Direct and inverse spectral transform for the relativistic Toda lattice and the connection with Laurent orthogonal polynomials

We introduce a spectral transform for the finite relativistic Toda lattice (RTL) in generalized form. In the nonrelativistic case, Moser constructed a spectral transform from the spectral theory of symmetric Jacobi matrices. Here we use a non-symmetric generalized eigenvalue problem for a pair of bidiagonal matrices (L,M) to define the spectral transform for the RTL. The inverse spectral transform is described in terms of a terminating T-fraction. The generalized eigenvalues are constants of motion and the auxiliary spectral data have explicit time evolution. Using the connection with the theory of Laurent orthogonal polynomials, we study the long-time behaviour of the RTL. As in the case of the Toda lattice the matrix entries have asymptotic limits. We show that L tends to an upper Hessenberg matrix with the generalized eigenvalues sorted on the diagonal, while M tends to the identity matrix.Comment: 24 pages, 9 figure

The legacy of cover crops on the soil habitat and ecosystem services in a heavy clay, minimum tillage rotation

Abstract Cover crops are grown as potential ways to improve soil fertility, soil structure, and biodiversity, while reducing weed/pest burdens. Yet, increased costs (in both time and fuel), farmer knowledge requirements, and yield uncertainty (green bridge effect and variable crop establishment) have led to hesitation among farmers. This study was conducted at the field scale (covering an area of nearly 20 hectares) to determine whether different cover crop mixtures affected soil properties and ecosystem services on a heavy clay soil. Measurements of soil chemistry, physics, biology, weed abundance, and subsequent crop performance were taken within a minimum tillage management system, across three cover crop mixtures (commonly sold to UK farmers). The cover crop mixtures included oats (Avena sativa), radish (Raphanus sativus), phacelia (Phacelia tanacetifolia), vetch (Vicia sativa), legumes, buckwheat (Fagopyrum esculentum) and a bare stubble control followed by a spring oat crop. Soil physics (penetrometer and bulk density) and chemistry (N, P, K, Mg, Ca, and organic matter) varied little across treatments, although there was significantly lower Mg in the cover crop including legumes and an increase in NO3 within this treatment. Soil biology and botanical composition were also assessed, monitoring earthworm and mesofauna abundance; and sown and unsown (weed) biomass. Epigeic earthworms were found to have significantly larger abundance in cover crop mixtures with radish present, although other meso- and macrofauna did not differ. Significant weed suppression was found during both the cover crop growing period and as a legacy in the subsequent crop, leading to significant yield increases and economic benefits in some treatments. Our study confirms that cover crops are providing benefits, even on heavy clay soils, including improvements in nutrient leaching risk reduction, weed suppression, and crop yield, coupled with wider ecosystem benefits. We therefore consider cover crops to have a role in sustainable management of arable rotations

Silica-magnesium-titanium Ziegler–Natta catalysts. Part II. Properties of the active sites and fragmentation behaviour

In this work, which follows Part I that is dedicated to the precatalyst, we investigate the electronic properties and the accessibility of the Ti active sites in a highly active silica-supported Ziegler–Natta catalyst for industrial polyethylene production, applying a multi-scale, multi-technique approach. Complementary electronic spectroscopies (i.e. Ti K-edge XANES, Ti L2,3-edge NEXAFS and DR UV–Vis-NIR) reveal the coexistence of several titanium phases, whose relative amount depends on the concentration of the alkyl aluminum activator. In addition to β-TiCl3-like clusters and monomeric Ti(IV) sites, which are already present in the precatalyst, isolated Ti(III) sites and α-TiCl3-like clusters are formed in the presence of the activator. Two families of alkylated Ti(III) sites characterized by a different electron density are detected by IR spectroscopy of adsorbed CO, and two types of Ti-acyl species are formed upon CO insertion into the Ti-alkyl bond, characterized by a different extent of η2-coordination. The whole set of data suggests that TiCl3 clusters are preferentially formed at the exterior of the catalyst particles, likely as a consequence of Ti(III) mobility in the presence of strong Lewis acids, in most cases hampering the spectroscopic detection of isolated Ti(III) sites. In contrast, only monomeric Ti(III) sites are formed at the interior of the catalyst particles, characterized by a high electron density evocative of the presence of electron donors in the close proximity (e.g. aluminum alkoxide by-products). These sites are less accessible because of diffusion limitations, and only become visible by surface-sensitive spectroscopic methods (such as Ti L2,3-edge TEY-NEXAFS) upon the fragmentation of the catalyst particles

Estimating the effects of Cry1F Bt-maize pollen on non-target Lepidoptera using a mathematical model of exposure

