Adaptivity and a posteriori error control for bifurcation problems I: the Bratu problem

This article is concerned with the numerical detection of bifurcation points of nonlinear partial differential equations as some parameter of interest is varied. In particular, we study in detail the numerical approximation of the Bratu problem, based on exploiting the symmetric version of the interior penalty discontinuous Galerkin finite element method. A framework for a posteriori control of the discretization error in the computed critical parameter value is developed based upon the application of the dual weighted residual (DWR) approach. Numerical experiments are presented to highlight the practical performance of the proposed a posteriori error estimator.

Adaptivity and a posteriori error control for bifurcation problems II: Incompressible fluid flow in open systems with Z_2 symmetry

In this article we consider the a posteriori error estimation and adaptive mesh refinement of discontinuous Galerkin finite element approximations of the bifurcation problem associated with the steady incompressible Navier-Stokes equations. Particular attention is given to the reliable error estimation of the critical Reynolds number at which a steady pitchfork or Hopf bifurcation occurs when the underlying physical system possesses reflectional or Z_2 symmetry. Here, computable a posteriori error bounds are derived based on employing the generalization of the standard Dual-Weighted-Residual approach, originally developed for the estimation of target functionals of the solution, to bifurcation problems. Numerical experiments highlighting the practical performance of the proposed a posteriori error indicator on adaptively refined computational meshes are presented.

Beyond the human genome: microbes, metaphors and what it means to be human in an interconnected post-genomic world

Four years after the completion of the Human Genome Project, the US National Institutes for Health launched the Human Microbiome Project on 19 December 2007. Using metaphor analysis, this article investigates reporting in English-language newspapers on advances in microbiomics from 2003 onwards, when the word “microbiome” was first used. This research was said to open up a “new frontier” and was conceived as a “second human genome project”, this time focusing on the genomes of microbes that inhabit and populate humans rather than focusing on the human genome itself. The language used by scientists and by the journalists who reported on their research employed a type of metaphorical framing that was very different from the hyperbole surrounding the decipherment of the “book of life”. Whereas during the HGP genomic successes had been mainly framed as being based on a unidirectional process of reading off information from a passive genetic or genomic entity, the language employed to discuss advances in microbiomics frames genes, genomes and life in much more active and dynamic ways.