Harmonic generation and wave mixing in nonlinear metamaterials and photonic crystals (Invited paper)

The basic concepts and phenomenology of wave mixing and harmonic generation are reviewed in context of the recent advances in the enhanced nonlinear activity in metamaterials and photonic crystals. The effects of dispersion, field confinement and phase synchronism are illustrated by the examples of the on-purpose designed artificial nonlinear structures. (c) 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE 22:469482, 2012.

Application of Volterra series in nonlinear mechanical system identification and in structural health monitoring problems

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

Effects of adiabatic exponent on Richtmyer-Meshkov instability

We present a systematical numerical study of the effects of adiabatic exponent gamma on Richtmyer-Meshkov instability (RMI) driven by cylindrical shock waves, based on the gamma model for the multi-component problems and numerical simulation with high-order and high-resolution method for compressible Euler equations. The results show that the RMI of different gamma across the interface exhibits different evolution features with the case of single gamma. Moreover, the large gamma can hold back the development of nonlinear structures, such as spikes and bubbles.

Modulated wavepackets associated with longitudinal dust grain oscillations in a dusty plasma crystal

The nonlinear amplitude modulation of longitudinal dust lattice waves (LDLWs) propagating in a dusty plasma crystal is investigated in a continuum approximation. It is shown that long wavelength LDLWs are modulationally stable, while shorter wavelengths may be unstable. The possibility for the formation and propagation of different envelope localized excitations is discussed. It is shown that the total grain displacement bears a (weak) constant displacement (zeroth harmonic mode), due to the asymmetric form of the nonlinear interaction potential. The existence of asymmetric envelope localized modes is predicted. The types and characteristics of these coherent nonlinear structures are discussed. (C) 2004 American Institute of Physics.

Electrostatic solitary waves in the presence of excess superthermal electrons: modulational instability and envelope soliton modes

The nonlinear dynamics of electrostatic solitary waves in the form of localized modulated wavepackets is investigated from first principles. Electron-acoustic (EA) excitations are considered in a two-electron plasma, via a fluid formulation. The plasma, assumed to be collisionless and uniform (unmagnetized), is composed of two types of electrons (inertial cold electrons and inertialess kappa-distributed superthermal electrons) and stationary ions. By making use of a multiscale perturbation technique, a nonlinear Schrodinger equation is derived for the modulated envelope, relying on which the occurrence of modulational instability (MI) is investigated in detail. Stationary profile localized EA excitations may exist, in the form of bright solitons (envelope pulses) or dark envelopes (voids). The presence of superthermal electrons modifies the conditions for MI to occur, as well as the associated threshold and growth rate. The concentration of superthermal electrons (i.e., the deviation from a Maxwellian electron distribution) may control or even suppress MI. Furthermore, superthermality affects the characteristics of solitary envelope structures, both qualitatively (supporting one or the other type, for different.) and quantitatively, changing their characteristics (width, amplitude). The stability of bright and dark-type nonlinear structures is confirmed by numerical simulations.

Solitary waves on a free surface of a heated Maxwell fluid

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On two-current realization of KP hierarchy

A simple description of the KP hierarchy and its multi-hamiltonian structure is given in terms of two Bose currents. A deformation scheme connecting various W-infinity algebras and the relation between two fundamental nonlinear structures are discussed. Properties of Faá di Bruno polynomials are extensively explored in this construction. Applications of our method are given for the Conformal Affine Toda model, WZNW models and discrete KP approach to Toda lattice chain.

On the theory of self-similar parabolic optical pulses

Self-similar optical pulses (or “similaritons”) of parabolic intensity profile can be found as asymptotic solutions of the nonlinear Schr¨odinger equation in a gain medium such as a fiber amplifier or laser resonator. These solutions represent a wide-ranging significance example of dissipative nonlinear structures in optics. Here, we address some issues related to the formation and evolution of parabolic pulses in a fiber gain medium by means of semi-analytic approaches. In particular, the effect of the third-order dispersion on the structure of the asymptotic solution is examined. Our analysis is based on the resolution of ordinary differential equations, which enable us to describe the main properties of the pulse propagation and structural characteristics observable through direct numerical simulations of the basic partial differential equation model with sufficient accuracy.

On the theory of self-similar parabolic optical pulses

Self-similar optical pulses (or “similaritons”) of parabolic intensity profile can be found as asymptotic solutions of the nonlinear Schr¨odinger equation in a gain medium such as a fiber amplifier or laser resonator. These solutions represent a wide-ranging significance example of dissipative nonlinear structures in optics. Here, we address some issues related to the formation and evolution of parabolic pulses in a fiber gain medium by means of semi-analytic approaches. In particular, the effect of the third-order dispersion on the structure of the asymptotic solution is examined. Our analysis is based on the resolution of ordinary differential equations, which enable us to describe the main properties of the pulse propagation and structural characteristics observable through direct numerical simulations of the basic partial differential equation model with sufficient accuracy.

Hydrogen-Bond-Directed Nonlinear-Optical Organic Materials - Evidence For The Control Of 2nd-Harmonic Generation Activities From The X-Ray Crystal-Structures Of The Complexes Of L-Tartaric Acid With M-Anisidine and P-Toluidine

Several substituted anilines were converted to binary salts with L-tartaric acid. Second harmonic generation (SHG) activities of these salts were determined. The crystal packing in two structures, (i) m-anisidinium-L-tartrate monohydrate (i) and (ii) p-toluidinium-L-tartrate (2), studied using X-ray diffraction demonstrates that extensive hydrogen bonding steers the components into a framework which has a direct bearing on the SHG activity

Nonlinear dynamic state estimation in instrumented structures with conditionally linear Gaussian substructures

Many problems of state estimation in structural dynamics permit a partitioning of system states into nonlinear and conditionally linear substructures. This enables a part of the problem to be solved exactly, using the Kalman filter, and the remainder using Monte Carlo simulations. The present study develops an algorithm that combines sequential importance sampling based particle filtering with Kalman filtering to a fairly general form of process equations and demonstrates the application of a substructuring scheme to problems of hidden state estimation in structures with local nonlinearities, response sensitivity model updating in nonlinear systems, and characterization of residual displacements in instrumented inelastic structures. The paper also theoretically demonstrates that the sampling variance associated with the substructuring scheme used does not exceed the sampling variance corresponding to the Monte Carlo filtering without substructuring. (C) 2012 Elsevier Ltd. All rights reserved.