectrum of stochastic perturbations of the shift and Julia sets

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Band-edge states of the zero(th)-order gap in quasi-periodic photonic superlattices

The photonic modes of Thue-Morse and Fibonacci lattices with generating layers A and B, of positive and negative indices of refraction, are calculated by the transfer-matrix technique. For Thue-Morse lattices, as well for periodic lattices with AB unit cell, the constructive interference of reflected waves, corresponding to the zero(th)-order gap, takes place when the optical paths in single layers A and B are commensurate. In contrast, for Fibonacci lattices of high order, the same phenomenon occurs when the ratio of those optical paths is close to the golden ratio. In the long wavelength limit, analytical expressions defining the edge frequencies of the zero(th) order gap are obtained for both quasi-periodic lattices. Furthermore, analytical expressions that define the gap edges around the zero(th) order gap are shown to correspond to the = 0 and = 0 conditions.

Anderson localization and Brewster anomalies in photonic disordered quasiperiodic lattices

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On the photonic dispersion of periodic superlattices made of left-handed materials

Studies of the band gap properties of one-dimensional superlattices with alternate layers of air and left-handed materials are carried out within the framework of Maxwell's equations. By left-handed material, we mean a material with dispersive negative electric and magnetic responses. Modeling them by Drude-type responses or by fabricated ones, we characterize the n(ω) = 0 gap, i.e., the zeroth order gap, which has been predicted and detected. The band structure and analytic equations for the band edges have been obtained in the long wavelength limit in case of periodic, Fibonacci, and Thue-Morse superlattices. Our studies reveal the nature of the width of the zeroth order band gap, whose edge equations are defined by null averages of the response functions. Oblique incidence is also investigated, yielding remarkable results. © 2010 Springer Science+Business Media B.V.

Explorando a matemática do número Ф, o número de ouro

Pós-graduação em Matemática em Rede Nacional - IBILCE

O número de ouro no ensino da matemática na educação básica

Pós-graduação em Matemática em Rede Nacional - IBILCE

Máquinas de somar estocásticas e conjuntos de Julia

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Equações de diferenças: aplicações no ensino médio

Pós-graduação em Matemática em Rede Nacional - IBILCE