On the generation mechanisms of short-scale unbalanced modes in rotating two-layer flows with vertical shear

We report on the results of a laboratory investigation using a rotating two-layer annulus experiment, which exhibits both large-scale vortical modes and short-scale divergent modes. A sophisticated visualization method allows us to observe the flow at very high spatial and temporal resolution. The balanced long-wavelength modes appear only when the Froude number is supercritical (i.e. $F\,{>}\,F_\mathrm{critical}\,{\equiv}\, \upi^2/2$), and are therefore consistent with generation by a baroclinic instability. The unbalanced short-wavelength modes appear locally in every single baroclinically unstable flow, providing perhaps the first direct experimental evidence that all evolving vortical flows will tend to emit freely propagating inertia–gravity waves. The short-wavelength modes also appear in certain baroclinically stable flows. We infer the generation mechanisms of the short-scale waves, both for the baro-clinically unstable case in which they co-exist with a large-scale wave, and for the baroclinically stable case in which they exist alone. The two possible mechanisms considered are spontaneous adjustment of the large-scale flow, and Kelvin–Helmholtz shear instability. Short modes in the baroclinically stable regime are generated only when the Richardson number is subcritical (i.e. $\hbox{\it Ri}\,{<}\,\hbox{\it Ri}_\mathrm{critical}\,{\equiv}\, 1$), and are therefore consistent with generation by a Kelvin–Helmholtz instability. We calculate five indicators of short-wave generation in the baroclinically unstable regime, using data from a quasi-geostrophic numerical model of the annulus. There is excellent agreement between the spatial locations of short-wave emission observed in the laboratory, and regions in which the model Lighthill/Ford inertia–gravity wave source term is large. We infer that the short waves in the baroclinically unstable fluid are freely propagating inertia–gravity waves generated by spontaneous adjustment of the large-scale flow.

The role of phase separation and feed cycle length in leach beds coupled to methanogenic reactors for digestion of a solid substrate (Part 2): Hydrolysis, acidification and methanogenesis in a two-phase system

The effect of phase separation and batch duration on the trophic stages of anaerobic digestion was assessed for the first time in leach beds coupled to methanogenic reactors digesting maize (Zea mays). The system was operated for consecutive batches of 7, 14 and 28 days for ~120 days. Hydrolysis rate was higher the shorter the batch, reaching 8.5 gTSdestroyed d-1 in the 7-day system. Phase separation did not affect acidification but methanogenesis was enhanced in the short feed cycle leach beds. Phase separation was inefficient on the 7-day system, where ~89% of methane was produced in the leach bed. Methane production rate increased with shortening the feed cycle, reaching 3.523 l d-1 average in the 7-day system. Low strength leachate from the leach beds decreased methanogenic activity of methanogenic reactors’ sludges. Enumeration of cellulolytic and methanogenic microorganisms indicated a constant inoculation of leach beds and methanogenic reactors through leachate recirculation.

Energy consistent discontinuous Galerkin methods for a quasi-incompressible diffuse two phase flow model

We design consistent discontinuous Galerkin finite element schemes for the approximation of a quasi-incompressible two phase flow model of Allen–Cahn/Cahn–Hilliard/Navier–Stokes–Korteweg type which allows for phase transitions. We show that the scheme is mass conservative and monotonically energy dissipative. In this case the dissipation is isolated to discrete equivalents of those effects already causing dissipation on the continuous level, that is, there is no artificial numerical dissipation added into the scheme. In this sense the methods are consistent with the energy dissipation of the continuous PDE system.

Flux difference splitting for open channel flows

A finite difference scheme based on flux difference splitting is presented for the solution of the one-dimensional shallow-water equations in open channels, together with an extension to two-dimensional flows. A linearized problem, analogous to that of Riemann for gas dynamics, is defined and a scheme, based on numerical characteristic decomposition, is presented for obtaining approximate solutions to the linearized problem. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second-order scheme which avoids non-physical, spurious oscillations. The scheme is applied to a one-dimensional dam-break problem, and to a problem of flow in a river whose geometry induces a region of supercritical flow. The scheme is also applied to a two-dimensional dam-break problem. The numerical results are compared with the exact solution, or other numerical results, where available.

