Boundary value problems for third-order linear PDEs in time-dependent domains

We present the extension of a methodology to solve moving boundary value problems from the second-order case to the case of the third-order linear evolution PDE qt + qxxx = 0. This extension is the crucial step needed to generalize this methodology to PDEs of arbitrary order. The methodology is based on the derivation of inversion formulae for a class of integral transforms that generalize the Fourier transform and on the analysis of the global relation associated with the PDE. The study of this relation and its inversion using the appropriate generalized transform are the main elements of the proof of our results.

The Klein-Gordon equation on the half line: a Riemann-Hilbert approach

We solve an initial-boundary problem for the Klein-Gordon equation on the half line using the Riemann-Hilbert approach to solving linear boundary value problems advocated by Fokas. The approach we present can be also used to solve more complicated boundary value problems for this equation, such as problems posed on time-dependent domains. Furthermore, it can be extended to treat integrable nonlinearisations of the Klein-Gordon equation. In this respect, we briefly discuss how our results could motivate a novel treatment of the sine-Gordon equation.

Long-term effectiveness of sowing high and low diversity seed mixtures to enhance plant community development on ex-arable fields

Questions: How is succession on ex-arable land affected by sowing high and low diversity mixtures of grassland species as compared to natural succession? How long do effects persist? Location: Experimental plots installed in the Czech Republic, The Netherlands, Spain, Sweden and the United Kingdom. Methods: The experiment was established on ex-arable land, with five blocks, each containing three 10 m x 10 m experiment tal plots: natural colonization, a low- (four species) and high-diversity (15 species) seed mixture. Species composition and biomass was followed for eight years. Results: The sown plants considerably affected the whole successional pathway and the effects persisted during the whole eight year period. Whilst the proportion of sown species (characterized by their cover) increased during the study period, the number of sown species started to decrease from the third season onwards. Sowing caused suppression of natural colonizing species, and the sown plots had more biomass. These effects were on average larger in the high diversity mixtures. However, the low diversity replicate sown with the mixture that produced the largest biomass or largest suppression of natural colonizers fell within the range recorded at the five replicates of the high diversity plots. The natural colonization plots usually had the highest total species richness and lowest productivity at the end of the observation period. Conclusions: The effect of sowing demonstrated dispersal limitation as a factor controlling the rate of early secondary succession. Diversity was important primarily for its 'insurance effect': the high diversity mixtures were always able to compensate for the failure of some species.

The impact of Rhinanthus minor in newly established meadows on a productive site

Question: What is the impact of the presence of Rhinanthus minor on forb abundance in newly established swards? Location: Wetherby, West Yorkshire, UK (53 degrees 55' N, 1 degrees 22(1) W). Method: A standard meadow mix containing six forbs and six grasses was sown on an ex-arable field and immediately over-sown using a randomised plot design with three densities of Rhinanthus minor (0, 600, and 1000 seeds per m(2)). Above-ground biomass was analysed over a period of three years, while detailed assessments of sward composition were performed during the first two years. Results: Values of grass biomass were reduced in the presence of Rhinanthus, especially at the higher sowing density. The ratio of grass: forb biomass was also lower in association with Rhinanthus, but only at the higher sowing density. The presence of Rhinanthus, had no effect on species number or diversity, which decreased between years regardless of treatment. Conclusions: Although not tested in a multi-site experiment, the benefit of introducing Rhinanthus into newly established swards to promote for abundance was determined. The efficacy of Rhinanthus presence is likely to depend on whether species not susceptible to the effects of parasitism are present.

Modelling the structure of a polymer glass poly(methylmethacrylate) through neutron scattering experiments

Determination of the local structure of a polymer glass by scattering methods is complex due to the number of spatial and orientational correlations, both from within the polymer chain (intrachain) and between neighbouring chains (interchain), from which the scattering arises. Recently considerable advances have been made in the structural analysis of relatively simple polymers such as poly(ethylene) through the use of broad Q neutron scattering data tightly coupled to atomistic modelling procedures. This paper presents the results of an investigation into the use of these procedures for the analysis of the local structure of a-PMMA which is chemically more complex with a much greater number of intrachain structural parameters. We have utilised high quality neutron scattering data obtained using SANDALS at ISIS coupled with computer models representing both the single chain and bulk polymer system. Several different modelling approaches have been explored which encompass such techniques as Reverse Monte Carlo refinement and energy minimisation and their relative merits and successes are discussed. These different approaches highlight structural parameters which any realistic model of glassy atactic PMMA must replicate.

Effect of processed and red meat on endogenous nitrosation and DNA damage

Haem in red meat (RM) stimulates the endogenous production of mutagenic nitroso compounds (NOC). Processed (nitrite-preserved red) meat additionally contains high concentrations of preformed NOC. In two studies, of a fresh RM versus a vegetarian (VEG) diet (six males and six females) and of a nitrite-preserved red meat (PM) versus a VEG diet (5 males and 11 females), we investigated whether processing of meat might increase colorectal cancer risk by stimulating nitrosation and DNA damage. Meat diets contained 420 g (males) or 366 g (females) meat/per day. Faecal homogenates from day 10 onwards were analysed for haem and NOC and asso- ciated supernatants for genotoxicity. Means are adjusted for differ- ences in male to female ratios between studies. Faecal NOC concentrations on VEG diets were low (2.6 and 3.5 mmol/g) but significantly higher on meat diets (PM 175 ± 19 nmol/g versus RM 185 ± 22 nmol/g; P 5 0.75). The RM diet resulted in a larger pro- portion of nitrosyl iron (RM 78% versus PM 54%; P < 0.0001) and less nitrosothiols (RM 12% versus PM 19%; P < 0.01) and other NOC (RM 10% versus PM 27%; P < 0.0001). There was no statis- tically significant difference in DNA breaks induced by faecal water (FW) following PM and RM diets (P 5 0.80). However, PM re- sulted in higher levels of oxidized pyrimidines (P < 0.05). Surpris- ingly, VEG diets resulted in significantly more FW-induced DNA strand breaks than the meat diets (P < 0.05), which needs to be clarified in further studies. Meats cured with nitrite have the same effect as fresh RM on endogenous nitrosation but show increased FW-induced oxidative DNA damage.

