Pseudo-nonlinear and athermal lensing effects on transverse properties of Cr(3+) based solid-state lasers

Several experiments (time-resolved Z-scan experiments based on pulsed and CW pump lasers, time-resolved divergence diagnostics) have been performed to examine and clarify the question of the converging or diverging population lensing effect occurring in a Cr(3+):Al(2)O(3) ruby laser. The dynamics of the laser far-field divergence of such a laser indeed indicated initially a diverging effect while Z-scan measurements conclude to a converging one. The origin of this discrepancy is thus analysed and elucidated here by introducing the general concept of correlation collapse between the centre and the wings of a laser beam having some clipping. (C) 2010 Elsevier B.V. All rights reserved.

Nonautonomous difference equations with applications

This work is divided in two parts. In the first part we develop the theory of discrete nonautonomous dynamical systems. In particular, we investigate skew-product dynamical system, periodicity, stability, center manifold, and bifurcation. In the second part we present some concrete models that are used in ecology/biology and economics. In addition to developing the mathematical theory of these models, we use simulations to construct graphs that illustrate and describe the dynamics of the models. One of the main contributions of this dissertation is the study of the stability of some concrete nonlinear maps using the center manifold theory. Moreover, the second contribution is the study of bifurcation, and in particular the construction of bifurcation diagrams in the parameter space of the autonomous Ricker competition model. Since the dynamics of the Ricker competition model is similar to the logistic competition model, we believe that there exists a certain class of two-dimensional maps with which we can generalize our results. Finally, using the Brouwer’s fixed point theorem and the construction of a compact invariant and convex subset of the space, we present a proof of the existence of a positive periodic solution of the nonautonomous Ricker competition model.

Egg production curve fitting using nonlinear models for selected and nonselected lines of White Leghorn hens

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

Investigation of the two-photon absorption cross-section in perylene tetracarboxylic derivatives: Nonlinear spectra and molecular structure

We investigated the 2PA absorption spectrum of a family of perylene tetracarboxylic derivatives ( PTCDs): bis( benzimidazo) perylene ( AzoPTCD), bis( benzimidazo) thioperylene ( Monothio BZP), n-pentylimidobenzimidazoperylene ( PazoPTCD), and bis( n-butylimido) perylene ( BuPTCD). These compounds present extremely high two-photon absorption, which makes them attractive for applications in photonics devices. The two-photon absorption cross-section spectra of perylene derivatives obtained via Z-scan technique were fitted by means of a sum-over-states ( SOS) model, which described with accuracy the different regions of the 2PA cross-section spectra. Frontier molecular orbital calculations show that all molecules present similar features, indicating that nonlinear optical properties in PTCDs are mainly determined by the central portion of the molecule, with minimal effect from the lateral side groups. In general, our results pointed out that the differences in the 2PA cross-sections among the compounds are mainly due to the nonlinearity resonance enhancement.

Dynamical evolution of Saturn's F ring dust particles

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

Dynamical erosion of asteroid groups in the region of the Phocaea family

In a previous paper, the current state of knowledge of the region containing the Phocaea dynamical family was revised. Here, the dynamical evolution and possible origin of the Phocaea dynamical family and asteroid groups in the region are investigated. First, I study the case of asteroids at high eccentricity (e > 0.31). I find that these objects are unstable because of encounters with Mars on time-scales of up to 270 Myr. The minimum time needed by members of the Phocaea classical family to reach the orbital locations of these objects, 370 Myr, can be used to set a lower limit on the age of the Phocaea family.Next, attention is focused on the chaotic layer previously identified near the nu(6) secular resonance border. Using analytical and numerical tools, I find that the presence of the nu(6) secular resonance forces asteroids with vertical bar g-g(6)vertical bar < 2.55 arcsec yr(-1) to reach eccentricities high enough to allow them to experience deep, close encounters with Mars. Results of the analytical model of Yoshikawa and of my numerical simulations fully explain the low-inclination chaotic region found by Carruba.Finally, I investigate the long-term stability of the minor families and clumps identified in the previous paper, with particular emphasis on a clump only identifiable in the domain of proper frequencies (n, g, g - s) around (6246) Komurotoru. I find that while the clumps identified in the space of proper elements quickly disperse when the Yarkovsky effect is considered, the family around (19536) is still observable for time-scales of more than 50 Myr. The (6246) clump, characterized by its interaction with the nu(5) + nu(16) and 2 nu(6) - nu(16) secular resonances, is robust on time-scales of 50 Myr. I confirm that this group may be the first clump ever detected in the frequency domain that can be associated with a real collisional event.

