Excited-state dynamics of meso-tetrakis(sulfonatophenyl) porphyrin J-aggregates

The excited-state dynamics of free-base meso-tetrakis(sulfonatophenyl) porphyrin J-aggregates obtained by the Z-scan technique in femto- and picosecond time scales, along with UV-Vis spectroscopy and flash photolysis is reported. Besides obtaining the S-1 state lifetime, the discrimination between internal conversion and intersystem crossing nonradiative processes from that state was also possible, and their rates and respective quantum yields were found. The aggregates present reverse saturable absorption at 532 nm for both singlet and triplet excited states. The data shown is important for several applications such as optical limiting, photodynamic therapy and others. (C) 2011 Elsevier B.V. All rights reserved.

Error Upper Bounds for a Computational Method for Nonlinear Boundary and Initial-Value Problems

This work develops a computational approach for boundary and initial-value problems by using operational matrices, in order to run an evolutive process in a Hilbert space. Besides, upper bounds for errors in the solutions and in their derivatives can be estimated providing accuracy measures.

Investigation of the optical absorption of a magnetic colloid from the thermal to the electronic time-scale regime: measurement of the free-carrier absorption cross-section

The free-carrier absorption cross-section sigma of a magnetic colloid composed of magnetite nanoparticles dispersed in oil is obtained by using the Z-scan technique in different experimental conditions of the laser beam. We show that it is possible to obtain sigma with picosecond pulsed and millisecond chopped beams with pulse frequencies smaller than about 30 Hz. For higher pulse frequencies, the heating of the colloidal system triggers the appearance of the Soret effect. This effect artificially increases the value of sigma calculated from the experimental results. The limits of the different experimental setups are discussed. (C) 2012 Optical Society of America

Structural refinement, optical and microwave dielectric properties of BaZrO3

In this work, barium zirconate (BaZrO3) ceramics synthesized by solid state reaction method and sintered at 1670 degrees C for 4 h were characterized by X-ray diffraction (XRD), Rietveld refinement, and Fourier transform infrared (FT-IR) spectroscopy. XRD patterns, Rietveld refinement data and FT-IR spectra which confirmed that BaZrO3 ceramics have a perovskite-type cubic structure. Optical properties were investigated by ultraviolet-visible (UV-vis) absorption and photoluminescence (PL) measurements. UV-vis absorption spectra suggested an indirect allowed transition with the existence of intermediary energy levels within the band gap. Intense visible green PL emission was observed in BaZrO3 ceramics upon excitation with a 350 nm wavelength. This behavior is due to a majority of deep defects within the band gap caused by symmetry breaking in octahedral [ZrO6] clusters in the lattice. The microwave dielectric constant and quality factor were measured using the method proposed by Hakki-Coleman. The dielectric resonator antenna (DRA) was investigated experimentally and numerically using a monopole antenna through an infinite ground plane and Ansoft's high frequency structure simulator software, respectively. The required resonance frequency and bandwidth of DRA were investigated by adjusting the dimension of the same material. (C) 2011 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

Dynamical analysis of turbulence in fusion plasmas and nonlinear waves

Turbulence is one of the key problems of classical physics, and it has been the object of intense research in the last decades in a large spectrum of problems involving fluids, plasmas, and waves. In order to review some advances in theoretical and experimental investigations on turbulence a mini-symposium on this subject was organized in the Dynamics Days South America 2010 Conference. The main goal of this mini-symposium was to present recent developments in both fundamental aspects and dynamical analysis of turbulence in nonlinear waves and fusion plasmas. In this paper we present a summary of the works presented at this mini-symposium. Among the questions to be addressed were the onset and control of turbulence and spatio-temporal chaos. (C) 2011 Elsevier B. V. All rights reserved.

Generation of copper nanoparticles induced by fs-laser irradiation in borosilicate glass

Glasses containing metallic nanoparticles are promising materials for technological applications in optics and photonics. Although several methods are available to generate nanoparticles in glass, only femtosecond lasers allow controlling it three-dimensionally. In this direction, the present work investigates the generation of copper nanoparticles on the surface and in the bulk of a borosilicate glass by fs-laser irradiation. We verified the formation of copper nanoparticles, after heat treatment, by UV-Vis absorption, transmission electron microscopy and electron diffraction. A preferential growth of copper nanoparticles was observed in the bottom of the irradiated region, which was attributed to self-focusing in the glass. (c) 2012 Optical Society of America

Bartlett corrections in Birnbaum-Saunders nonlinear regression models

Lemonte and Cordeiro [Birnbaum-Saunders nonlinear regression models, Comput. Stat. Data Anal. 53 (2009), pp. 4441-4452] introduced a class of Birnbaum-Saunders (BS) nonlinear regression models potentially useful in lifetime data analysis. We give a general matrix Bartlett correction formula to improve the likelihood ratio (LR) tests in these models. The formula is simple enough to be used analytically to obtain several closed-form expressions in special cases. Our results generalize those in Lemonte et al. [Improved likelihood inference in Birnbaum-Saunders regressions, Comput. Stat. DataAnal. 54 (2010), pp. 1307-1316], which hold only for the BS linear regression models. We consider Monte Carlo simulations to show that the corrected tests work better than the usual LR tests.

