Stokes flow in a half-filled annulus between rotating coaxial cylinders

A model is presented for viscous flow in a cylindrical cavity (a half-filled annulus lying between horizontal, infinitely long concentric cylinders of radii R-i,R-0 rotating with peripheral speeds U-i,U-0). Stokes' approximation is used to formulate a boundary value problem which is solved for the streamfunction, phi, as a function of radius ratio (R) over bar = R-i/R-0 and speed ratio S = U-i/U-0. Results show that for S > 0 (S 1, a sequence of 'flow bifurcations' leads to a flow structure consisting of a set of nested separatrices, and provides the means by which the two-dimensional cavity flow approaches quasi-unidirectional flow in the small gap limit. Control-space diagrams reveal that speed ratio has little effect on the flow structure when S 0 and aspect ratios are small (except near S = 1). For S > 0 and moderate to large aspect ratios the bifurcation characteristics of the two large eddies are quite different and depend on both (R) over bar and S

Efficient and accurate time adaptive multigrid simulations of droplet spreading

An efficient full approximation storage (FAS) Multigrid algorithm is used to solve a range of droplet spreading flows modelled as a coupled set of non-linear lubrication equations. The algorithm is fully implicit and has embedded within it an adaptive time-stepping scheme that enables the same to be optimized in a controlled manner subject to a specific error tolerance. The method is first validated against a range of analytical and existing numerical predictions commensurate with droplet spreading and then used to simulate a series of new, three-dimensional flows consisting of droplet motion on substrates containing topographic and wetting heterogeneities. The latter are of particular interest and reveal how droplets can be made to spread preferentially on substrates owing to an interplay between different topographic and surface wetting characteristics

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

Markers of automaticity in sleep-associated consolidation of novel words

Two experiments investigated effects of sleep on consolidation and integration of novel form-meaning mappings using size congruity and semantic distance paradigms. Both paradigms have been used in previous studies to measure automatic access to word meanings. When participants compare semantic or physical font size of written word-pairs (e.g. BEE–COW), judgments are typically faster if relative sizes are congruent across both dimensions. Semantic distance effects are also found for wellestablished words, with semantic size judgements faster for pairs that differ substantially on this dimension. English-speaking participants learned novel form-meaning mappings with Mandarin (Experiment 1) or Malay (Experiment 2) words and were tested following overnight sleep or a similar duration awake. Judgements on English words controlled for circadian effects. The sleep group demonstrated selective stronger size congruity and semantic distance effects for novel word-pairs. This benefit occurred in Experiment 1 for semantic size comparisons of novel words, and in Experiment 2 on comparisons where novel pairs had large distances and font differences (for congruity effects) or in congruent trials (for semantic distance effects). Conversely, these effects were equivalent across sleep and wake for English words. Experiment 2 included polysomnography data and revealed that changes in the strength of semantic distance and congruity effects were positively correlated with slow-wave sleep and sleep spindles respectively. These findings support systems consolidation accounts of declarative learning and suggest that sleep plays an active role in integrating new words with existing knowledge, resulting in increased automatic access of the acquired knowledge

Mechanisms of memory retrieval in slow-wave sleep : memory retrieval in slow-wave sleep

Study Objectives: Memories are strengthened during sleep. The benefits of sleep for memory can be enhanced by re-exposing the sleeping brain to auditory cues; a technique known as targeted memory reactivation (TMR). Prior studies have not assessed the nature of the retrieval mechanisms underpinning TMR: the matching process between auditory stimuli encountered during sleep and previously encoded memories. We carried out two experiments to address this issue. Methods: In Experiment 1, participants associated words with verbal and non-verbal auditory stimuli before an overnight interval in which subsets of these stimuli were replayed in slow-wave sleep. We repeated this paradigm in Experiment 2 with the single difference that the gender of the verbal auditory stimuli was switched between learning and sleep. Results: In Experiment 1, forgetting of cued (vs. non-cued) associations was reduced by TMR with verbal and non-verbal cues to similar extents. In Experiment 2, TMR with identical non-verbal cues reduced forgetting of cued (vs. non-cued) associations, replicating Experiment 1. However, TMR with non-identical verbal cues reduced forgetting of both cued and non-cued associations. Conclusions: These experiments suggest that the memory effects of TMR are influenced by the acoustic overlap between stimuli delivered at training and sleep. Our findings hint at the existence of two processing routes for memory retrieval during sleep. Whereas TMR with acoustically identical cues may reactivate individual associations via simple episodic matching, TMR with non-identical verbal cues may utilise linguistic decoding mechanisms, resulting in widespread reactivation across a broad category of memories

The relative wavelength independence of IR lags in active galactic nuclei: implications for the distribution of the hot dust