Dynamics at infinity and other global dynamical aspects of Shimizu-Morioka equations

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Fresnel analysis of wave propagation in nonlinear electrodynamics

We study wave propagation in local nonlinear electrodynamical models. Particular attention is paid to the derivation and the analysis of the Fresnel equation for the wave covectors. For the class of local nonlinear Lagrangian nondispersive models, we demonstrate how the originally quartic Fresnel equation factorizes, yielding the generic birefringence effect. We show that the closure of the effective constitutive (or jump) tensor is necessary and sufficient for the absence of birefringence, i.e., for the existence of a unique light cone structure. As another application of the Fresnel approach, we analyze the light propagation in a moving isotropic nonlinear medium. The corresponding effective constitutive tensor contains nontrivial skewon and axion pieces. For nonmagnetic matter, we find that birefringence is induced by the nonlinearity, and derive the corresponding optical metrics.

Stability analysis of the D-dimensional nonlinear Schrodinger equation with trap and two- and three-body interactions

Considering the static solutions of the D-dimensional nonlinear Schrodinger equation with trap and attractive two-body interactions, the existence of stable solutions is limited to a maximum critical number of particles, when D greater than or equal to 2. In case D = 2, we compare the variational approach with the exact numerical calculations. We show that, the addition of a positive three-body interaction allows stable solutions beyond the critical number. In this case, we also introduce a dynamical analysis of the conditions for the collapse. (C) 2000 Published by Elsevier B.V. B.V. All rights reserved.

Chiral symmetry breaking in QCD-like gauge theories with a confining propagator and dynamical gauge boson mass generation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dynamical properties of a dissipative hybrid Fermi-Ulam-bouncer model

Some consequences of dissipation are studied for a classical particle suffering inelastic collisions in the hybrid Fermi-Ulam bouncer model. The dynamics of the model is described by a two-dimensional nonlinear area-contracting map. In the limit of weak and moderate dissipation we report the occurrence of crisis and in the limit of high dissipation the model presents doubling bifurcation cascades. Moreover, we show a phenomena of annihilation by pairs of fixed points as the dissipation varies. (c) 2007 American Institute of Physics.

On the V-type asteroids outside the Vesta family - II. Is (21238) 1995 WV7 a fragment of the long-lost basaltic crust of (15) Eunomia?

Context. The V-type asteroids are associated with basaltic composition. Apart from ( 1459) Magnya, an asteroid that is clearly dynamically and mineralogically unconnected to the Vesta family, all currently known V-type asteroids are either members of the Vesta family, or are hypothesized to be former members of the dynamical family that migrated to their current orbital positions. The recent identification of ( 21238) 1995 WV7 as a V-type asteroid introduces the possibility that a second basaltic asteroid not connected with the Vesta family exists. This asteroid is on the opposite side of the 3: 1 mean motion resonance with respect to Vesta, and it would be very unlikely that a member of the Vesta family of its size (D > 5km) migrating via either the Yarkovsky effect or repeated close encounters with Vesta survived the passage through such a resonance.Aims. In this work we investigate the possibility that ( 21238) 1995 WV7 originated as a fragment of the parent body of the Eunomia family and then migrated via the interplay of the Yarkovsky effect and some powerful nonlinear secular resonances, such as the (s - s(6)) - ( g(5) - g(6)). If (15) Eunomia is, as claimed, a differentiated object whose originally pyroxene-enriched crust layer was lost in a collision that either created the Eunomia family or preceded its formation, can (21238) be a fragment of its long-lost basaltic crust that migrated to the current position?Methods. We mapped the phase space around (21238) and determined which of the nonlinear secular resonances that we identified are stronger and more capable of having caused the current difference in proper i between (21238) and members of the Eunomia family. We simulated the Yarkovsky effect by using the SWIFT-RMVSY integrator.Results. Our results suggest that it is possible to migrate from the Eunomia dynamical family to the current orbital location of ( 21238) via the interplay of the Yarkovsky effect and the (s - s6) - (g5 - g6) nonlinear secular resonance, on time-scales of at least 2.6 Gyr.Conclusions. (15) Eunomia might be the third currently known parent body for V-type asteroids.

Statements on chaos control designs, including a fractional order dynamical system, applied to a MEMS comb-drive actuator

In this work, we deal with a micro electromechanical system (MEMS), represented by a micro-accelerometer. Through numerical simulations, it was found that for certain parameters, the system has a chaotic behavior. The chaotic behaviors in a fractional order are also studied numerically, by historical time and phase portraits, and the results are validated by the existence of positive maximal Lyapunov exponent. Three control strategies are used for controlling the trajectory of the system: State Dependent Riccati Equation (SDRE) Control, Optimal Linear Feedback Control, and Fuzzy Sliding Mode Control. The controls proved effective in controlling the trajectory of the system studied and robust in the presence of parametric errors.

Nonlinear Interactions in a Piezoceramic Bar Transducer Powered by a Vacuum Tube Generated by a Nonideal Source

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)