A comparison of photoinduced poling and thermal poling of azo‐dye‐doped polymer films for second order nonlinear optical applications

Photoinduced poling (PIP) is a new technique which allows the room‐temperature preparation of guest/host polymer films exhibiting significant polar order for nonlinear optical applications. We report a comparison of this novel technique with the conventional electrode poling procedure performed at the glass transition temperature of the polymer using disperse red 1/poly(methylmethacrylate) films. In particular, in situ second harmonic generation measurements show that levels of polar order achieved using these two techniques are similar. In contrast, the stability of the polar order is reduced by up to 20 times in terms of the decay time constant in films prepared using PIP although the stability is very dependent upon the temperature at which the poling was performed.

Stable Nonlinear Receding Horizon Regulator Using RBF Neural Network Models

The general stability theory of nonlinear receding horizon controllers has attracted much attention over the last fifteen years, and many algorithms have been proposed to ensure closed-loop stability. On the other hand many reports exist regarding the use of artificial neural network models in nonlinear receding horizon control. However, little attention has been given to the stability issue of these specific controllers. This paper addresses this problem and proposes to cast the nonlinear receding horizon control based on neural network models within the framework of an existing stabilising algorithm.

Evidence of dispersion relations for the nonlinear response of the Lorenz 63 system

Along the lines of the nonlinear response theory developed by Ruelle, in a previous paper we have proved under rather general conditions that Kramers-Kronig dispersion relations and sum rules apply for a class of susceptibilities describing at any order of perturbation the response of Axiom A non equilibrium steady state systems to weak monochromatic forcings. We present here the first evidence of the validity of these integral relations for the linear and the second harmonic response for the perturbed Lorenz 63 system, by showing that numerical simulations agree up to high degree of accuracy with the theoretical predictions. Some new theoretical results, showing how to derive asymptotic behaviors and how to obtain recursively harmonic generation susceptibilities for general observables, are also presented. Our findings confirm the conceptual validity of the nonlinear response theory, suggest that the theory can be extended for more general non equilibrium steady state systems, and shed new light on the applicability of very general tools, based only upon the principle of causality, for diagnosing the behavior of perturbed chaotic systems and reconstructing their output signals, in situations where the fluctuation-dissipation relation is not of great help.

Bistable systems with stochastic noise: virtues and limits of effective one-dimensional Langevin equations

The understanding of the statistical properties and of the dynamics of multistable systems is gaining more and more importance in a vast variety of scientific fields. This is especially relevant for the investigation of the tipping points of complex systems. Sometimes, in order to understand the time series of given observables exhibiting bimodal distributions, simple one-dimensional Langevin models are fitted to reproduce the observed statistical properties, and used to investing-ate the projected dynamics of the observable. This is of great relevance for studying potential catastrophic changes in the properties of the underlying system or resonant behaviours like those related to stochastic resonance-like mechanisms. In this paper, we propose a framework for encasing this kind of studies, using simple box models of the oceanic circulation and choosing as observable the strength of the thermohaline circulation. We study the statistical properties of the transitions between the two modes of operation of the thermohaline circulation under symmetric boundary forcings and test their agreement with simplified one-dimensional phenomenological theories. We extend our analysis to include stochastic resonance-like amplification processes. We conclude that fitted one-dimensional Langevin models, when closely scrutinised, may result to be more ad-hoc than they seem, lacking robustness and/or well-posedness. They should be treated with care, more as an empiric descriptive tool than as methodology with predictive power.

Exact design manifold control of a class of nonlinear singularly perturbed systems

The integral manifold approach captures from a geometric point of view the intrinsic two-time-scale behavior of singularly perturbed systems. An important class of nonlinear singularly perturbed systems considered in this note are fast actuator-type systems. For a class of fast actuator-type systems, which includes many physical systems, an explicit corrected composite control, the sum of a slow control and a fast control, is derived. This corrected control will steer the system exactly to a required design manifold.

Exact design manifold control of a class of nonlinear singularly perturbed systems

The integral manifold approach captures from a geometric point of view the intrinsic two-time-scale behavior of singularly perturbed systems. An important class of nonlinear singularly perturbed systems considered in this note are fast actuator-type systems. For a class of fast actuator-type systems, which includes many physical systems, an explicit corrected composite control, the sum of a slow control and a fast control, is derived. This corrected control will steer the system exactly to a required design manifold.

