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.

Non-ergodicity of inviscid two-dimensional flow on a beta-plane and on the surface of a rotating sphere

It is shown that, for a sufficiently large value of β, two-dimensional flow on a doubly-periodic beta-plane cannot be ergodic (phase-space filling) on the phase-space surface of constant energy and enstrophy. A corresponding result holds for flow on the surface of a rotating sphere, for a sufficiently rapid rotation rate Ω. This implies that the higher-order, non-quadratic invariants are exerting a significant influence on the statistical evolution of the flow. The proof relies on the existence of a finite-amplitude Liapunov stability theorem for zonally symmetric basic states with a non-vanishing absolute-vorticity gradient. When the domain size is much larger than the size of a typical eddy, then a sufficient condition for non-ergodicity is that the wave steepness ε < 1, where ε = 2[surd radical]2Z/βU in the planar case and $\epsilon = 2^{\frac{1}{4}} a^{\frac{5}{2}}Z^{\frac{7}{4}}/\Omega U^{\frac{5}{2}}$ in the spherical case, and where Z is the enstrophy, U the r.m.s. velocity, and a the radius of the sphere. This result may help to explain why numerical simulations of unforced beta-plane turbulence (in which ε decreases in time) seem to evolve into a non-ergodic regime at large scales.

Sensitivity analysis of a cyanobacterial growth and movement model under two different flow regimes

Bloom-forming and toxin-producing cyanobacteria remain a persistent nuisance across the world. Modelling cyanobacterial behaviour in freshwaters is an important tool for understanding their population dynamics and predicting the location and timing of the bloom events in lakes, reservoirs and rivers. A new deterministic–mathematical model was developed, which simulates the growth and movement of cyanobacterial blooms in river systems. The model focuses on the mathematical description of the bloom formation, vertical migration and lateral transport of colonies within river environments by taking into account the major factors that affect the cyanobacterial bloom formation in rivers including light, nutrients and temperature. A parameter sensitivity analysis using a one-at-a-time approach was carried out. There were two objectives of the sensitivity analysis presented in this paper: to identify the key parameters controlling the growth and movement patterns of cyanobacteria and to provide a means for model validation. The result of the analysis suggested that maximum growth rate and day length period were the most significant parameters in determining the population growth and colony depth, respectively.

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.

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.

Particle image velocimetry measurements of turbulent flow within outdoor and indoor urban scale models and flushing motions in urban canopy layers

We investigate the spatial characteristics of urban-like canopy flow by applying particle image velocimetry (PIV) to atmospheric turbulence. The study site was a Comprehensive Outdoor Scale MOdel (COSMO) experiment for urban climate in Japan. The PIV system captured the two-dimensional flow field within the canopy layer continuously for an hour with a sampling frequency of 30 Hz, thereby providing reliable outdoor turbulence statistics. PIV measurements in a wind-tunnel facility using similar roughness geometry, but with a lower sampling frequency of 4 Hz, were also done for comparison. The turbulent momentum flux from COSMO, and the wind tunnel showed similar values and distributions when scaled using friction velocity. Some different characteristics between outdoor and indoor flow fields were mainly caused by the larger fluctuations in wind direction for the atmospheric turbulence. The focus of the analysis is on a variety of instantaneous turbulent flow structures. One remarkable flow structure is termed 'flushing', that is, a large-scale upward motion prevailing across the whole vertical cross-section of a building gap. This is observed intermittently, whereby tracer particles are flushed vertically out from the canopy layer. Flushing phenomena are also observed in the wind tunnel where there is neither thermal stratification nor outer-layer turbulence. It is suggested that flushing phenomena are correlated with the passing of large-scale low-momentum regions above the canopy.

The gut microbiota elicits a profound metabolic reorientation in the mouse jejunal mucosa during conventionalisation

Objective: Proper interactions between the intestinal mucosa, gut microbiota and nutrient flow are required to establish homoeostasis of the host. Since the proximal part of the small intestine is the first region where these interactions occur, and since most of the nutrient absorption occurs in the jejunum, it is important to understand the dynamics of metabolic responses of the mucosa in this intestinal region.Design: Germ-free mice aged 8-10 weeks were conventionalised with faecal microbiota, and responses of the jejunal mucosa to bacterial colonisation were followed over a 30-day time course. Combined transcriptome, histology, (1)H NMR metabonomics and microbiota phylogenetic profiling analyses were used.Results: The jejunal mucosa showed a two-phase response to the colonising microbiota. The acute-phase response, which had already started 1 day after conventionalisation, involved repression of the cell cycle and parts of the basal metabolism. The secondary-phase response, which was consolidated during conventionalisation (days 4-30), was characterised by a metabolic shift from an oxidative energy supply to anabolic metabolism, as inferred from the tissue transcriptome and metabonome changes. Detailed transcriptome analysis identified tissue transcriptional signatures for the dynamic control of the metabolic reorientation in the jejunum. The molecular components identified in the response signatures have known roles in human metabolic disorders, including insulin sensitivity and type 2 diabetes mellitus.Conclusion: This study elucidates the dynamic jejunal response to the microbiota and supports a prominent role for the jejunum in metabolic control, including glucose and energy homoeostasis. The molecular signatures of this process may help to find risk markers in the declining insulin sensitivity seen in human type 2 diabetes mellitus, for instance.

