A preliminary systems study of interface equipment for digitally programmed flight simulators

Design study of digitally programmed supersonic transport flight simulato

Contributions to the Third CGIAR System Review from a Latin American Perspective

Input to the discussion of the report of the third CGIAR system review by representatives from Brazil, Colombia, El Salvador, Mexico, Paraguay, Peru, Uruguay, and Venezuela at CGIAR International Centers Week 1998

A complex Ca, Al-rich inclusion from allende meteorite : the study of petrology, chemistry, and isotopic composition

筑波大学University of Tsukuba博士（理学）Doctor of Philosophy in Science1997【要旨】thesi

Combination of WENO and Explicit Runge–Kutta Methods for Wind Transport in the Meso-NH Model

This paper investigates the use of the weighted essentially nonoscillatory (WENO) space discretization methods of third and fifth order for momentum transport in the Meso-NH meteorological model, and their association with explicit Runge–Kutta (ERK) methods, with the specific purpose of finding an optimal combination in terms of wall-clock time to solution. A linear stability analysis using von Neumann theory is first conducted that considers six different ERK time integration methods. A new graphical representation of linear stability is proposed, which allows a first discrimination between the ERK methods. The theoretical analysis is then completed by tests on numerical problems of increasing complexity (linear advection of high wind gradient, orographic waves, density current, large eddy simulation of fog, and windstorm simulation), using a fourth-order-centered scheme as a reference basis. The five-stage third-order and fourth-order ERK combinations appear as the time integration methods of choice for coupling with WENO schemes in terms of stability. An explicit time-splitting method added to the ERK temporal scheme for WENO improves the stability properties slightly more. When the spatial discretizations are compared, WENO schemes present the main advantage of maintaining stable, nonoscillatory transitions with sharp discontinuities, but WENO third order is excessively damping, while WENO fifth order provides better accuracy. Finally, WENO fifth order combined with the ERK method makes the whole physics of the model 3 times faster compared to the classical fourth-order centered scheme associated with the leapfrog temporal scheme

Rayleigh-Taylor Instability in Elastoplastic Solids: A Local Catastrophic Process