Bifurcation Analysis of Eigenstructure Assignment Control in a Simple Nonlinear Aircraft Model

Aircraft systems are highly nonlinear and time varying. High-performance aircraft at high angles of incidence experience undesired coupling of the lateral and longitudinal variables, resulting in departure from normal controlled � ight. The construction of a robust closed-loop control that extends the stable and decoupled � ight envelope as far as possible is pursued. For the study of these systems, nonlinear analysis methods are needed. Previously, bifurcation techniques have been used mainly to analyze open-loop nonlinear aircraft models and to investigate control effects on dynamic behavior. Linear feedback control designs constructed by eigenstructure assignment methods at a � xed � ight condition are investigated for a simple nonlinear aircraft model. Bifurcation analysis, in conjunction with linear control design methods, is shown to aid control law design for the nonlinear system.

Closed loop design for a simple nonlinear aircraft model using eigenstructure assignment

Aircraft systems are highly nonlinear and time varying. High-performance aircraft at high angles of incidence experience undesired coupling of the lateral and longitudinal variables, resulting in departure from normal controlled flight. The aim of this work is to construct a robust closed-loop control that optimally extends the stable and decoupled flight envelope. For the study of these systems nonlinear analysis methods are needed. Previously, bifurcation techniques have been used mainly to analyze open-loop nonlinear aircraft models and investigate control effects on dynamic behavior. In this work linear feedback control designs calculated by eigenstructure assignment methods are investigated for a simple aircraft model at a fixed flight condition. Bifurcation analysis in conjunction with linear control design methods is shown to aid control law design for the nonlinear system.

Nonlinear set-membership estimation: a support vector machine approach

In this paper a support vector machine (SVM) approach for characterizing the feasible parameter set (FPS) in non-linear set-membership estimation problems is presented. It iteratively solves a regression problem from which an approximation of the boundary of the FPS can be determined. To guarantee convergence to the boundary the procedure includes a no-derivative line search and for an appropriate coverage of points on the FPS boundary it is suggested to start with a sequential box pavement procedure. The SVM approach is illustrated on a simple sine and exponential model with two parameters and an agro-forestry simulation model.

The multisensory attentional consequences of tool use: a functional magnetic resonance imaging study

Background: Tool use in humans requires that multisensory information is integrated across different locations, from objects seen to be distant from the hand, but felt indirectly at the hand via the tool. We tested the hypothesis that using a simple tool to perceive vibrotactile stimuli results in the enhanced processing of visual stimuli presented at the distal, functional part of the tool. Such a finding would be consistent with a shift of spatial attention to the location where the tool is used. Methodology/Principal Findings: We tested this hypothesis by scanning healthy human participants' brains using functional magnetic resonance imaging, while they used a simple tool to discriminate between target vibrations, accompanied by congruent or incongruent visual distractors, on the same or opposite side to the tool. The attentional hypothesis was supported: BOLD response in occipital cortex, particularly in the right hemisphere lingual gyrus, varied significantly as a function of tool position, increasing contralaterally, and decreasing ipsilaterally to the tool. Furthermore, these modulations occurred despite the fact that participants were repeatedly instructed to ignore the visual stimuli, to respond only to the vibrotactile stimuli, and to maintain visual fixation centrally. In addition, the magnitude of multisensory (visual-vibrotactile) interactions in participants' behavioural responses significantly predicted the BOLD response in occipital cortical areas that were also modulated as a function of both visual stimulus position and tool position. Conclusions/Significance: These results show that using a simple tool to locate and to perceive vibrotactile stimuli is accompanied by a shift of spatial attention to the location where the functional part of the tool is used, resulting in enhanced processing of visual stimuli at that location, and decreased processing at other locations. This was most clearly observed in the right hemisphere lingual gyrus. Such modulations of visual processing may reflect the functional importance of visuospatial information during human tool use

Nonlinear error dynamics for cycled data assimilation methods

We investigate the error dynamics for cycled data assimilation systems, such that the inverse problem of state determination is solved at tk, k = 1, 2, 3, ..., with a first guess given by the state propagated via a dynamical system model from time tk − 1 to time tk. In particular, for nonlinear dynamical systems that are Lipschitz continuous with respect to their initial states, we provide deterministic estimates for the development of the error ||ek|| := ||x(a)k − x(t)k|| between the estimated state x(a) and the true state x(t) over time. Clearly, observation error of size δ > 0 leads to an estimation error in every assimilation step. These errors can accumulate, if they are not (a) controlled in the reconstruction and (b) damped by the dynamical system under consideration. A data assimilation method is called stable, if the error in the estimate is bounded in time by some constant C. The key task of this work is to provide estimates for the error ||ek||, depending on the size δ of the observation error, the reconstruction operator Rα, the observation operator H and the Lipschitz constants K(1) and K(2) on the lower and higher modes of controlling the damping behaviour of the dynamics. We show that systems can be stabilized by choosing α sufficiently small, but the bound C will then depend on the data error δ in the form c||Rα||δ with some constant c. Since ||Rα|| → ∞ for α → 0, the constant might be large. Numerical examples for this behaviour in the nonlinear case are provided using a (low-dimensional) Lorenz '63 system.