We show that, contrary to simple predictions, most AGNs show at best only a small increase of lags in the J, H, K, and L bands with increasing wavelength. We suggest that a possible cause of this near simultaneity of the variability from the near-IR to the mid-IR is that the hot dust is in a hollow bi-conical outflow of which we only see the near side. Although most AGNs show near simultaneity of IR variability, there was at least one epoch when NGC 4151 showed the sharply increasing IR lag with the increase of the wavelength. This behaviour might also be present in GQ Comae. We discuss these results briefly. The relative wavelength independence of IR lags simplifies the use of IR lags for estimating cosmological parameters.Comment: 6 pages, 5 figures, for the Odessa Astronomical Publicatio

Gravity-driven flow of continuous thin liquid films on non-porous substrates with topography

A range of two- and three-dimensional problems is explored featuring the gravity-driven flow of a continuous thin liquid film over a non-porous inclined flat surface containing well-defined topography. These are analysed principally within the framework of the lubrication approximation, where accurate numerical solution of the governing nonlinear equations is achieved using an efficient multigrid solver. Results for flow over one-dimensional steep-sided topographies are shown to be in very good agreement with previously reported data. The accuracy of the lubrication approximation in the context of such topographies is assessed and quantified by comparison with finite element solutions of the full Navier–Stokes equations, and results support the consensus that lubrication theory provides an accurate description of these flows even when its inherent assumptions are not strictly satisfied. The Navier–Stokes solutions also illustrate the effect of inertia on the capillary ridge/trough and the two-dimensional flow structures caused by steep topography. Solutions obtained for flow over localized topography are shown to be in excellent agreement with the recent experimental results of Decré & Baret (2003) for the motion of thin water films over finite trenches. The spread of the ‘bow wave’, as measured by the positions of spanwise local extrema in free-surface height, is shown to be well-represented both upstream and downstream of the topography by an inverse hyperbolic cosine function. An explanation, in terms of local flow rate, is given for the presence of the ‘downstream surge’ following square trenches, and its evolution as trench aspect ratio is increased is discussed. Unlike the upstream capillary ridge, this feature cannot be completely suppressed by increasing the normal component of gravity. The linearity of free-surface response to topographies is explored by superposition of the free surfaces corresponding to two ‘equal-but-opposite’ topographies. Results confirm the findings of Decré & Baret (2003) that, under the conditions considered, the responses behave in a near-linear fashion

Realism and idealism in the harmonization of contract law in the European Union

The advantages of enhanced cross-border trade among the member states are emphasized by advocates of the harmonization of law in the European Union, a principle which has been included in each of the treaties of accession. Following political events in 1989, the concept of a Europe-wide law of obligations received renewed impetus. The leading advocates, who comprised a Study Group under the chairmanship of Professor Christian von Bar, were academic lawyers supported by the European Commission and by journals devoted to legal integration. The impact of decisions of the Court of Justice of the European Union in 2000 and 2006, however, ensured that only a modest proposal, as distinct from a European Civil Code, would be put forward. The Common European Sales Law, an optional instrument, is assessed both in terms of how it is expected to work and in the light of benefits arising from the existence of standard European terms. Also in this thesis historical-legal arguments in favour of ‘Europeanized’ contract law are evaluated and found to be not wholly convincing. The counter-argument, put forward by the Canadian Professor Pierre Legrand, maintains that the principal European legal traditions are epistemologically distinct, rendering convergence impossible. Legrand’s contribution to the debate is possibly overstated but has never been shown to be misconceived. However, this thesis draws attention to the degree of affinity – greater than is generally recognized – which always existed between the Common and Civil Law traditions. It is argued that this underlying affinity is more likely to lead to durable results by European lawyers seeking solutions to shared problems than by the artificial process of codification

Flow of evaporating, gravity-driven thin liquid films over topography

The effect of topography on the free surface and solvent concentration profiles of an evaporating thin film of liquid flowing down an inclined plane is considered. The liquid is assumed to be composed of a resin dissolved in a volatile solvent with the associated solvent concentration equation derived on the basis of the well-mixed approximation. The dynamics of the film is formulated as a lubrication approximation and the effect of a composition-dependent viscosity is included in the model. The resulting time-dependent, nonlinear, coupled set of governing equations is solved using a full approximation storage multigrid method. The approach is first validated against a closed-form analytical solution for the case of a gravity-driven, evaporating thin film flowing down a flat substrate. Analysis of the results for a range of topography shapes reveal that although a full-width, spanwise topography such as a step-up or a step-down does not affect the composition of the film, the same is no longer true for the case of localized topography, such as a peak or a trough, for which clear nonuniformities of the solvent concentration profile can be observed in the wake of the topography