Large-scale length and time scales for use with stochastic convective parameterization

Many numerical models for weather prediction and climate studies are run at resolutions that are too coarse to resolve convection explicitly, but too fine to justify the local equilibrium assumed by conventional convective parameterizations. The Plant-Craig (PC) stochastic convective parameterization scheme, developed in this paper, solves this problem by removing the assumption that a given grid-scale situation must always produce the same sub-grid-scale convective response. Instead, for each timestep and gridpoint, one of the many possible convective responses consistent with the large-scale situation is randomly selected. The scheme requires as input the large-scale state as opposed to the instantaneous grid-scale state, but must nonetheless be able to account for genuine variations in the largescale situation. Here we investigate the behaviour of the PC scheme in three-dimensional simulations of radiative-convective equilibrium, demonstrating in particular that the necessary space-time averaging required to produce a good representation of the input large-scale state is not in conflict with the requirement to capture large-scale variations. The resulting equilibrium profiles agree well with those obtained from established deterministic schemes, and with corresponding cloud-resolving model simulations. Unlike the conventional schemes the statistics for mass flux and rainfall variability from the PC scheme also agree well with relevant theory and vary appropriately with spatial scale. The scheme is further shown to adapt automatically to changes in grid length and in forcing strength.

Efficiency of pseudo-spectral algorithms with Anderson mixing for the SCFT of periodic block-copolymer phases

This study examines the numerical accuracy, computational cost, and memory requirements of self-consistent field theory (SCFT) calculations when the diffusion equations are solved with various pseudo-spectral methods and the mean field equations are iterated with Anderson mixing. The different methods are tested on the triply-periodic gyroid and spherical phases of a diblock-copolymer melt over a range of intermediate segregations. Anderson mixing is found to be somewhat less effective than when combined with the full-spectral method, but it nevertheless functions admirably well provided that a large number of histories is used. Of the different pseudo-spectral algorithms, the 4th-order one of Ranjan, Qin and Morse performs best, although not quite as efficiently as the full-spectral method.

The effect of the spacer length on the nature of coupling in side chain liquid crystals polymers and elastomers

Side chain liquid crystal polymers and elastomers exhibit a rich phase behaviour which arises from the antagonistic influences of the entropically disordered polymer chain configuration and the long range orientational ordering of the mesogenic units. This competition arises since the natural macroscopic phase separation is inhibited by the inherent chemical connectivity of the system. At the heart of this connectivity is the spacer link and we consider here its influence on the phase behaviour. In particular we consider a series of elastomers in which the number of alkyl units in the spacer is systematically varied from 2 to 6. The lengthening of the coupling spacer is accompanied by an alternation of the sign of coupling between the polymer chain and the mesogenic unit. These results demonstrate the dominating influence of the so-called hinge effect in determining the phase behaviour. In addition to the alternation of the sign there is some decrease in the magnitude of the coupling with increasing spacer length.

Side-chain liquid crystalline elastomers: the relationship between the orientational ordering of the polymer backbone and the length of the coupling chain

The influence of cross-linking on the phase behaviour of a series of side-chain liquid crystalline elastomers has been studied. For samples cross-linked in the temperature range corresponding to the nematic phase, the phase transition was shifted compared to that observed when an identical sample was cross-linked in the isotropic phase. This shift represented a stabilisation of the nematic phase in the former case, in line with theoretical expectations. By utilising a novel, slow cross-linking method, which allows the polymer backbone to take up an equilibrium conformation prior to network formation, it proved possible to monitor the shifts in phase transition temperature as a function of the length of the methylene chain coupling the mesogenic units to the polymer backbone. The results obtained are related to the backbone anisotropy and indicate that the level of orientational order of the polymer in the nematic phase backbone increases with a reduction in the length of the coupling chain.

