Stirring and transport enhancement in a continuously modulated free-surface flow

The transport of fluid from a recirculation region adjacent to a free surface is studied using a numerical method validated with experimental flow visualization. The flow is an example of a liquid film coating process, and consists of two counter-rotating rolls placed side-by-side and half-submerged in a bath of fluid. In the gap between the rolls a recirculation zone exists just below the free surface, around which the flow splits into two films. Fluid recirculating for long periods has been identified as a source of coating defects, so this paper considers a possible method of inducing stirring. The flow is modulated by driving one of the rolls through a Hooke's joint, which delivers a well-characterized periodic perturbation to the roll speed. In response to this speed modulation, the free surface undergoes a periodic change in position and shape which drives an exchange of fluid between the recirculation region and the surrounding flow. The amplitude of the free-surface motion is strongly dependent on modulation frequency. The dynamics of the free surface preclude a quasi-steady approach, even in the small-frequency limit, and so a fully time-dependent analysis based on the finite element method is employed. Trigonometric temporal interpolation of the finite element data is used to make passive tracer advection calculations more efficient, and excellent agreement is seen between simulation and experiment. Computations of the stable and unstable invariant manifolds associated with periodic points on the free surface reveal that the exchange of fluid is governed by a self-intersecting turnstile mechanism, by which most fluid entrained during a modulation cycle is ejected later in the same cycle. Transport over several cycles is explored by observation of the evacuation of passive tracers initially distributed uniformly in the recirculation zone. Results demonstrate the persistence of unmixed cores whose size is dependent on the modulation frequency. By considering the percentage of tracers remaining after a fixed number of cycles, contours in frequency-amplitude space show that for each modulation amplitude there is a frequency which produces the most effective transport, with up to 80 % of tracers removed by a modulation which produces only a 5 % change in film thickness. Finally it is shown how modulation of both rolls at slightly different phases can reduce the film thickness variation to about 1 % while maintaining the level of transport

Variability of Active Galactic Nuclei from the Optical to X-ray Regions

Some progress in understanding AGN variability is reviewed. Reprocessing of X-ray radiation to produce significant amounts of longer-wavelength continua seems to be ruled out. In some objects where there has been correlated X-ray and optical variability, the amplitude of the optical variability has exceeded the amplitude of X-ray variability. We suggest that accelerated particles striking material could be linking X-ray and optical variability (as in activity in the solar chromosphere). Beaming effects could be significant in all types of AGN. The diversity in optical/X-ray relationships at different times in the same object, and between different objects, might be explained by changes in geometry and directions of motion relative to our line of sight. Linear shot-noise models of the variability are ruled out; instead there must be large-scale organization of variability. Variability occurs on light-crossing timescales rather than viscous timescales and this probably rules out the standard Shakura-Sunyaev accretion disk. Radio-loud and radio-quiet AGNs have similar continuum shapes and similar variability properties. This suggests similar continuum origins and variability mechanisms. Despite their extreme X-ray variability, narrow-line Seyfert 1s (NLS1s) do not show extreme optical variability.Comment: Invited talk given at Euro Asian Astronomical Society meeting in Moscow, June 2002. 20 pages, 4 figures. References update

Generator Matrix Elements For G2⊃SU(3)G_2 \supset SU(3) II

Basis states and generator matrix elements are given for the generic representation $(a,b)$ of $G_2$ in an $SU(3)$ basis.Comment: Latex, 17 pages, one figure using epsf published in J. Phys. A: Math. Gen 28 (1995) 2581-258

Reassessing agrarian policy and practice in local environmental management: the case of beef cattle

There are policy pressures to make agriculture more environmentally sustainable and to give a more local expression to agri-environmental priorities. This paper considers these moves, with particular reference to the beef sector, and speculates on the further policy responses required to facilitate benign local agri-environmental management. The UK beef sector is characterized by its complexity and diversity but four major systems can be identified operating at varying levels of intensity. Of these, suckler herds and grass-rearing systems have long been associated with high natural value forms of agricultural land management. Many of the cherished habitats and landscapes of the UK are dependent upon grazing for their ecological and amenity value. However a combination of the BSE crisis, the strength of sterling and the recent Foot & Mouth epidemic threatens the sustainability of these high nature value grazing systems. The importance of grazing to fifty selected Sites of Special Scientific Interest is highlighted in the paper. Survey work identified a wide range of systems to be particularly vulnerable to changes in profitability in the beef sector, including: coastal grazing marsh, wet acidic grassland / marshland, upland moor and heath, calcareous grassland and neutral grassland. To maintain these systems requires agricultural policy to be more sensitive to local conditions than appears currently to be the case. There is little policy support for beef farmers in a regional context, still less giving special prominence to those farming within particular biotopes. Nor has there been sufficient policy encouragement to markets for traditional and local beef breeds. The continuing pressure for CAP reform offers further opportunity for policies to be devolved to regions and localities

A model for film-forming with Newtonian and shear-thinning fluids

The formation of a thin film by (i) the slow penetration of a gas bubble into a liquid filled tube, (ii) the withdrawal of a planar substrate from a liquid filled gap, is investigated theoretically for the cases of both Newtonian and shear-thinning liquids; the latter conforming to either a power-law or Ellis model. Formulated as a boundary value problem underpinned by lubrication theory, the analysis gives rise to a system of ordinary differential equations which are solved numerically subject to appropriate boundary conditions. For Newtonian liquids comparison of the predicted residual film thickness for a wide range of capillary number, Ca ∈ (10-4, 10), is made with others obtained using existing expressions, including the classical one of Bretherton, in the region of parameter space over which they apply. In the case of (i), prediction of the behaviour of the residual fluid fraction and gap-to-film thickness ratio, for a Newtonian liquid and one that is shear-thinning and modelled via a power-law, is found to be in particularly good agreement with experimental data for Ca < 0.2. For (ii), both shear-thinning models are utilized and contour plots of residual film thickness generated as a function of Ca and the defining parameters characteristic of each model. © 2009 Elsevier B.V. All rights reserved

A robust enhancement to the Clarke-Wright savings algorithm

We address the Clarke and Wright (CW) savings algorithm proposed for the Capacitated Vehicle Routing Problem (CVRP). We first consider a recent enhancement which uses the put first larger items idea originally proposed for the bin packing problem and show that the conflicting idea of putting smaller items first has a comparable performance. Next, we propose a robust enhancement to the CW savings formulation. The proposed formulation is normalized to efficiently solve different problems, independent from the measurement units and parameter intervals. To test the performance of the proposed savings function, we conduct an extensive computational study on a large set of well-known instances from the literature. Our results show that the proposed savings function provides shorter distances in the majority of the instances and the average performance is significantly better than previously presented enhancements

A combined experimental and computational fluid dynamics analysis of the dynamics of drop formation

This article presents a complementary experimental and computational investigation of the effect of viscosity and flowrate on the dynamics of drop formation in the dripping mode. In contrast to previous studies, numerical simulations are performed with two popular commercial computational fluid dynamics (CFD) packages, CFX and FLOW-3D, both of which employ the volume of fluid (VOF) method. Comparison with previously published experimental and computational data and new experimental results reported here highlight the capabilities and limitations of the aforementioned packages