Isomap nonlinear dimensionality reduction and bimodality of Asian monsoon convection

It is known that the empirical orthogonal function method is unable to detect possible nonlinear structure in climate data. Here, isometric feature mapping (Isomap), as a tool for nonlinear dimensionality reduction, is applied to 1958–2001 ERA-40 sea-level pressure anomalies to study nonlinearity of the Asian summer monsoon intraseasonal variability. Using the leading two Isomap time series, the probability density function is shown to be bimodal. A two-dimensional bivariate Gaussian mixture model is then applied to identify the monsoon phases, the obtained regimes representing enhanced and suppressed phases, respectively. The relationship with the large-scale seasonal mean monsoon indicates that the frequency of monsoon regime occurrence is significantly perturbed in agreement with conceptual ideas, with preference for enhanced convection on intraseasonal time scales during large-scale strong monsoons. Trend analysis suggests a shift in concentration of monsoon convection, with less emphasis on South Asia and more on the East China Sea.

The troposphere-to-stratosphere transition in kinetic energy spectra and nonlinear spectral fluxes as seen in ECMWF analyses

Global horizontal wavenumber kinetic energy spectra and spectral fluxes of rotational kinetic energy and enstrophy are computed for a range of vertical levels using a T799 ECMWF operational analysis. Above 250 hPa, the kinetic energy spectra exhibit a distinct break between steep and shallow spectral ranges, reminiscent of dual power-law spectra seen in aircraft data and high-resolution general circulation models. The break separates a large-scale ‘‘balanced’’ regime in which rotational flow strongly dominates divergent flow and a mesoscale ‘‘unbalanced’’ regime where divergent energy is comparable to or larger than rotational energy. Between 230 and 100 hPa, the spectral break shifts to larger scales (from n 5 60 to n 5 20, where n is spherical harmonic index) as the balanced component of the flow preferentially decays. The location of the break remains fairly stable throughout the stratosphere. The spectral break in the analysis occurs at somewhat larger scales than the break seen in aircraft data. Nonlinear spectral fluxes defined for the rotational component of the flow maximize between about 300 and 200 hPa. Large-scale turbulence thus centers on the extratropical tropopause region, within which there are two distinct mechanisms of upscale energy transfer: eddy–eddy interactions sourcing the transient energy peak in synoptic scales, and zonal mean–eddy interactions forcing the zonal flow. A well-defined downscale enstrophy flux is clearly evident at these altitudes. In the stratosphere, the transient energy peak moves to planetary scales and zonal mean–eddy interactions become dominant.

Towards a model-based integration of co-registered electroencephalography/functional magnetic resonance imaging data with realistic neural population meshes

Brain activity can be measured with several non-invasive neuroimaging modalities, but each modality has inherent limitations with respect to resolution, contrast and interpretability. It is hoped that multimodal integration will address these limitations by using the complementary features of already available data. However, purely statistical integration can prove problematic owing to the disparate signal sources. As an alternative, we propose here an advanced neural population model implemented on an anatomically sound cortical mesh with freely adjustable connectivity, which features proper signal expression through a realistic head model for the electroencephalogram (EEG), as well as a haemodynamic model for functional magnetic resonance imaging based on blood oxygen level dependent contrast (fMRI BOLD). It hence allows simultaneous and realistic predictions of EEG and fMRI BOLD from the same underlying model of neural activity. As proof of principle, we investigate here the influence on simulated brain activity of strengthening visual connectivity. In the future we plan to fit multimodal data with this neural population model. This promises novel, model-based insights into the brain's activity in sleep, rest and task conditions.

Nonlinear stability of Euler flows in two-dimensional periodic domains

The non-quadratic conservation laws of the two-dimensional Euler equations are used to show that the gravest modes in a doubly-periodic domain with aspect ratio L = 1 are stable up to translations (or structurally stable) for finite-amplitude disturbances. This extends a previous result based on conservation of energy and enstrophy alone. When L 1, a saturation bound is established for the mode with wavenumber |k| = L −1 (the next-gravest mode), which is linearly unstable. The method is applied to prove nonlinear structural stability of planetary wave two on a rotating sphere.