Developments in steady and unsteady aerodynamics for use in aeroelastic analysis and design

A review is given of seven research projects which are aimed at improving the generality, accuracy, and computational efficiency of steady and unsteady aerodynamic theory for use in aeroelastic analysis and design. These projects indicate three major thrusts of current research efforts: (1) more realistic representation of steady and unsteady subsonic and supersonic loads on aircraft configurations of general shape with emphasis on structural-design applications, (2) unsteady aerodynamics for application in active-controls analyses, and (3) unsteady aerodynamics for the frequently critical transonic speed range. The review of each project includes theoretical background, description of capabilities, results of application, current status, and plans for further development and use

Going from microscopic to macroscopic on nonuniform growing domains

Throughout development, chemical cues are employed to guide the functional specification of underlying tissues while the spatiotemporal distributions of such chemicals can be influenced by the growth of the tissue itself. These chemicals, termed morphogens, are often modeled using partial differential equations (PDEs). The connection between discrete stochastic and deterministic continuum models of particle migration on growing domains was elucidated by Baker, Yates, and Erban [ Bull. Math. Biol. 72 719 (2010)] in which the migration of individual particles was modeled as an on-lattice position-jump process. We build on this work by incorporating a more physically reasonable description of domain growth. Instead of allowing underlying lattice elements to instantaneously double in size and divide, we allow incremental element growth and splitting upon reaching a predefined threshold size. Such a description of domain growth necessitates a nonuniform partition of the domain. We first demonstrate that an individual-based stochastic model for particle diffusion on such a nonuniform domain partition is equivalent to a PDE model of the same phenomenon on a nongrowing domain, providing the transition rates (which we derive) are chosen correctly and we partition the domain in the correct manner. We extend this analysis to the case where the domain is allowed to change in size, altering the transition rates as necessary. Through application of the master equation formalism we derive a PDE for particle density on this growing domain and corroborate our findings with numerical simulations

Prediction of transonic flutter for a supercritical wing by modified strip analysis and comparison with experiment

Use of a supercritical airfoil can adversely affect wing flutter speeds in the transonic range. As adequate theories for three dimensional unsteady transonic flow are not yet available, the modified strip analysis was used to predict the transonic flutter boundary for the supercritical wing. The steady state spanwise distributions of section lift curve slope and aerodynamic center, required as input for the flutter calculations, were obtained from pressure distributions. The calculated flutter boundary is in agreement with experiment in the subsonic range. In the transonic range, a transonic bucket is calculated which closely resembles the experimental one with regard to both shape and depth, but it occurs at about 0.04 Mach number lower than the experimental one

Development of a carbon fibre composite active mirror: Design and testing

Carbon fibre composite technology for lightweight mirrors is gaining increasing interest in the space- and ground-based astronomical communities for its low weight, ease of manufacturing, excellent thermal qualities and robustness. We present here first results of a project to design and produce a 27 cm diameter deformable carbon fibre composite mirror. The aim was to produce a high surface form accuracy as well as low surface roughness. As part of this programme, a passive mirror was developed to investigate stability and coating issues. Results from the manufacturing and polishing process are reported here. We also present results of a mechanical and thermal finite element analysis, as well as early experimental findings of the deformable mirror. Possible applications and future work are discussed.Comment: Accepted by Optical Engineering. Figures 1-7 on http://www.star.ucl.ac.uk/~sk/OEpaper_files

Isotropic model for cluster growth on a regular lattice

There exists a plethora of mathematical models for cluster growth and/or aggregation on regular lattices. Almost all suffer from inherent anisotropy caused by the regular lattice upon which they are grown. We analyze the little-known model for stochastic cluster growth on a regular lattice first introduced by Ferreira Jr. and Alves [J. Stat. Mech. Theo. & Exp. (2006) P11007], which produces circular clusters with no discernible anisotropy. We demonstrate that even in the noise-reduced limit the clusters remain circular. We adapt the model by introducing a specific rearrangement algorithm so that, rather than adding elements to the cluster from the outside (corresponding to apical growth), our model uses mitosis-like cell splitting events to increase the cluster size. We analyze the surface scaling properties of our model and compare it to the behavior of more traditional models. In “1+1” dimensions we discover and explore a new, nonmonotonic surface thickness scaling relationship which differs significantly from the Family-Vicsek scaling relationship. This suggests that, for models whose clusters do not grow through particle additions which are solely dependent on surface considerations, the traditional classification into “universality classes” may not be appropriate