Influence of the quasi-biennial oscillation on the extratropical winter stratosphere in an atmospheric general circulation model and in reanalysis data

The interannual variability of the stratospheric polar vortex during winter in both hemispheres is observed to correlate strongly with the phase of the quasi-biennial oscillation (QBO) in tropical stratospheric winds. It follows that the lack of a spontaneously generated QBO in most atmospheric general circulation models (AGCMs) adversely affects the nature of polar variability in such models. This study examines QBO–vortex coupling in an AGCM in which a QBO is spontaneously induced by resolved and parameterized waves. The QBO–vortex coupling in the AGCM compares favorably to that seen in reanalysis data [from the 40-yr ECMWF Re-Analysis (ERA-40)], provided that careful attention is given to the definition of QBO phase. A phase angle representation of the QBO is employed that is based on the two leading empirical orthogonal functions of equatorial zonal wind vertical profiles. This yields a QBO phase that serves as a proxy for the vertical structure of equatorial winds over the whole depth of the stratosphere and thus provides a means of subsampling the data to select QBO phases with similar vertical profiles of equatorial zonal wind. Using this subsampling, it is found that the QBO phase that induces the strongest polar vortex response in early winter differs from that which induces the strongest late-winter vortex response. This is true in both hemispheres and for both the AGCM and ERA-40. It follows that the strength and timing of QBO influence on the vortex may be affected by the partial seasonal synchronization of QBO phase transitions that occurs both in observations and in the model. This provides a mechanism by which changes in the strength of QBO–vortex correlations may exhibit variability on decadal time scales. In the model, such behavior occurs in the absence of external forcings or interannual variations in sea surface temperatures.

Irreversible compressible work and APE dissipation in turbulent stratified fluid

Although it plays a key role in the theory of stratified turbulence, the concept of available potential energy (APE) dissipation has remained until now a rather mysterious quantity, owing to the lack of rigorous result about its irreversible character or energy conversion type. Here, we show by using rigorous energetics considerations rooted in the analysis of the Navier-Stokes for a fully compressible fluid with a nonlinear equation of state that the APE dissipation is an irreversible energy conversion that dissipates kinetic energy into internal energy, exactly as viscous dissipation. These results are established by showing that APE dissipation contributes to the irreversible production of entropy, and by showing that it is a part of the work of expansion/contraction. Our results provide a new interpretation of the entropy budget, that leads to a new exact definition of turbulent effective diffusivity, which generalizes the Osborn-Cox model, as well as a rigorous decomposition of the work of expansion/contraction into reversible and irreversible components. In the context of turbulent mixing associated with parallel shear flow instability, our results suggests that there is no irreversible transfer of horizontal momentum into vertical momentum, as seems to be required when compressible effects are neglected, with potential consequences for the parameterisations of momentum dissipation in the coarse-grained Navier-Stokes equations.

Continuous-flow processing of gaseous ammonia using a Teflon AF-2400 tube-in-tube reactor: synthesis of thioureas and in-line titrations

A simple tube-in-tube reactor based on the gas-permeable membrane Teflon AF-2400 was used in the continuous flow reaction of gaseous ammonia with isothiocyanates and one isocyanate. A colourimetric in-line titration technique is also reported as a simple method to quantify the amount of ammonia taken up by the solvent in the system.

A SNP-based consensus genetic map for synteny-based trait targeting in faba bean (Vicia faba L.)

Faba bean (Vicia faba L.) is a globally important nitrogen-fixing legume, which is widely grown in a diverse range of environments. In this work, we mine and validate a set of 845 SNPs from the aligned transcriptomes of two contrasting inbred lines. Each V. faba SNP is assigned by BLAST analysis to a single Medicago orthologue. This set of syntenically anchored polymorphisms were then validated as individual KASP assays, classified according to their informativeness and performance on a panel of 37 inbred lines, and the best performing 757 markers used to genotype six mapping populations. The six resulting linkage maps were merged into a single consensus map on which 687 SNPs were placed on six linkage groups, each presumed to correspond to one of the six V. faba chromosomes. This sequence-based consensus map was used to explore synteny with the most closely-related crop species, lentil, and the most closely related fully sequenced genome, Medicago. Large tracts of uninterrupted colinearity were found between faba bean and Medicago, making it relatively straightforward to predict gene content and order in mapped genetic interval. As a demonstration of this, we mapped a flower colour gene to a 2 cM interval of Vf chromosome 2 which was highly collinear with Mt3. The obvious candidate gene from 77 gene models in the collinear Medicago chromosome segment was the previously characterized MtWD40-1 gene (Mt3g092830, Mt3g092840) controlling anthocyanin production in Medicago and re-sequencing of the Vf orthologue showed a putative causative deletion of the entire 5’ end of the gene.