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.

Multiple PID mapping using neural networks in a MIMO steam generator system

A neural network was used to map three PID operating regions for a two-input two-output steam generator system. The network was used in stand alone feedforward operation to control the whole operating range of the process, after being trained from the PID controllers corresponding to each control region. The network inputs are the plant error signals, their integral, their derivative and a 4-error delay train.

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.

Mapping therapy for sentence production impairments in nonfluent aphasia

This study investigated a new treatment in which sentence production abilities were trained in a small group of individuals and nonfluent aphasia. It was based upon a mapping therapy approach which holds that sentence production and comprehension impairments are due to difficulties in mapping between the meaning form (thematic roles) and the syntactic form of sentences. We trained production of both canonical and noncanonical reversible sentences.Three patients received treatment and two served as control participants. Patients who received treatment demonstrated acquisition of all trained sentence structures. They also demonstrated across-task generalisation of treated and some untreated sentence structures on two tasks of constrained sentence production, and showed some improvements on a narrative task. One control participant improved on some of these measures and the other did not. There was no noted improvement in sentence comprehension abilities following treatment. Results are discussed with reference to the heterogeneity of underlying impairments in sentence production impairments in nonfluent patients, and the possible mechanisms by which improvement in sentence production might have been achieved in treatment.

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

‘Pre-plan mapping’, networks, capital resources and community strategies in England

In this working paper we discuss current attempts to engage communities in planning policy formulation in the UK. In particular we focus on the preparation of Community Strategies (CS) in England to inform local public policy and the wider proposals recently published by the UK government to move towards enhanced community engagement in planning (DTLR, 2001). We discuss how such strategies could be operationalised with a conceptual framework developed following ideas derived from ANT (cf. Murdoch, 1997, 1998; Selman, 2000; Parker & Wragg, 1999; Callon, 1986, 1998) and the ‘capitals’ literature (Lin, 2002; Fine, 2001; Selman, 2000; Putnam, 1993). We see this as an expression of neo-pragmatic planning theory, (Hoch, 1996; Stein & Harper, 2000) to develop a form of ‘pre-plan mapping’.