The importance of the Voronoi domain partition for position-jump reaction-diffusion processes on non-uniform rectilinear lattices

Position-jump processes are used for the mathematical modeling of spatially extended chemical and biological systems with increasing frequency. A large subset of the literature concerning such processes is concerned with modeling the effect of stochasticity on reaction-diffusion systems. Traditionally, computational domains have been divided into regular voxels. Molecules are assumed well mixed within each of these voxels and are allowed to react with other molecules within the same voxel or to jump to neighboring voxels with predefined transition rates. For a variety of reasons implementing position-jump processes on irregular grids is becoming increasingly important. However, it is not immediately clear what form an appropriate irregular partition of the domain should take if it is to allow the derivation of mean molecular concentrations that agree with a given partial differential equation for molecular concentrations. It has been demonstrated, in one dimension, that the Voronoi domain partition is the appropriate method with which to divide the computational domain. In this Brief Report, we investigate theoretically the propriety of the Voronoi domain partition as an appropriate method to partition domains for position-jump models in higher dimensions. We also provide simulations of diffusion processes in two dimensions in order to corroborate our results

Modelling cell migration and adhesion during development

Cell–cell adhesion is essential for biological development: cells migrate to their target sites, where cell–cell adhesion enables them to aggregate and form tissues. Here, we extend analysis of the model of cell migration proposed by Anguige and Schmeiser (J. Math. Biol. 58(3):395–427, 2009) that incorporates both cell–cell adhesion and volume filling. The stochastic space-jump model is compared to two deterministic counterparts (a system of stochastic mean equations and a non-linear partial differential equation), and it is shown that the results of the deterministic systems are, in general, qualitatively similar to the mean behaviour of multiple stochastic simulations. However, individual stochastic simulations can give rise to behaviour that varies significantly from that of the mean. In particular, individual simulations might admit cell clustering when the mean behaviour does not. We also investigate the potential of this model to display behaviour predicted by the differential adhesion hypothesis by incorporating a second cell species, and present a novel approach for implementing models of cell migration on a growing domain

Response to: "Renal biopsies should be performed whenever treatment strategies depend on renal involvement"

We thank Chemouny et al for their letter and concur with their conclusions. As we state (1): “A positive biopsy for AAV is helpful when considering an initial diagnosis or recurrent disease.” In our view, renal biopsy is important to establish diagnosis and may also provide an indication of prognostic trajectory and although existing classification systems need further validation, changes like glomerular sclerosis have obvious adverse prognostic value for patients with AAV (2-4). The Delphi process, for the scope of the current recommendations, identified the role of biopsy at both diagnosis and follow-up as an important item for update. Histopathological evidence of vasculitis, such as pauci-immune glomerulonephritis or necrotising vasculitis in any organ, remains the gold standard for diagnostic purposes. The likely diagnostic yield varies and is dependent on the organ targeted and in patients with GPA with renal involvement can be as high as 91.5% from renal biopsy (5). As Chemouny and colleagues have demonstrated, a renal biopsy was definitive in determining their management decisions. However during follow-up when relapses occur, it may be prudent to consider judicious use of further kidney biopsy during suspected renal relapse since the cause for acute kidney injury may be due to another cause other than AAV (6). Kind regards, M Yates, C Mukhtyar and DR Jayne on behalf of co-authors

Research and applications: Artificial intelligence

The program is reported for developing techniques in artificial intelligence and their application to the control of mobile automatons for carrying out tasks autonomously. Visual scene analysis, short-term problem solving, and long-term problem solving are discussed along with the PDP-15 simulator, LISP-FORTRAN-MACRO interface, resolution strategies, and cost effectiveness