A Fast Nonlinear Model Identification Method

The identification of nonlinear dynamic systems using linear-in-the-parameters models is studied. A fast recursive algorithm (FRA) is proposed to select both the model structure and to estimate the model parameters. Unlike orthogonal least squares (OLS) method, FRA solves the least-squares problem recursively over the model order without requiring matrix decomposition. The computational complexity of both algorithms is analyzed, along with their numerical stability. The new method is shown to require much less computational effort and is also numerically more stable than OLS.

Nonlinear response of permanent dipoles in a uniaxial potential to alternating fields

It is shown how the existing theory of the dynamic Kerr effect and nonlinear dielectric relaxation based on the noninertial Brownian rotation of noninteracting rigid dipolar particles may be generalized to take into account interparticle interactions using the Maier-Saupe mean field potential. The results (available in simple closed form) suggest that the frequency dependent nonlinear response provides a method of measuring the Kramers escape rate (or in the analogous problem of magnetic relaxation of fine single domain ferromagnetic particles, the superparamagnetic relaxation time).

Optical bistability in nonlinear surface-plasmon polaritonic crystals

Nonlinear optical transmission through periodically nanostructured metal films (surface-plasmon polaritonic crystals) has been studied. The surface polaritonic crystals have been coated with a nonlinear polymer. The optical transmission of such nanostructures has been shown to depend on the control-light illumination conditions. The resonant transmission exhibits bistable behavior with the control-light intensity. The bistability is different at different resonant signal wavelengths and for different wavelengths of the control light. The effect is explained by the strong sensitivity of the surface-plasmon mode resonances at the signal wavelength to the surrounding dielectric environment and the electromagnetic field enhancement due to plasmonic excitations at the controlled light wavelengths.

Nonlinear transport and localization in single-walled carbon nanotubes

We have measured the electrical transport properties of mats of single-walled carbon nanotubes (SWNT) as a function of applied electric and magnetic fields. We find that at low temperatures the resistance as a function of temperature R(T) follows the Mott variable range hopping (VRH) formula for hopping in three dimensions. Measurement of the electric field dependence of the resistance R(E) allows for the determination of the Bohr radius of a localized state a = 700nm. The magnetoresistance (MR) of SWNT mat samples is large and negative at all temperatures and fields studied. The low field negative MR is proportional to H2, in agreement with variable range hopping in two or three dimensions. 3D VRH indicates good intertube contacts, implying that the localization is due to the disorder experienced by the individual tubes. The 3D localization radius gives a measure of the ID localization length on the individual tubes, which we estimate to be >700 nm. Implications for the electron-phonon mean free path are discussed.

Experimental characterization of the nonlinear optical and magneto-optical properties of interfaces

An effective ellipsometric technique to determine parameters that characterize second-harmonic optical and magneto-optical effects in centrosymmetric media within the electric-dipole approximation is proposed and outlined in detail. The parameters, which are ratios of components of the nonlinear-surface-susceptibility tensors, are obtained from experimental data related to the state of polarization of the second-harmonic-generated radiation as a function of the angle between the plane of incidence and the polarization plane of the incident, linearly polarized, fundamental radiation. Experimental details of the technique are described. A corresponding theoretical model is given as an example for a single isotropic surface assuming polycrystalline samples. The surfaces of air-Au and air-Ni (in magnetized and demagnetized states) have been investigated ex situ in ambient air, and the results are presented. A nonlinear, least-squares-minimization fitting procedure between experimental data and theoretical formulas has been shown to yield realistic, unambiguous results for the ratios corresponding to each of the above materials. Independent methods for verifying the validity of the fitting parameters are also presented. The influence of temporal variations at the surfaces on the state of polarization (due to adsorption, contamination, or oxidation) is also illustrated for the demagnetized air-Ni surface. (C) 2005 Optical Society of America

Signal-to-Noise Ratio Analysis for Nonlinear N-ary Phase Filters

The problem of recognising targets in non-overlapping clutter using nonlinear N-ary phase filters is addressed. Using mathematical analysis, expressions were derived for an N-ary phase filter and the intensity variance of an optical correlator output. The N-ary phase filter was shown to consist of an infinite sum of harmonic terms whose periodicity was determined by N. For the intensity variance, it was found that under certain conditions the variance was minimised due to a hitherto undiscovered phase quadrature effect. Comparison showed that optimal real filters produced greater SNR values than the continuous phase versions as a consequence of this effect.

Self-focusing and envelope pulse generation in nonlinear magnetic metamaterials

The self-modulation of waves propagating in nonlinear magnetic metamaterials is investigated. Considering the propagation of a modulated amplitude magnetic field in such a medium, we show that the self-modulation of the carrier wave leads to a spontaneous energy localization via the generation of localized envelope structures (envelope solitons), whose form and properties are discussed. These results are also supported by numerical calculations.

Nonlinear PCA with Local Approach for Diesel Engine Fault Detection and Diagnosis

This brief examines the application of nonlinear statistical process control to the detection and diagnosis of faults in automotive engines. In this statistical framework, the computed score variables may have a complicated nonparametric distri- bution function, which hampers statistical inference, notably for fault detection and diagnosis. This brief shows that introducing the statistical local approach into nonlinear statistical process control produces statistics that follow a normal distribution, thereby enabling a simple statistical inference for fault detection. Further, for fault diagnosis, this brief introduces a compensation scheme that approximates the fault condition signature. Experimental results from a Volkswagen 1.9-L turbo-charged diesel engine are included.

Fully nonlinear ion-sound waves in a dense Fermi magnetoplasma

The nonlinear propagation of ion-sound waves in a collisionless dense electron-ion magnetoplasma is investigated. The inertialess electrons are assumed to follow a non-Boltzmann distribution due to the pressure for the Fermi plasma and the ions are described by the hydrodynamic (HD) equations. An energy balance-like equation involving a new Sagdeev-type pseudo-potential is derived in the presence of the quantum statistical effects. Numerical calculations reveal that the profiles of the Sagdeev-like potential and the ion-sound density excitations are significantly affected by the wave direction cosine and the Mach number. The present studies might be helpful to understand the excitation of nonlinear ion-sound waves in dense plasmas such as those in superdense white dwarfs and neutron stars as well as in intense laser-solid density plasma experiments.