A moving-mesh finite element method and its application to the numerical solution of phase-change problems

A distributed Lagrangian moving-mesh finite element method is applied to problems involving changes of phase. The algorithm uses a distributed conservation principle to determine nodal mesh velocities, which are then used to move the nodes. The nodal values are obtained from an ALE (Arbitrary Lagrangian-Eulerian) equation, which represents a generalization of the original algorithm presented in Applied Numerical Mathematics, 54:450--469 (2005). Having described the details of the generalized algorithm it is validated on two test cases from the original paper and is then applied to one-phase and, for the first time, two-phase Stefan problems in one and two space dimensions, paying particular attention to the implementation of the interface boundary conditions. Results are presented to demonstrate the accuracy and the effectiveness of the method, including comparisons against analytical solutions where available.

The role of phase separation and feed cycle length in leach beds coupled to methanogenic reactors for digestion of a solid substrate (Part 1): Optimisation of reactors’ performance

A two-phase system composed by a leach bed and a methanogenic reactor was modified for the first time to improve volumetric substrate degradation and methane yields from a complex substrate (maize; Zea mays). The system, which was operated for consecutive feed cycles of different durations for 120 days, was highly flexible and its performance improved by altering operational conditions. Daily substrate degradation was higher the shorter the feed cycle, reaching 8.5 g TSdestroyed d�1 (7-day feed cycle) but the overall substrate degradation was higher by up to 55% when longer feed cycles (14 and 28 days) were applied. The same occurred with volumetric methane yields, reaching 0.839 m3 (m3)�1 d�1. The system performed better than others on specific methane yields, reaching 0.434 m3 kg�1 TSadded, in the 14-day and 28-day systems. The UASB and AF designs performed similarly as second stage reactors on methane yields, SCOD and VFA removal efficiencies.

Polydispersity-induced macrophase separation in diblock copolymer melts

The effect of A-block polydispersity on the phase behavior of AB diblock copolymer melts is examined using a complete self-consistent field theory treatment that allows for fractionation of the parent molecular-weight distribution. In addition to observing the established shift in phase boundaries, we find the emergence of significant two-phase coexistence regions causing, for instance, the disappearance of the complex phase window. Furthermore, we find evidence that polydispersity relieves packing frustration, which will reduce the tendency for long-range order.

A contour-advective semi-lagrangian numerical algorithm for simulating fine-scale conservative dynamical fields

This paper describes a novel numerical algorithm for simulating the evolution of fine-scale conservative fields in layer-wise two-dimensional flows, the most important examples of which are the earth's atmosphere and oceans. the algorithm combines two radically different algorithms, one Lagrangian and the other Eulerian, to achieve an unexpected gain in computational efficiency. The algorithm is demonstrated for multi-layer quasi-geostrophic flow, and results are presented for a simulation of a tilted stratospheric polar vortex and of nearly-inviscid quasi-geostrophic turbulence. the turbulence results contradict previous arguments and simulation results that have suggested an ultimate two-dimensional, vertically-coherent character of the flow. Ongoing extensions of the algorithm to the generally ageostrophic flows characteristic of planetary fluid dynamics are outlined.

What do patients want to know about their medicines, and what do doctors want to tell them?: a comparative study

A two phase study is reported. In the first phase, we asked a number of doctors to rate a list of information categories (identified by Berry, Gillie and Banbury 1995) in terms of how important they felt it was for the items to be included in an explanation to a patient about a drug prescription. In the second phase, we presented a large sample of people with a scenario about visiting their doctor and being prescribed medication, together with an explanation about the prescription which was said to be provided by the doctor. Four different explanations were compared, which were either based on what people in our earlier study wanted to know about drug prescriptions or on what the doctors thought it was important lo tell them. We also manipulated whether or not the explanations conveyed negative information (e.g. about the possible side effects of the medication). The results showed that people 'preferred' the explanations based on what the participants in the earlier study wanted to know about their medicines, rather than those based on what the doctors thought they should be told. They also 'preferred' the explanations that did not convey negative information, rather than those that did convey some negative information. In addition, the inclusion of negative information affected ratings of likely compliance with the prescribed medication.