International audienceWe show that the Rayleigh-Taylor instability in elastoplastic solids takes the form of local perturbations penetrating the material independently of the interface size, in contrast with the theory for simple elastic materials. Then, even just beyond the stable domain, the instability abruptly develops as bursts rapidly moving through the other medium. We show that this is due to the resistance to penetration of a finger which is minimal for a specific finger size and drops to a much lower value beyond a small depth (a few millimeters). The Rayleigh-Taylor instability (RTI) is a well-known instability which occurs when a denser fluid rests on top of a lighter one [1]. As it develops, the two fluids penetrate one another, in the form of fingers. Instability is driven by the density difference and the acceleration to which the fluids are submitted, while surface tension provides a stabilizing effect. In contrast, RTI in solids is much less studied and understood, even though it relates to many application fields and can cause irreversible damage to structures. Examples include metal plates submitted to strong pressure or acceleration in high-energy density physics experiments [2], magnetic implosion of impactor liners [3,4], assessment of solid strength under high strain rate [5], slowly accreting neutron stars [6]. Other applications are found in geology: volcanic island formation [7], salt dome formation [8], and more generally, magmatic diapirism in Earth's mantle and continental crust [9,10], correspond to situations where a liquid opens its way through a layer of denser solid material above it. In most approaches to this problem [7–9,11], the upper material was considered as a highly viscous fluid, which allowed simple simulations of the process, but could also be misleading. Another situation concerns oil well cementing operations, in which yield stress fluids of different densities (drilling muds and cement, e.g.), which behave as solids at rest, may be pumped into the well in an ill-favored density order [12]. The basic approach to RTI for solids assumes linear elastic materials. The problem appears similar to that for simple fluids, except that the role of surface tension effects, neglected for solids, is played by elasticity. For a single solid above a liquid with a (positive) density difference Δρ, the instability criterion (A) is given by gΔρ > 4απG=L, where G and L are the shear modulus and length of the sample, respectively, and g denotes the gravitational acceleration. Depending on boundary conditions, factor α was found to be 1 [3,13], 1.6 [14], or 2 [15]. A couple of experiments on metal plates [16] and with a yogurt [17] provided some support to this theory. From a more complete study [18] using soft elastic solids, the overall validity of this approach was proved but the wavelength was shown to be smaller than expected from theory and dependent on uncontrollable, slight disturbances of the surface [19]. RTI for solids is further complicated by the fact that yielding may occur beyond a critical deformation. So far, this aspect has been considered separately, leading to the conclusion that instability results from a sufficiently large initial perturbation amplitude ε 0 (penetration depth). The instability criterion (B) then reads gΔρ > βτ c =ε 0 , where τ c denotes the material's yield stress (in simple shear), and where 0.5 ≤ β ≤ 2 depending on the sample aspect ratio [13–15,18,24,25]. Some tests with a single material were apparently in agreement with this criterion [17] but the plastic regime for this material was not so well-defined [19]. Finally, it was suggested [2] that elastic and plastic stability criteria should be taken into account successively, and deep theoretical analysis [26] predicted that for plastic materials, once the threshold is reached somewhere, the perturbation grows unlimitedly. These approaches have the advantage of considering independently the elasticity and the yielding effects. However, one cannot exclude that the interplay of both mechanisms could play a crucial role in the early stage of the perturbation growth. Here we aim at clarifying this problem through experiments on well-characterized materials, linearly elastic below a critical deformation and elastoplastic beyond this deformation. We show that the RTI in solids does not develop as predicted by the theory for simple elastic materials, but results from the ability of local perturbations to penetrate the material by involving, from the start, both elastic and plastic effects. At some point during the process, resistance to penetration drops, causing an abrup

Mathematical modelling of cell layer growth in a hollow fibre bioreactor

Generating autologous tissue grafts of a clinically useful volume requires efficient and controlled expansion of cell populations harvested from patients. Hollow fibre bioreactors show promise as cell expansion devices, owing to their potential for scale-up. However, further research is required to establish how to specify appropriate hollow fibre bioreactor operating conditions for expanding different cell types. In this study we develop a simple model for the growth of a cell layer seeded on the outer surface of a single fibre in a perfused hollow fibre bioreactor. Nutrient-rich culture medium is pumped through the fibre lumen and leaves the bioreactor via the lumen outlet or passes through the porous fibre walls and cell layer, and out via ports on the outer wall of the extra-capillary space. Stokes and Darcy equations for fluid flow in the fibre lumen, fibre wall, cell layer and extra-capillary space are coupled to reaction–advection–diffusion equations for oxygen and lactate transport through the bioreactor, and to a simple growth law for the evolution of the free boundary of the cell layer. Cells at the free boundary are assumed to proliferate at a rate that increases with the local oxygen concentration, and to die and detach from the layer if the local fluid shear stress or lactate concentration exceed critical thresholds. We use the model to predict operating conditions that maximise the cell layer growth for different cell types. In particular, we predict the optimal flow rate of culture medium into the fibre lumen and fluid pressure imposed at the lumen outlet for cell types with different oxygen demands and fluid shear stress tolerances, and compare the growth of the cell layer when the exit ports on the outside of the bioreactor are open with that when they are closed. Model simulations reveal that increasing the inlet flow rate and outlet fluid pressure increases oxygen delivery to the cell layer and, therefore, the growth rate of cells that are tolerant to high shear stresses, but may be detrimental for shear-sensitive cells. The cell layer growth rate is predicted to increase, and be less sensitive to the lactate tolerance of the cells, when the exit ports are opened, as the radial flow through the bioreactor is enhanced and the lactate produced by the cells cleared more rapidly from the cell layer