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An h‐adaptive finite element code for solving coupled Navier‐Stokes and energy equations is used to solve the thermally driven cavity problem. The buoyancy forces are represented using the Boussinesq approximation. The problem is characterised by very thin boundary layers at high values of Rayleigh number (>10⁶). However, steady state solutions are achievable with adequate discretisation. This is where the auto‐adaptive finite element method provides a powerful means of achieving optimal solutions without having to pre‐define a mesh, which may be either inadequate or too expensive. Steady state and transient results are given for six different Rayleigh numbers in the range 10³ to 10⁸ for a Prandtl number of 0.71. The use of h‐adaptivity, based on a posteriori error estimation, is found to ensure a very accurate problem solution at a reasonable computational cost.

An h‐adaptive finite element code for solving coupled Navier‐Stokes and energy equations is used to solve the thermally driven cavity problem for Rayleigh numbers at which no steady state exists (greater than 1.9 × 10⁸). This problem is characterised by sharp thermal and flow boundary layers and highly advection dominated transport, which normally requires special algorithms, such as streamline upwinding, to achieve stable and smooth solutions. It will be shown that h‐adaptivity provides a suitable solution to both of these problems (sharp gradients and advection dominated transport). Adaptivity is also very effective in resolving the flow physics, characterised by unsteady internal waves, are calculated for three Rayleigh numbers; 2 × 10⁸, 3 × 10⁸ and 4 × 10⁸ using a Prandtl number of 0.71 and results are compared with other published results.

Knight's Industrial Law Reports goes into a new style and format as Managerial Law This issue of KILR is restyled Managerial Law and it now appears on a continuous updating basis rather than as a monthly routine affair.

Locates the onset of oscillatory instability in the fluid flow inside a differentially heated cavity with aspect ratio 2 by computing a steady‐state and analyzing the stability of the system via eigenvalue approximation. Discusses the choice of parameters for the Cayley transformation so that the calculation of selected eigenvalues of the transformed system will reliably answer the question of stability. Also presents an argument that due to the symmetry of the problem, the first two unstable modes will have eigenvalues that are nearly identical, and the numerical experiments confirm this. Finally, locates a co‐dimension 2 bifurcation signifying where there is a switch in the mode of initial instability. The results were obtained using a parallel finite element CFD code (MPSalsa) along with an Arnoldi‐based eigensolver (ARPACK), a preconditioned Krylov method code for the necessary linear solves (Aztec), and a stability analysis library (LOCA).

This paper aims to give further insights into Alzheimer's disease (AD), a devastating neurodegenerative disorder which accounts for 60‐80 per cent of late‐onset dementia. AD is genetically complex where three genes are known to cause the early‐onset familial form of disease and ten genes have been identified to contribute to the risk of developing late‐onset sporadic AD.

The paper discusses the recently identified AD susceptibility loci and outlines the various hypotheses of how these loci and the pathways in which they function may elucidate the aetiology and pathogenesis of sporadic late‐onset AD.

The loci identified to increase susceptibility to sporadic AD are not random, but instead point to defects in specific biological processes and pathways that contribute to the development of the disease. These include impairments in: innate/adaptive immunity, specifically inflammation and the complement system; endocytosis/intracellualar trafficking, which includes the internalisation of material from the cell surface and the mechanisms by which molecules are transported; and lipid processing. High levels of lipids such as cholesterol have been associated with development of AD in later life.

The paper highlights that determining the function of the known susceptibility loci, and establishing how they increase risk for AD will aid in the development of new treatments.