Phase-Locked loops lock-in range in Frequency Modulated-Atomic Force Microscope nonlinear control system

Since the mid 1980s the Atomic Force Microscope is one the most powerful tools to perform surface investigation, and since 1995 Non-Contact AFM achieved true atomic resolution. The Frequency-Modulated Atomic Force Microscope (FM-AFM) operates in the dynamic mode, which means that the control system of the FM-AFM must force the micro-cantilever to oscillate with constant amplitude and frequency. However, tip-sample interaction forces cause modulations in the microcantilever motion. A Phase-Locked loop (PLL) is used to demodulate the tip-sample interaction forces from the microcantilever motion. The demodulated signal is used as the feedback signal to the control system, and to generate both topographic and dissipation images. As a consequence, a proper design of the PLL is vital to the FM-AFM performance. In this work, using bifurcation analysis, the lock-in range of the PLL is determined as a function of the frequency shift (Q) of the microcantilever and of the other design parameters, providing a technique to properly design the PLL in the FM-AFM system. (C) 2011 Elsevier B.V. All rights reserved.

Femtosecond third-order nonlinear spectra of lead-germanium oxide glasses containing silver nanoparticles

This work reports on the spectral dependence of both nonlinear refraction and absorption in lead-germanium oxide glasses (PbO-GeO2) containing silver nanoparticles. We have found that this material is suitable for all-optical switching at telecom wavelengths but at the visible range it behaves either as a saturable absorber or as an optical limiter. (C) 2012 Optical Society of America

On S-asymptotically omega-periodic functions and applications

Let (X, parallel to . parallel to) be a Banach space and omega is an element of R. A bounded function u is an element of C([0, infinity); X) is called S-asymptotically omega-periodic if lim(t ->infinity)[u(t + omega) - u(t)] = 0. In this paper, we establish conditions under which an S-asymptotically omega-periodic function is asymptotically omega-periodic and we discuss the existence of S-asymptotically omega-periodic and asymptotically omega-periodic solutions for an abstract integral equation. Some applications to partial differential equations and partial integro-differential equations are considered. (C) 2011 Elsevier Ltd. All rights reserved.

Transverse pseudo-nonlinear effects measured in solid-state laser materials using a sensitive time-resolved technique

We present a detailed study of the Baryscan technique, a new efficient alternative to the widespread Z-scan technique which has been demonstrated [Opt. Lett. 36:8, 2011] to reach among the highest sensitivity levels. This method is based upon the measurement of optical nonlinearities by means of beam centroid displacements with a position sensitive detector and is able to deal with any kind of lensing effect. This technique is applied here to measure pump-induced electronic refractive index changes (population lens), which can be discriminated from parasitic thermal effects by using a time-resolved Baryscan experiment. This method is validated by evaluating the polarizability variation at the origin of the population lens observed in the reference Cr3+:GSGG laser material.

TYPE-ZERO SADDLE-NODE BIFURCATIONS AND STABILITY REGION ESTIMATION OF NONLINEAR AUTONOMOUS DYNAMICAL SYSTEMS

A complete characterization of the stability boundary of a class of nonlinear dynamical systems that admit energy functions is developed in this paper. This characterization generalizes the existing results by allowing the type-zero saddle-node nonhyperbolic equilibrium points on the stability boundary. Conceptual algorithms to obtain optimal estimates of the stability region (basin of attraction) in the form of level sets of a given family of energy functions are derived. The behavior of the stability region and the corresponding estimates are investigated for parameter variation in the neighborhood of a type-zero saddle-node bifurcation value.

TWO NEW WEAK CONSTRAINT QUALIFICATIONS AND APPLICATIONS

We present two new constraint qualifications (CQs) that are weaker than the recently introduced relaxed constant positive linear dependence (RCPLD) CQ. RCPLD is based on the assumption that many subsets of the gradients of the active constraints preserve positive linear dependence locally. A major open question was to identify the exact set of gradients whose properties had to be preserved locally and that would still work as a CQ. This is done in the first new CQ, which we call the constant rank of the subspace component (CRSC) CQ. This new CQ also preserves many of the good properties of RCPLD, such as local stability and the validity of an error bound. We also introduce an even weaker CQ, called the constant positive generator (CPG), which can replace RCPLD in the analysis of the global convergence of algorithms. We close this work by extending convergence results of algorithms belonging to all the main classes of nonlinear optimization methods: sequential quadratic programming, augmented Lagrangians, interior point algorithms, and inexact restoration.

SUFFICIENT CONDITIONS ON DIFFUSIVITY FOR THE EXISTENCE AND NONEXISTENCE OF STABLE EQUILIBRIA WITH NONLINEAR FLUX ON THE BOUNDARY

A reaction-diffusion equation with variable diffusivity and non-linear flux boundary condition is considered. The goal is to give sufficient conditions on the diffusivity function for nonexistence and also for existence of nonconstant stable stationary solutions. Applications are given for the main result of nonexistence.

On the optical properties of copper nanocubes as a function of the edge length as modeled by the discrete dipole approximation

This Letter reports an investigation on the optical properties of copper nanocubes as a function of size as modeled by the discrete dipole approximation. In the far-field, our results showed that the extinction resonances shifted from 595 to 670 nm as the size increased from 20 to 100 nm. Also, the highest optical efficiencies for absorption and scattering were obtained for nanocubes that were 60 and 100 nm in size, respectively. In the near-field, the electric-field amplitudes were investigated considering 514, 633 and 785 nm as the excitation wavelengths. The E-fields increased with size, being the highest at 633 nm. (c) 2012 Elsevier B.V. All rights reserved.