Symmetry breaking, mixing, instability, and low frequency variability in a minimal Lorenz-like system

Starting from the classical Saltzman two-dimensional convection equations, we derive via a severe spectral truncation a minimal 10 ODE system which includes the thermal effect of viscous dissipation. Neglecting this process leads to a dynamical system which includes a decoupled generalized Lorenz system. The consideration of this process breaks an important symmetry and couples the dynamics of fast and slow variables, with the ensuing modifications to the structural properties of the attractor and of the spectral features. When the relevant nondimensional number (Eckert number Ec) is different from zero, an additional time scale of O(Ec−1) is introduced in the system, as shown with standard multiscale analysis and made clear by several numerical evidences. Moreover, the system is ergodic and hyperbolic, the slow variables feature long-term memory with 1/f3/2 power spectra, and the fast variables feature amplitude modulation. Increasing the strength of the thermal-viscous feedback has a stabilizing effect, as both the metric entropy and the Kaplan-Yorke attractor dimension decrease monotonically with Ec. The analyzed system features very rich dynamics: it overcomes some of the limitations of the Lorenz system and might have prototypical value in relevant processes in complex systems dynamics, such as the interaction between slow and fast variables, the presence of long-term memory, and the associated extreme value statistics. This analysis shows how neglecting the coupling of slow and fast variables only on the basis of scale analysis can be catastrophic. In fact, this leads to spurious invariances that affect essential dynamical properties (ergodicity, hyperbolicity) and that cause the model losing ability in describing intrinsically multiscale processes.

Enhancing the catalytic repertoire of nucleic acids: a systematic study of linker length and rigidity

The incorporation of potentially catalytic groups in DNA is of interest for the in vitro selection of novel deoxyribozymes, A series of 10 C5-modified analogues of 2'-deoxyuridine triphosphate have been synthesised that possess side chains of differing flexibility and bearing a primary amino or imidazole functionality, For each series of nucleotide analogues differing degrees of flexibility of the C5 side chain was achieved through the use of alkynyl, alkenyl and alkyl moieties, The imidazole function was conjugated to these CS-amino-modified nucleotides using either imidazole 4-acetic acid or imidazole 4-acrylic acid (urocanic acid), The substrate properties of the nucleotides (fully replacing dTTP) with Taq polymerase during PCR have been investigated in order to evaluate their potential applications for in vitro selection experiments, 5-(3-Aminopropynyl)dUTP and 5-(E-3-aminopropenyl)dUTP and their imidazole 4-acetic acid- and urocanic acid-modified conjugates were found to be substrates, In contrast, C5-amino-modified dUTPs with alkane or Z-alkene linkers and their corresponding conjugates were not substrates, The incorporation of these analogues during PCR has been confirmed by inhibition of restriction enzyme digestion using XbaI and by mass spectrometry of the PCR products.

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.

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.

Restriction fragment length polymorphism of polymerase chain reaction products applied to the differentiation of poultry campylobacters for epidemiological investigations

A technique for subtyping Camplobacter jejuni isolates has been developed by using the restriction fragment length polymorphism (Rnp) of polymerase chain reaction (PCR) products of the fluA and flaB genes. The technique was validated by using strains representing 28 serotypes of C jejuni and it may also be applied to C coli. From these strains 12 distinct RFLP profiles were observed but there was no direct relationship between the RFLP profile and the serotype. One hundred and thirty-five campylobacter isolates from 15 geographically distinct broiler flocks were investigated. All the isolates could be subtyped by using the RFLP method. Isolates from most of the flocks had a single RFLP profile despite data indicating that several serotypes were involved. Although it is possible that further restriction analysis may have demonstrated profile variations in these strains, it is more likely that antigenic variation can occur within genotypically related campylobacters. As a result, serotyping may give conflicting information for veterinary epidemiological purposes. This RFLP typing scheme appears to provide a suitable tool for the investigation of the sources and routes of transmission of campylobacters in chickens.