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.

Nonlinear stability of multilayer quasi-geostrophic flow

New nonlinear stability theorems are derived for disturbances to steady basic flows in the context of the multilayer quasi-geostrophic equations. These theorems are analogues of Arnol’d's second stability theorem, the latter applying to the two-dimensional Euler equations. Explicit upper bounds are obtained on both the disturbance energy and disturbance potential enstrophy in terms of the initial disturbance fields. An important feature of the present analysis is that the disturbances are allowed to have non-zero circulation. While Arnol’d's stability method relies on the energy–Casimir invariant being sign-definite, the new criteria can be applied to cases where it is sign-indefinite because of the disturbance circulations. A version of Andrews’ theorem is established for this problem, and uniform potential vorticity flow is shown to be nonlinearly stable. The special case of two-layer flow is treated in detail, with particular attention paid to the Phillips model of baroclinic instability. It is found that the short-wave portion of the marginal stability curve found in linear theory is precisely captured by the new nonlinear stability criteria.

Spectral nonlocality, absolute equilibria and Kraichnan-Leith-Batchelor phenomenology in two-dimensional turbulent energy cascades

We study the degree to which Kraichnan–Leith–Batchelor (KLB) phenomenology describes two-dimensional energy cascades in α turbulence, governed by ∂θ/∂t+J(ψ,θ)=ν∇2θ+f, where θ=(−Δ)α/2ψ is generalized vorticity, and ψ^(k)=k−αθ^(k) in Fourier space. These models differ in spectral non-locality, and include surface quasigeostrophic flow (α=1), regular two-dimensional flow (α=2) and rotating shallow flow (α=3), which is the isotropic limit of a mantle convection model. We re-examine arguments for dual inverse energy and direct enstrophy cascades, including Fjørtoft analysis, which we extend to general α, and point out their limitations. Using an α-dependent eddy-damped quasinormal Markovian (EDQNM) closure, we seek self-similar inertial range solutions and study their characteristics. Our present focus is not on coherent structures, which the EDQNM filters out, but on any self-similar and approximately Gaussian turbulent component that may exist in the flow and be described by KLB phenomenology. For this, the EDQNM is an appropriate tool. Non-local triads contribute increasingly to the energy flux as α increases. More importantly, the energy cascade is downscale in the self-similar inertial range for 2.5<α<10. At α=2.5 and α=10, the KLB spectra correspond, respectively, to enstrophy and energy equipartition, and the triad energy transfers and flux vanish identically. Eddy turnover time and strain rate arguments suggest the inverse energy cascade should obey KLB phenomenology and be self-similar for α<4. However, downscale energy flux in the EDQNM self-similar inertial range for α>2.5 leads us to predict that any inverse cascade for α≥2.5 will not exhibit KLB phenomenology, and specifically the KLB energy spectrum. Numerical simulations confirm this: the inverse cascade energy spectrum for α≥2.5 is significantly steeper than the KLB prediction, while for α<2.5 we obtain the KLB spectrum.

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.

Preferred structures in large-scale circulation and the effect of doubling greenhouse gas concentration in HadCM3

Preferred structures in the surface pressure variability are investigated in and compared between two 100-year simulations of the Hadley Centre climate model HadCM3. In the first (control) simulation, the model is forced with pre-industrial carbon dioxide concentration (1×CO2) and in the second simulation the model is forced with doubled CO2 concentration (2×CO2). Daily winter (December-January-February) surface pressures over the Northern Hemisphere are analysed. The identification of preferred patterns is addressed using multivariate mixture models. For the control simulation, two significant flow regimes are obtained at 5% and 2.5% significance levels within the state space spanned by the leading two principal components. They show a high pressure centre over the North Pacific/Aleutian Islands associated with a low pressure centre over the North Atlantic, and its reverse. For the 2×CO2 simulation, no such behaviour is obtained. At higher-dimensional state space, flow patterns are obtained from both simulations. They are found to be significant at the 1% level for the control simulation and at the 2.5% level for the 2×CO2 simulation. Hence under CO2 doubling, regime behaviour in the large-scale wave dynamics weakens. Doubling greenhouse gas concentration affects both the frequency of occurrence of regimes and also the pattern structures. The less frequent regime becomes amplified and the more frequent regime weakens. The largest change is observed over the Pacific where a significant deepening of the Aleutian low is obtained under CO2 doubling.

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.