Error estimation and adaptivity for incompressible, non–linear (hyper–)elasticity

A Galerkin finite element method is developed for non–linear, incompressible (hyper) elasticity, and a posteriori error estimates are derived for both linear functionals of the solution and linear functionals of the stress on a boundary where Dirichlet boundary conditions are applied. A second, higher order method for calculating a linear functional of the stress on a Dirichlet boundary is also presented together with an a posteriori error estimator for this approach. An implementation for a 2D model problem with known solution demonstrates the accuracy of the error estimators. Finally the a posteriori error estimate is shown to provide a basis for effective mesh adaptivity

Bayesian learning of noisy Markov decision processes

We consider the inverse reinforcement learning problem, that is, the problem of learning from, and then predicting or mimicking a controller based on state/action data. We propose a statistical model for such data, derived from the structure of a Markov decision process. Adopting a Bayesian approach to inference, we show how latent variables of the model can be estimated, and how predictions about actions can be made, in a unified framework. A new Markov chain Monte Carlo (MCMC) sampler is devised for simulation from the posterior distribution. This step includes a parameter expansion step, which is shown to be essential for good convergence properties of the MCMC sampler. As an illustration, the method is applied to learning a human controller

The rigidity of periodic body-bar frameworks on the three-dimensional fixed torus

We present necessary and sufficient conditions for the generic rigidity of body-bar frameworks on the three-dimensional fixed torus. These frameworks correspond to infinite periodic body-bar frameworks in $\mathbb{R}^3$ with a fixed periodic lattice.Comment: 31 pages, 12 figure

Knowledge and the artefact

This paper discusses ways that knowledge may be found in or through artefacts. One purpose is to suggest situations where artefacts might be central to a narrative, rather than secondary to a text. A second purpose is to suggest ways that design and production of artefacts might be instrumental in eliciting knowledge. Four general situations are proposed: (1) Simple Forms - an artefact demonstrates or describes a principle or technique. (2) Communication of Process - artefacts arising from a process make the process explicit. (3) Artefacts Within the Research - artefacts are instrumental in advancing the research by communicating ideas or information. (4) Knowledge Elicited by Artefacts - artefacts provide a stimulus or context which enables information to be uncovered. .</p

A study into the validation of ATP testing devices for integrated cleanliness monitoring within healthcare settings

There is a problem in hospital cleaning. There is currently no scientific monitoring method that provides timely and reliable assurance that harmful bacteria have been removed by the cleaning processes. This PhD investigates the validation of commercially available testing devices intended for the rapid detection of adenosine triphosphate (ATP), which may provide a quantitative surrogate estimate of surface cleanliness based on ATP measurements. The findings indicate that ATP testing devices, despite problems with scaling and imprecision, provide immediacy in readings which enables the incorporation of ATP testing into an improved and integrated cleanliness monitoring process for applications within healthcare settings

Cardiac Electromechanics: The effect of contraction model on the mathematical problem and accuracy of the numerical scheme

Models of cardiac electromechanics usually contain a contraction model determining the active tension induced at the cellular level, and the equations of nonlinear elasticity to determine tissue deformation in response to this active tension. All contraction models are dependent on cardiac electro-physiology, but can also be dependent on\ud the stretch and stretch-rate in the fibre direction. This fundamentally affects the mathematical problem being solved, through classification of the governing PDEs, which affects numerical schemes that can be used to solve the governing equations. We categorise contraction models into three types, and for each consider questions such as classification and the most appropriate choice from two numerical methods (the explicit and implicit schemes). In terms of mathematical classification, we consider the question of strong ellipticity of the total strain energy (important for precluding ‘unnatural’ material behaviour) for stretch-rate-independent contraction models; whereas for stretch-rate-dependent contraction models we introduce a corresponding third-order problem and explain how certain choices of boundary condition could lead to constraints on allowable initial condition. In terms of suitable numerical methods, we show that an explicit approach (where the contraction model is integrated in the timestep prior to the bulk deformation being computed) is: (i) appropriate for stretch-independent contraction models; (ii) only conditionally-stable, with the stability criterion independent of timestep, for contractions models which just depend on stretch (but not stretch-rate), and (iii) inappropriate for stretch-rate-dependent models

Error bounds on block Gauss Seidel solutions of coupled\ud multiphysics problems

Mathematical models in many fields often consist of coupled sub–models, each of which describe a different physical process. For many applications, the quantity of interest from these models may be written as a linear functional of the solution to the governing equations. Mature numerical solution techniques for the individual sub–models often exist. Rather than derive a numerical solution technique for the full coupled model, it is therefore natural to investigate whether these techniques may be used by coupling in a block Gauss–Seidel fashion. In this study, we derive two a posteriori bounds for such linear functionals. These bounds may be used on each Gauss–Seidel iteration to estimate the error in the linear functional computed using the single physics solvers, without actually solving the full, coupled problem. We demonstrate the use of the bound first by using a model problem from linear algebra, and then a linear ordinary differential equation example. We then investigate the effectiveness of the bound using a non–linear coupled fluid–temperature problem. One of the bounds derived is very sharp for most linear functionals considered, allowing us to predict very accurately when to terminate our block Gauss–Seidel iteration.\ud \ud Copyright c 2000 John Wiley & Sons, Ltd

Origins of NASA names

Names are selected for NASA spaceflight projects and programs from various sources. Some have their foundations in mythology and astrology or legend and folklore. Some have historic connotations; others are based on a description of their mission, often resulting in an acronym. Included are names of launch vehicles, spacecraft, manned spaceflight programs, sounding rockets, and NASA field installations. This study is limited to names of approved projects through 1974; it does not include names of numerous projects which have been or are being studied or projects that were canceled or postponed before reaching actual flight

Reader response research in stylistics

This article introduces the special issue. In it, we argue that research into reader response should be recognised as a vital aspect of contemporary stylistics, and we establish our focus on work which explicitly investigates such responses through the collection and analysis of extra-textual datasets. Reader response research in stylistics is characterised by a commitment to rigorous and evidence-based approaches to the study of readers’ interactions with and around texts, and the application of such datasets in the service of stylistic concerns: to contribute to stylistic textual analysis and/or wider discussion of stylistic theory and methods. We trace the influence of reader response criticism and reception theory on stylistics and discuss the productive dialogues which exist between stylistics and the related fields of the empirical study of literature and naturalistic study of reading. After offering an overview of methods available to reader response researchers and a contextualising survey of existing work, we argue that both experimental and naturalistic methods should be regarded as ‘empirical’, and that stylistics is uniquely positioned to embrace diverse approaches to readers and reading. We summarise contributions to the special issue and the valuable insights they offer into the historical context of reader response research and the way readers perceive and evaluate texts (either poetry or narrative prose). Stylistic reader response research enables both the testing and development of stylistic methods, in accordance with the progressive spirit of the discipline, and also the establishment of new and renewed connections between stylistic research and work in other fields