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.

High-order hp-adaptive discontinuous Galerkin finite element methods for compressible fluid flows

This article is concerned with the construction of general isotropic and anisotropic adaptive strategies, as well as hp-mesh refinement techniques, in combination with dual-weighted-residual a posteriori error indicators for the discontinuous Galerkin finite element discretization of compressible fluid flow problems.

Using intelligent agents to understand organisational behaviour

This paper introduces two ongoing research projects which seek to apply computer modelling techniques in order to simulate human behaviour within organisations. Previous research in other disciplines has suggested that complex social behaviours are governed by relatively simple rules which, when identified, can be used to accurately model such processes using computer technology. The broad objective of our research is to develop a similar capability within organisational psychology.

Chaotic mixing of a competitive-consecutive reaction

The evolution of a competitive-consecutive chemical reaction is computed numerically in a two-dimensional chaotic fluid flow with initially segregated reactants. Results from numerical simulations are used to evaluate a variety of reduced models commonly adopted to model the full advection-reaction-diffusion problem. Particular emphasis is placed upon fast reactions, where the yield varies most significantly with Peclet number (the ratio of diffusive to advective time scales). When effects of the fluid mechanical mixing are strongest, we find that the yield of the reaction is underestimated by a one-dimensional lamellar model that ignores the effects of fluid mixing, but overestimated by two other lamellar models that include fluid mixing.

Ontogeny and nutritional programming of mitochondrial proteins in the ovine kidney, liver and lung

This study investigated the developmental and nutritional programming of two important mitochondrial proteins, namely voltage dependent anion channel (VDAC) and cytochrome c in the sheep kidney, liver and lung. The effect of maternal nutrient restriction between early to mid gestation (i.e. 28 to 80 days gestation, the period of maximal placental growth) on the abundance of these proteins was also examined in fetal and juvenile offspring. Fetuses were sampled at 80 and 140 days gestation (term ~147 days), and postnatal animals at 1 and 30 days and 6 months of age. The abundance of VDAC peaked at 140 days gestation in the lung, compared with 1 day after birth in the kidney and liver, whereas cytochrome c abundance was greatest at 140 days gestation in the liver, 1 day after birth in the kidney and 6 months of age in lungs. This differential ontogeny in mitochondrial protein abundance between tissues was accompanied with very different tissue specific responses to changes in maternal food intake. In the liver, maternal nutrient restriction only increased mitochondrial protein abundance at 80 days gestation, compared with no effect in the kidney. In contrast, in the lung mitochondrial protein abundance was raised near to term, whereas VDAC abundance was decreased by 6 months of age. These findings demonstrate the tissue specific nature of mitochondrial protein development that reflects differences in functional adaptation after birth. The divergence in mitochondrial response between tissues to maternal nutrient restriction early in pregnancy further reflects these differential ontogeny’s.

A two-fluid model for tissue growth within a dynamic flow environment

We study the growth of a tissue construct in a perfusion bioreactor, focussing on its response to the mechanical environment. The bioreactor system is modelled as a two-dimensional channel containing a tissue construct through which a flow of culture medium is driven. We employ a multiphase formulation of the type presented by G. Lemon, J. King, H. Byrne, O. Jensen and K. Shakesheff in their study (Multiphase modelling of tissue growth using the theory of mixtures. J. Math. Biol. 52(2), 2006, 571–594) restricted to two interacting fluid phases, representing a cell population (and attendant extracellular matrix) and a culture medium, and employ the simplifying limit of large interphase viscous drag after S. Franks in her study (Mathematical Modelling of Tumour Growth and Stability. Ph.D. Thesis, University of Nottingham, UK, 2002) and S. Franks and J. King in their study Interactions between a uniformly proliferating tumour and its surrounding: Uniform material properties. Math. Med. Biol. 20, 2003, 47–89). The novel aspects of this study are: (i) the investigation of the effect of an imposed flow on the growth of the tissue construct, and (ii) the inclusion of a chanotransduction mechanism regulating the response of the cells to the local mechanical environment. Specifically, we consider the response of the cells to their local density and the culture medium pressure. As such, this study forms the first step towards a general multiphase formulation that incorporates the effect of mechanotransduction on the growth and morphology of a tissue construct. The model is analysed using analytic and numerical techniques, the results of which illustrate the potential use of the model to predict the dominant regulatory stimuli in a cell population.