Enhanced second order non-linear optical properties of silica sol-gel thin films through photo-induced poling

Sol-gel derived inorganic materials are of interest as hosts for non-linear optically active guest molecules and they offer particular advantages in the field of non-linear optics. Orientationally ordered glasses have been prepared using a sol-gel system based on tetramethoxysilane, methyltrimethoxysilane and a non-linear optical chromophore Disperse Red 1. The novel technique of photo-induced poling was used to generate enhanced levels of polar order. The level of enhancement is strongly dependent on the extent of gelation and an optimum preparation time of ∼100 h led to an enhancement factor of ∼5. Films prepared in this manner exhibited a high stability of the polar order.

A two-dimensional X-ray scattering system for in-situ time-resolving studies of polymer structures subjected to controlled deformations

A two-dimensional X-ray scattering system developed around a CCD-based area detector is presented, both in terms of hardware employed and software designed and developed. An essential feature is the integration of hardware and software, detection and sample environment control which enables time-resolving in-situ wide-angle X-ray scattering measurements of global structural and orientational parameters of polymeric systems subjected to a variety of controlled external fields. The development and operation of a number of rheometers purpose-built for the application of such fields are described. Examples of the use of this system in monitoring degrees of shear-induced orientation in liquid-crystalline systems and crystallization of linear polymers subsequent to shear flow are presented.

Linear-wavelet networks

This paper proposes a nonlinear regression structure comprising a wavelet network and a linear term. The introduction of the linear term is aimed at providing a more parsimonious interpolation in high-dimensional spaces when the modelling samples are sparse. A constructive procedure for building such structures, termed linear-wavelet networks, is described. For illustration, the proposed procedure is employed in the framework of dynamic system identification. In an example involving a simulated fermentation process, it is shown that a linear-wavelet network yields a smaller approximation error when compared with a wavelet network with the same number of regressors. The proposed technique is also applied to the identification of a pressure plant from experimental data. In this case, the results show that the introduction of wavelets considerably improves the prediction ability of a linear model. Standard errors on the estimated model coefficients are also calculated to assess the numerical conditioning of the identification process.

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.

Relevance of sampling schemes in light of Ruelle's linear response theory

We reconsider the theory of the linear response of non-equilibrium steady states to perturbations. We �rst show that by using a general functional decomposition for space-time dependent forcings, we can de�ne elementary susceptibilities that allow to construct the response of the system to general perturbations. Starting from the de�nition of SRB measure, we then study the consequence of taking di�erent sampling schemes for analysing the response of the system. We show that only a speci�c choice of the time horizon for evaluating the response of the system to a general time-dependent perturbation allows to obtain the formula �rst presented by Ruelle. We also discuss the special case of periodic perturbations, showing that when they are taken into consideration the sampling can be �ne-tuned to make the de�nition of the correct time horizon immaterial. Finally, we discuss the implications of our results in terms of strategies for analyzing the outputs of numerical experiments by providing a critical review of a formula proposed by Reick.

Composite control of non-linear singularly perturbed systems: a geometric approach

Using a geometric approach, a composite control—the sum of a slow control and a fast control—is derived for a general class of non-linear singularly perturbed systems. A new and simpler method of composite control design is proposed whereby the fast control is completely designed at the outset. The slow control is then free to be chosen such that the slow integral manifold of the original system approximates a desired design manifold to within any specified order of ε accuracy.

Composite control of non-linear singularly perturbed systems: a geometric approach

Using a geometric approach, a composite control—the sum of a slow control and a fast control—is derived for a general class of non-linear singularly perturbed systems. A new and simpler method of composite control design is proposed whereby the fast control is completely designed at the outset. The slow control is then free to be chosen such that the slow integral manifold of the original system approximates a desired design manifold to within any specified order of ε accuracy.

Modal coupling in linear control systems using robust eigenstructure assignment

Eigenvalue assignment methods are used widely in the design of control and state-estimation systems. The corresponding eigenvectors can be selected to ensure robustness. For specific applications, eigenstructure assignment can also be applied to achieve more general performance criteria. In this paper a new output feedback design approach using robust eigenstructure assignment to achieve prescribed mode input and output coupling is described. A minimisation technique is developed to improve both the mode coupling and the robustness of the system, whilst allowing the precision of the eigenvalue placement to be relaxed. An application to the design of an automatic flight control system is demonstrated.