The structure of crystallisable copolymers of L-lactide, epsilon-caprolactone and glycolide

We apply a new X-ray scattering approach to the study of melt-spun filaments of tri-block and random terpolymers prepared from lactide, caprolactone and glycolide. Both terpolymers contain random sequences, in both cases the overall fraction of lactide units is similar to 0.7 and C-13 and H-1 NMR shows the lactide sequence length to be similar to 9-10. A novel representation of the X-ray fibre pattern as series of spherical harmonic functions considerably facilitates the comparison of the scattering from the minority crystalline phase with hot drawn fibres prepared from the poly(L-lactide) homopolymer. Although the fibres exhibit rather disordered structures we show that the crystal structure is equivalent to that displayed by poly(L-lactide) for both the block and random terpolymers. There are variations in the development of a two-phase structure which reflect the differences in the chain architectures. There is evidence that the random terpolymer includes non-lactide units in to the crystal interfaces to achieve a well defined two-phase structure. (c) 2005 Published by Elsevier Ltd.

Potential energy for slantwise parcel motion

Two formulations for the potential energy for slantwise motion are compared: one which applies strictly only to two-dimensional flows (SCAPE) and a three-dimensional formulation based on a Bernoulli equation. The two formulations share an identical contribution from the vertically integrated buoyancy anomaly and a contribution from different Coriolis terms. The latter arise from the neglect of (different) components of the total change in kinetic energy along a trajectory in the two formulations. This neglect is necessary in order to quantify the potential energy available for slantwise motion relative to a defined steady environment. Copyright © 2000 Royal Meteorological Society.

Synthesis, structure, and redox states of homoleptic d-block metal complexes with bis-1,2,4-triazin-3-yl-pyridine and 1,2,4-triazin-3-yl-bipyridine extractants

it has been established that triazinyl bipyridines (hemi-BTPs) and bis-triazinyl pyridines (BTPs), ligands which are currently being investigated as possible ligands for the separation of actinides from lanthanides in nuclear waste, are able to form homoleptic complexes with first row transition metals such as cobalt(IT), copper(II), iron(II), manganese(II), nickel(II) and zinc(II). The metal complexes exhibit six-co-ordinate octahedral structures and redox states largely analogous to those of the related terpyridine complexes. The reactivity of the different redox states of cobalt bis-hemi-BTP complex in aqueous environments has been studied with two-phase electrochemistry by immobilisation of the essentially water-insoluble metal complexes on graphite electrodes and the immersion of this modified electrode in an aqueous electrolyte. It was found that redox potentials for the metal-centred reactions were pH-independent whereas the potentials for the ligand-centred reactions were strongly pH-dependent. The reductive degradation of these complexes has been investigated by computational methods. Solvent extraction experiments have been carried out for a range of metals and these show that cobalt(II) and nickel(II) as well as palladium(II), cadmium(II) and lead(II) were all extracted with the ligands 1e and 2c with higher distribution ratios that was observed for americium(III) under the same conditions. The implications of this result for the use of these ligands to separate actinides from nuclear waste are discussed. (c) 2005 Elsevier Ltd. All rights reserved.

Velocity-based moving mesh methods for nonlinear partial differential equations

This article describes a number of velocity-based moving mesh numerical methods formultidimensional nonlinear time-dependent partial differential equations (PDEs). It consists of a short historical review followed by a detailed description of a recently developed multidimensional moving mesh finite element method based on conservation. Finite element algorithms are derived for both mass-conserving and non mass-conserving problems, and results shown for a number of multidimensional nonlinear test problems, including the second order porous medium equation and the fourth order thin film equation as well as a two-phase problem. Further applications and extensions are referenced.