Jordan cells in logarithmic limits of conformal field theory

It is discussed how a limiting procedure of conformal field theories may result in logarithmic conformal field theories with Jordan cells of arbitrary rank. This extends our work on rank-two Jordan cells. We also consider the limits of certain three-point functions and find that they are compatible with known results. The general construction is illustrated by logarithmic limits of (unitary) minimal models in conformal field theory. Characters of quasi-rational representations are found to emerge as the limits of the associated irreducible Virasoro characters.Comment: 16 pages, v2: discussion of three-point functions and characters included; ref. added, v3: version to be publishe

Higher su(N) tensor products

We extend our recent results on ordinary su(N) tensor product multiplicities to higher su(N) tensor products. Particular emphasis is put on four-point couplings where the tensor product of four highest weight modules is considered. The number of times the singlet occurs in the decomposition is the associated multiplicity. In this framework, ordinary tensor products correspond to three-point couplings. As in that case, the four-point multiplicity may be expressed explicitly as a multiple sum measuring the discretised volume of a convex polytope. This description extends to higher-point couplings as well. We also address the problem of determining when a higher-point coupling exists, i.e., when the associated multiplicity is non-vanishing. The solution is a set of inequalities in the Dynkin labels.Comment: 17 pages, LaTe

15Nitrogen uptake from shallow- versus deep-rooted plants in multi-species mixtures and monoculture grassland

Only few studies have explored the importance of functional diversity in temperate agricultural grasslands in relation to nitrogen (N) uptake. This study investigates the consequence of growing deep-rooted plants together with grass-clover mixtures in terms of N uptake efficiency from deep soil layers. The objective was to compare the N uptake of the shallow-rooted grassland species Lolium perenne and Trifolium repens; and the deep-rooted species Cichorium intybus and Medicago sativa in monocultures and mixtures. We hypothesized that growing deep-rooted plant species in mixture with shallow-rooted species increases the N uptake from deep soil layers partly through competition. A 15N tracer study was carried out with 15N enriched ammonium-sulphate placed at three different soil depths (40, 80 and 120 cm). To recover 15N, above-ground plant biomass was harvested after 10 days. We described the decline of 15N uptake with depth by using an exponential decay function. The studied plant communities showed the same relative decline in 15N uptake by increasing soil depths, but different capacities in total 15N uptake. Monoculture L. perenne foraged less 15N in all depths compared to the other four plant communities. The relative 15N uptake of individual plant species grown in mixture decreased stronger with depth than in monoculture. Thus, both findings rejected our hypothesis

Polynomial Fusion Rings of Logarithmic Minimal Models

We identify quotient polynomial rings isomorphic to the recently found fundamental fusion algebras of logarithmic minimal models.Comment: 18 page

15Nitrogen transfer from legumes to neighbouring plants in multi-species grassland

This study investigates the N transfer from legumes to neighbouring plants, grasses, legumes and herbs in a temperate grassland. In a field experiment white clover (Trifolium repens), red clover (Trifolium pratense) and lucerne (Medicago sativa) were leaf-labelled with 15N enriched urea. The 15N tracer was measured in above-ground plant tissue of eight neighbouring plants in two subsequent harvests in 2008. The three legumes donated 15N to all neighbouring plants, of which grasses, white and red clover were strong receivers. Results show that N transfer increases with N application and from the 1st to the 2nd cut

Biomass production and N2-fixation in seven grass-legume mixtures

Inclusion of forage legumes in low-input grassland mixtures improves biomass production and soil fertility trough addition of nitrogen (N) from N2-fixation. The impacts of different mixture of legumes and companion grasses on the N production of the forage mixture have rarely been investigated under comparable soil and climatic conditions. We conducted a field experiment on a sandy soil at two nitrogen levels with seven two-species grassland mixtures: alfalfa (Medicago sativa), bird’s-foot trefoil (Lotus corniculatus), red clover (Trifolium pratense), or white clover (Trifolium repens) in mixture with perennial ryegrass (Lolium perenne), and white clover in mixture with meadow fescue (Festuca pratensis), timothy (Phleum pratense), or hybrid ryegrass (Lolium hybridum). Red clover and alfalfa fixed 400-500 kg N ha-1 and bird ’s-foot trefoil just above 100 kg N ha-1 in aboveground biomass. The white clover N fixation was affected by the companion grass species and ranged from 150 to 175 kg N ha-1. Fertilization had different effects on N2-fixation among the legumes, but also significant effects on white clover N2-fixation depending on the companion grass species

Composting rapidly degrades DNA from genetically modified plants

Organic farmers are concerned about the use of genetically modified plants (GM plants) in conventional agriculture. The concern is mainly focused on the risk of spreading of pollen or seeds from GM plans to adjacent fields. There has been less focus on the environmental impact of exposing the soil to genetically modified DNA (i.e. transgenic DNA) from GM plants residues left in the field. Yet, the new EU directive on the deliberate release into the environment of genetically modified organisms (EU, 2001) requires a "description of post-release treatment methods for the genetically modified plant material including wastes"

Grassland carbon sequestration and emissions following cultivation in a mixed crop rotation

Grasslands are potential carbon sinks to reduce unprecedented increase in atmospheric CO2. Effect of age (1 to 4-yr-old) and management (slurry, grazing multispecies mixture) of a grass phase mixed crop rotation on carbon sequestration and emissions upon cultivation was compared with 17-yr-old grassland and a pea field as reference. Aboveground and root biomass were determined and soils were incubated to study CO2 emissions after soil disturbance. Aboveground biomass was highest in 1-yr-old grassland with slurry application and lowest in 4-yr-old grassland without slurry application. Root biomass was highest in 4-yr-old grassland, but all 1 to 4-yr-old grasslands were in between the pea field (0.81±0.094 g kg-1 soil) and the 17-yr-old grassland (3.17±0.22 g kg-1 soil). Grazed grasslands had significantly higher root biomass than cut grasslands. There was no significant difference in the CO2 emissions within 1 to 4-yr-old grasslands. Only the 17-yr-old grassland showed markedly higher CO2 emissions (4.9 ± 1.1 g CO2 kg-1 soil). Differences in aboveground and root biomass did not affect CO2 emissions, and slurry application did not either. The substantial increase in root biomass with age but indifference in CO2 emissions across the age and management in temporary grasslands, thus, indicates potential for long-term sequestration of soil C