Synergistic effects of mixing cocksfoot and sainfoin on in vitro rumen fermentation: role of condensed tannins

Some bioactive secondary metabolites in forage legumes can cause digestive interactions, so that the rumen fermentation pattern of a mixture of forages can differ from the average values of its components. The objective of this study was to investigate the potential role of condensed tannins (CT) on the synergistic effects between one grass species, cocksfoot, and one CT-containing legume species, sainfoin, on in vitro rumen fermentation characteristics. Cocksfoot and sainfoin in different proportions (in g/kg, 1000:0, 750:250, 500:500, 250:750 and 0:1000) were incubated under anaerobic conditions in culture bottles containing buffered rumen fluid from sheep. Incubations were carried out using artificial saliva with and without polyethylene glycol (PEG), which binds and thus inactivates CT. Rumen fermentation parameters describing the degradation and the fate of the energetic and nitrogenous substrates were measured at 3.5 and 24 h. At the early fermentation stage, when the sainfoin level increased from 0 to 1000 g/kg, the ammonia concentration in the medium quadratically decreased from 3.20 to 0.53 mmol/l in absence of PEG (P<0.01) but not in its presence. This result demonstrates that sainfoin CT decreased the rumen degradation of the proteins in the whole mixture, including the proteins in cocksfoot, rather than just the proteins in sainfoin. Interestingly, the total gas and methane productions were lower in mixtures incubated in absence of PEG than in presence of PEG (P<0.001) while no significant PEG effect was observed on digestibility. At the late fermentation stage, a positive quadratic effect on dry matter digestibility was detected without PEG (P<0.05), indicating a synergistic action of cocksfoot plus sainfoin on plant substrate degradation due to CT. The presence of PEG increased gas production (P<0.001) and NH3-N concentration in the medium (P<0.001). Our results suggest that CT could allow a better utilization of plant substrates in mixtures by the rumen ecosystem by improving the partitioning of degraded substrates toward lower gas losses, and decreasing the protein degradation.

Stirring and mixing in two-dimensional divergent flow

While stirring and mixing properties in the stratosphere are reasonably well understood in the context of balanced (slow) dynamics, as is evidenced in numerous studies of chaotic advection, the strongly enhanced presence of high-frequency gravity waves in the mesosphere gives rise to a significant unbalanced (fast) component to the flow. The present investigation analyses result from two idealized shallow-water numerical simulations representative of stratospheric and mesospheric dynamics on a quasi-horizontal isentropic surface. A generalization of the Hua–Klein Eulerian diagnostic to divergent flow reveals that velocity gradients are strongly influenced by the unbalanced component of the flow. The Lagrangian diagnostic of patchiness nevertheless demonstrates the persistence of coherent features in the zonal component of the flow, in contrast to the destruction of coherent features in the meridional component. Single-particle statistics demonstrate t2 scaling for both the stratospheric and mesospheric regimes in the case of zonal dispersion, and distinctive scaling laws for the two regimes in the case of meridional dispersion. This is in contrast to two-particle statistics, which in the mesospheric (unbalanced) regime demonstrate a more rapid approach to Richardson’s t3 law in the case of zonal dispersion and is evidence of enhanced meridional dispersion.

A Lagrangian model of air-mass photochemistry and mixing using a trajectory ensemble: the Cambridge Tropospheric Trajectory model of Chemistry And Transport (CiTTyCAT) version 4.2

A Lagrangian model of photochemistry and mixing is described (CiTTyCAT, stemming from the Cambridge Tropospheric Trajectory model of Chemistry And Transport), which is suitable for transport and chemistry studies throughout the troposphere. Over the last five years, the model has been developed in parallel at several different institutions and here those developments have been incorporated into one "community" model and documented for the first time. The key photochemical developments include a new scheme for biogenic volatile organic compounds and updated emissions schemes. The key physical development is to evolve composition following an ensemble of trajectories within neighbouring air-masses, including a simple scheme for mixing between them via an evolving "background profile", both within the boundary layer and free troposphere. The model runs along trajectories pre-calculated using winds and temperature from meteorological analyses. In addition, boundary layer height and precipitation rates, output from the analysis model, are interpolated to trajectory points and used as inputs to the mixing and wet deposition schemes. The model is most suitable in regimes when the effects of small-scale turbulent mixing are slow relative to advection by the resolved winds so that coherent air-masses form with distinct composition and strong gradients between them. Such air-masses can persist for many days while stretching, folding and thinning. Lagrangian models offer a useful framework for picking apart the processes of air-mass evolution over inter-continental distances, without being hindered by the numerical diffusion inherent to global Eulerian models. The model, including different box and trajectory modes, is described and some output for each of the modes is presented for evaluation. The model is available for download from a Subversion-controlled repository by contacting the corresponding authors.