Robust pole assignment in linear state feedback

Numerical methods are described for determining robust, or well-conditioned, solutions to the problem of pole assignment by state feedback. The solutions obtained are such that the sensitivity of the assigned poles to perturbations in the system and gain matrices is minimized. It is shown that for these solutions, upper bounds on the norm of the feedback matrix and on the transient response are also minimized and a lower bound on the stability margin is maximized. A measure is derived which indicates the optimal conditioning that may be expected for a particular system with a given set of closed-loop poles, and hence the suitability of the given poles for assignment.

Duality, observability, and controllability for linear time-varying descriptor systems

A characterization of observability for linear time-varying descriptor systemsE(t)x(t)+F(t)x(t)=B(t)u(t), y(t)=C(t)x(t) was recently developed. NeitherE norC were required to have constant rank. This paper defines a dual system, and a type of controllability so that observability of the original system is equivalent to controllability of the dual system. Criteria for observability and controllability are given in terms of arrays of derivatives of the original coefficients. In addition, the duality results of this paper lead to an improvement on a previous fundamental structure result for solvable systems of the formE(t)x(t)+F(t)x(t)=f(tt).

On the stability radius of a generalized state-space system

The concept of “distance to instability” of a system matrix is generalized to system pencils which arise in descriptor (semistate) systems. Difficulties arise in the case of singular systems, because the pencil can be made unstable by an infinitesimal perturbation. It is necessary to measure the distance subject to restricted, or structured, perturbations. In this paper a suitable measure for the stability radius of a generalized state-space system is defined, and a computable expression for the distance to instability is derived for regular pencils of index less than or equal to one. For systems which are strongly controllable it is shown that this measure is related to the sensitivity of the poles of the system over all feedback matrices assigning the poles.

An Earth Observation Land Data Assimilation System (EO-LDAS)

Current methods for estimating vegetation parameters are generally sub-optimal in the way they exploit information and do not generally consider uncertainties. We look forward to a future where operational dataassimilation schemes improve estimates by tracking land surface processes and exploiting multiple types of observations. Dataassimilation schemes seek to combine observations and models in a statistically optimal way taking into account uncertainty in both, but have not yet been much exploited in this area. The EO-LDAS scheme and prototype, developed under ESA funding, is designed to exploit the anticipated wealth of data that will be available under GMES missions, such as the Sentinel family of satellites, to provide improved mapping of land surface biophysical parameters. This paper describes the EO-LDAS implementation, and explores some of its core functionality. EO-LDAS is a weak constraint variational dataassimilationsystem. The prototype provides a mechanism for constraint based on a prior estimate of the state vector, a linear dynamic model, and EarthObservationdata (top-of-canopy reflectance here). The observation operator is a non-linear optical radiative transfer model for a vegetation canopy with a soil lower boundary, operating over the range 400 to 2500 nm. Adjoint codes for all model and operator components are provided in the prototype by automatic differentiation of the computer codes. In this paper, EO-LDAS is applied to the problem of daily estimation of six of the parameters controlling the radiative transfer operator over the course of a year (> 2000 state vector elements). Zero and first order process model constraints are implemented and explored as the dynamic model. The assimilation estimates all state vector elements simultaneously. This is performed in the context of a typical Sentinel-2 MSI operating scenario, using synthetic MSI observations simulated with the observation operator, with uncertainties typical of those achieved by optical sensors supposed for the data. The experiments consider a baseline state vector estimation case where dynamic constraints are applied, and assess the impact of dynamic constraints on the a posteriori uncertainties. The results demonstrate that reductions in uncertainty by a factor of up to two might be obtained by applying the sorts of dynamic constraints used here. The hyperparameter (dynamic model uncertainty) required to control the assimilation are estimated by a cross-validation exercise. The result of the assimilation is seen to be robust to missing observations with quite large data gaps.

Design of delay-tolerant linear dispersion codes

In cooperative communication networks, owing to the nodes' arbitrary geographical locations and individual oscillators, the system is fundamentally asynchronous. This will damage some of the key properties of the space-time codes and can lead to substantial performance degradation. In this paper, we study the design of linear dispersion codes (LDCs) for such asynchronous cooperative communication networks. Firstly, the concept of conventional LDCs is extended to the delay-tolerant version and new design criteria are discussed. Then we propose a new design method to yield delay-tolerant LDCs that reach the optimal Jensen's upper bound on ergodic capacity as well as minimum average pairwise error probability. The proposed design employs stochastic gradient algorithm to approach a local optimum. Moreover, it is improved by using simulated annealing type optimization to increase the likelihood of the global optimum. The proposed method allows for flexible number of nodes, receive antennas, modulated symbols and flexible length of codewords. Simulation results confirm the performance of the newly-proposed delay-tolerant LDCs.