2,022 research outputs found
Error estimation and adaptivity for incompressible, nonâlinear (hyperâ)elasticity
A Galerkin finite element method is developed for nonâlinear, 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
A Comparison of Numerical Methods used for\ud Finite Element Modelling of Soft Tissue\ud Deformation
Soft tissue deformation is often modelled using incompressible nonlinear elasticity, with solutions computed using the finite element method. There are a range of options available when using the finite element method, in particular, the polynomial degree of the basis functions used for interpolating position and pressure, and the type of element making up the mesh. We investigate the effect of these choices on the accuracy of the computed solution, using a selection of model problems motivated by typical deformations seen in soft tissue modelling. We set up model problems with discontinuous material properties (as is the case for the breast), steeply changing gradients in the body force (as found in contracting cardiac tissue), and discontinuous first derivatives in the solution at the boundary, caused by a discontinuous applied force (as in the breast during mammography). We find that the choice of pressure basis functions are vital in the presence of a material interface, higher-order schemes do not perform as well as may be expected when there are sharp gradients, and in general that it is important to take the expected regularity of the solution into account when choosing a numerical scheme
Party membership and campaign activity in Britain: The impact of electoral performance
The article examines the impact of electoral results on party membership and activity. Previous studies have focused on the long-term effects of electoral success or failure, suggesting that they may produce a spiral of demobilization or mobilization. The article shows that the dramatic change of electoral fortunes experienced by British parties at the 1997 general election broke this spiral, with the outcome leading to significant changes in the health and activity of local parties. It is concluded that dramatic election results can have significant implications for party organization
Why Did the Polls Get It Wrong in the 2015 General Election? Evaluating the Inquiry into Pre-Election Polls
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 âunnaturalâ 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 subâmodels, 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 subâmodels 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 GaussâSeidel fashion. In this study, we derive two a posteriori bounds for such linear functionals. These bounds may be used on each GaussâSeidel 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 nonâlinear coupled fluidâtemperature 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 GaussâSeidel iteration.\ud
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Copyright c 2000 John Wiley & Sons, Ltd
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 readersâ 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
âempiricalâ, 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
A note on heat and mass transfer from a sphere in Stokes\ud flow at low PĂ©clet number
We consider the low PĂ©clet number, Pe âȘ 1, asymptotic solution for steady-state heat and mass transfer from a sphere immersed in Stokes flow with a Robin boundary condition on its surface, representing Newton cooling or a first-order chemical reaction. The application of van Dykeâs rule up to terms of O(Pe3) shows that the O(Pe3 log Pe) terms in the expression for the average Nusselt/Sherwood number are double those previously derived in the literature. Inclusion of the O(Pe3) terms is shown to increase significantly the range of validity of the expansion
Fluctuations, stability and instability of a distributed particle filter with local exchange
We study a distributed particle filter proposed by Boli\'c et al.~(2005).
This algorithm involves groups of particles, with interaction between
groups occurring through a "local exchange" mechanism. We establish a central
limit theorem in the regime where is fixed and . A formula we
obtain for the asymptotic variance can be interpreted in terms of colliding
Markov chains, enabling analytic and numerical evaluations of how the
asymptotic variance behaves over time, with comparison to a benchmark algorithm
consisting of independent particle filters. We prove that subject to
regularity conditions, when is fixed both algorithms converge
time-uniformly at rate . Through use of our asymptotic variance
formula we give counter-examples satisfying the same regularity conditions to
show that when is fixed neither algorithm, in general, converges
time-uniformly at rate .Comment: 49 pages, 7 figure
Perfect sampling for nonhomogeneous Markov chains and hidden Markov models
We obtain a perfect sampling characterization of weak ergodicity for backward
products of finite stochastic matrices, and equivalently, simultaneous tail
triviality of the corresponding nonhomogeneous Markov chains. Applying these
ideas to hidden Markov models, we show how to sample exactly from the
finite-dimensional conditional distributions of the signal process given
infinitely many observations, using an algorithm which requires only an almost
surely finite number of observations to actually be accessed. A notion of
"successful" coupling is introduced and its occurrence is characterized in
terms of conditional ergodicity properties of the hidden Markov model and
related to the stability of nonlinear filters
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