Velocity-based moving mesh methods for nonlinear partial differential equations

This article describes a number of velocity-based moving mesh numerical methods formultidimensional nonlinear time-dependent partial differential equations (PDEs). It consists of a short historical review followed by a detailed description of a recently developed multidimensional moving mesh finite element method based on conservation. Finite element algorithms are derived for both mass-conserving and non mass-conserving problems, and results shown for a number of multidimensional nonlinear test problems, including the second order porous medium equation and the fourth order thin film equation as well as a two-phase problem. Further applications and extensions are referenced.

Inverting recurrent neural networks for internal model control of nonlinear systems

In this paper, we show how a set of recently derived theoretical results for recurrent neural networks can be applied to the production of an internal model control system for a nonlinear plant. The results include determination of the relative order of a recurrent neural network and invertibility of such a network. A closed loop controller is produced without the need to retrain the neural network plant model. Stability of the closed-loop controller is also demonstrated.

Internal model control of nonlinear systems through the inversion of recurrent neural networks

Recurrent neural networks can be used for both the identification and control of nonlinear systems. This paper takes a previously derived set of theoretical results about recurrent neural networks and applies them to the task of providing internal model control for a nonlinear plant. Using the theoretical results, we show how an inverse controller can be produced from a neural network model of the plant, without the need to train an additional network to perform the inverse control.

Identification of nonlinear systems with a dynamic recurrent neural network

Two approaches are presented to calculate the weights for a Dynamic Recurrent Neural Network (DRNN) in order to identify the input-output dynamics of a class of nonlinear systems. The number of states of the identified network is constrained to be the same as the number of states of the plant.

Towards a modular robotics standard for AGV design and programming

Across the world there are many bodies currently involved in researching into the design of autonomous guided vehicles (AGVs). One of the greatest problems at present however, is that much of the research work is being conducted in isolated groups, with the resulting AGVs sensor/control/command systems being almost completely nontransferable to other AGV designs. This paper describes a new modular method for robot design which when applied to AGVs overcomes the above problems. The method is explained here with respect to all forms of robotics but the examples have been specifically chosen to reflect typical AGV systems.

Manual response preparation and saccade programming are linked to attention shifts: ERP evidence for covert attentional orienting and spatially specific modulations of visual processing

The premotor theory of attention claims that attentional shifts are triggered during response programming, regardless of which response modality is involved. To investigate this claim, event-related brain potentials (ERPs) were recorded while participants covertly prepared a left or right response, as indicated by a precue presented at the beginning of each trial. Cues signalled a left or right eye movement in the saccade task, and a left or right manual response in the manual task. The cued response had to be executed or withheld following the presentation of a Go/Nogo stimulus. Although there were systematic differences between ERPs triggered during covert manual and saccade preparation, lateralised ERP components sensitive to the direction of a cued response were very similar for both tasks, and also similar to the components previously found during cued shifts of endogenous spatial attention. This is consistent with the claim that the control of attention and of covert response preparation are closely linked. N1 components triggered by task-irrelevant visual probes presented during the covert response preparation interval were enhanced when these probes were presented close to cued response hand in the manual task, and at the saccade target location in the saccade task. This demonstrates that both manual and saccade preparation result in spatially specific modulations of visual processing, in line with the predictions of the premotor theory.

Nonlinear data assimilation in geosciences: an extremely efficient particle filter

Almost all research fields in geosciences use numerical models and observations and combine these using data-assimilation techniques. With ever-increasing resolution and complexity, the numerical models tend to be highly nonlinear and also observations become more complicated and their relation to the models more nonlinear. Standard data-assimilation techniques like (ensemble) Kalman filters and variational methods like 4D-Var rely on linearizations and are likely to fail in one way or another. Nonlinear data-assimilation techniques are available, but are only efficient for small-dimensional problems, hampered by the so-called ‘curse of dimensionality’. Here we present a fully nonlinear particle filter that can be applied to higher dimensional problems by exploiting the freedom of the proposal density inherent in particle filtering. The method is illustrated for the three-dimensional Lorenz model using three particles and the much more complex 40-dimensional Lorenz model using 20 particles. By also applying the method to the 1000-dimensional Lorenz model, again using only 20 particles, we demonstrate the strong scale-invariance of the method, leading to the optimistic conjecture that the method is applicable to realistic geophysical problems. Copyright c 2010 Royal Meteorological Society

Classifying general nonlinear force laws in cell-based models via the continuum limit

though discrete cell-based frameworks are now commonly used to simulate a whole range of biological phenomena, it is typically not obvious how the numerous different types of model are related to one another, nor which one is most appropriate in a given context. Here we demonstrate how individual cell movement on the discrete scale modeled using nonlinear force laws can be described by nonlinear diffusion coefficients on the continuum scale. A general relationship between nonlinear force laws and their respective diffusion coefficients is derived in one spatial dimension and, subsequently, a range of particular examples is considered. For each case excellent agreement is observed between numerical solutions of the discrete and corresponding continuum models. Three case studies are considered in which we demonstrate how the derived nonlinear diffusion coefficients can be used to (a) relate different discrete models of cell behavior; (b) derive discrete, intercell force laws from previously posed diffusion coefficients, and (c) describe aggregative behavior in discrete simulations.

Study of the nonlinear optical properties of a crosslinkable chromophore for use in guest host polymer films

A guest/host material system in which the guest molecule is a functionalized, optically nonlinear, chromophore is described. A verification of the crosslinking process, an assessment of the nonlinear properties of the chromophore, using Solvatochromic methods, and an investigation of the electric field induced molecular orientation using second-harmonic generation are included.

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.