In farmland biodiversity, a potential risk to the larvae of non-target Lepidoptera from genetically modified (GM) Bt-maize expressing insecticidal Cry1 proteins is the ingestion of harmful amounts of pollen deposited on their host plants. A previous mathematical model of exposure quantified this risk for Cry1Ab protein. We extend this model to quantify the risk for sensitive species exposed to pollen containing Cry1F protein from maize event 1507 and to provide recommendations for management to mitigate this risk.A 14-parameter mathematical model integrating small- and large-scale exposure was used to estimate the larval mortality of hypothetical species with a range of sensitivities, and under a range of simulated mitigation measures consisting of non-Bt maize strips of different widths placed around the field edge.The greatest source of variability in estimated mortality was species sensitivity. Before allowance for effects of large-scale exposure, with moderate within-crop host-plant density and with no mitigation, estimated mortality locally was <10% for species of average sensitivity. For the worst-case extreme sensitivity considered, estimated mortality locally was 99·6% with no mitigation, although this estimate was reduced to below 40% with mitigation of 24-m-wide strips of non-Bt maize. For highly sensitive species, a 12-m-wide strip reduced estimated local mortality under 1·5%, when within-crop host-plant density was zero. Allowance for large-scale exposure effects would reduce these estimates of local mortality by a highly variable amount, but typically of the order of 50-fold.Mitigation efficacy depended critically on assumed within-crop host-plant density; if this could be assumed negligible, then the estimated effect of mitigation would reduce local mortality below 1% even for very highly sensitive species.Synthesis and applications. Mitigation measures of risks of Bt-maize to sensitive larvae of non-target lepidopteran species can be effective, but depend on host-plant densities which are in turn affected by weed-management regimes. We discuss the relevance for management of maize events where cry1F is combined (stacked) with a herbicide-tolerance trait. This exemplifies how interactions between biota may occur when different traits are stacked irrespective of interactions between the proteins themselves and highlights the importance of accounting for crop management in the assessment of the ecological impact of GM plants

Earthworm activity and availability for meadow birds is restricted in intensively managed grasslands

Earthworms are an important prey for the endangered meadow birds of northwest Europe. Although intensive grassland management with high manure inputs generally promotes earthworm abundance, it may reduce the effective food availability for meadow birds through desiccation of the topsoil, which causes earthworms to remain deeper in the soil. We studied the response of Red Worm Lumbricus rubellus, a detritivore, and Grey Worm Aporrectodea caliginosa, a geophage, to soil moisture profiles in the field and under experimental conditions. Surfacing earthworms were counted weekly in eight intensively managed grasslands (treated with high inputs of slurry by slit injection) with variable groundwater tables in the Netherlands. At each count, soil penetration resistance, soil moisture tension and groundwater level were measured, while air temperature and humidity were obtained from a nearby weather station. The response to variation in the vertical distribution of soil moisture was also experimentally studied in the two earthworm species. In the field, earthworms’ surfacing activity at night was negatively associated with soil moisture tension and positively by relative air humidity. Surprisingly, there was no effect of groundwater level; an important management variable in meadow bird conservation. Under experimental conditions, both L. rubellus and A. caliginosa moved to deeper soil layers (&gt;20 cm) in drier soil moisture treatments, avoiding the upper layer when moisture levels dropped below 30%. Synthesis and applications. We propose that in intensively managed grasslands with slurry application, topsoil desiccation reduces earthworm availability for meadow birds. This can be counteracted by keeping soil moisture tensions of the top soil above −15 kPa. We suggest that the late raising of groundwater tables in spring and the disturbance of the soil by slit injection of slurry increase topsoil desiccation. This decreases earthworm availability when it matters most for breeding meadow birds. Meadow bird conservation will benefit from revised manure application strategies that promote earthworm activity near or at the soil surface.</p

Effects of boundary conditions on magnetization switching in kinetic Ising models of nanoscale ferromagnets

Magnetization switching in highly anisotropic single-domain ferromagnets has been previously shown to be qualitatively described by the droplet theory of metastable decay and simulations of two-dimensional kinetic Ising systems with periodic boundary conditions. In this article we consider the effects of boundary conditions on the switching phenomena. A rich range of behaviors is predicted by droplet theory: the specific mechanism by which switching occurs depends on the structure of the boundary, the particle size, the temperature, and the strength of the applied field. The theory predicts the existence of a peak in the switching field as a function of system size in both systems with periodic boundary conditions and in systems with boundaries. The size of the peak is strongly dependent on the boundary effects. It is generally reduced by open boundary conditions, and in some cases it disappears if the boundaries are too favorable towards nucleation. However, we also demonstrate conditions under which the peak remains discernible. This peak arises as a purely dynamic effect and is not related to the possible existence of multiple domains. We illustrate the predictions of droplet theory by Monte Carlo simulations of two-dimensional Ising systems with various system shapes and boundary conditions.Comment: RevTex, 48 pages, 13 figure

Insights into the function of silver as an oxidation catalyst by ab initio, atomistic thermodynamics

To help understand the high activity of silver as an oxidation catalyst, e.g., for the oxidation of ethylene to epoxide and the dehydrogenation of methanol to formaldehyde, the interaction and stability of oxygen species at the Ag(111) surface has been studied for a wide range of coverages. Through calculation of the free energy, as obtained from density-functional theory and taking into account the temperature and pressure via the oxygen chemical potential, we obtain the phase diagram of O/Ag(111). Our results reveal that a thin surface-oxide structure is most stable for the temperature and pressure range of ethylene epoxidation and we propose it (and possibly other similar structures) contains the species actuating the catalysis. For higher temperatures, low coverages of chemisorbed oxygen are most stable, which could also play a role in oxidation reactions. For temperatures greater than about 775 K there are no stable oxygen species, except for the possibility of O atoms adsorbed at under-coordinated surface sites Our calculations rule out thicker oxide-like structures, as well as bulk dissolved oxygen and molecular ozone-like species, as playing a role in the oxidation reactions.Comment: 15 pages including 9 figures, Related publications can be found at http://www.fhi-berlin.mpg.de/th/paper.htm

The Three Rs: The Way Forward

This is the report of the eleventh of a series of workshops organised by the European Centre for the Validation of Alternative Methods (ECVAM), which was established in 1991 by the European Commission. ECVAM\u27s main goal, as defined in 1993 by its Scientific Advisory Committee, is to promote the scientific and regulatory acceptance of alternative methods which are of importance to the biosciences and which reduce, refine or replace the use of laboratory animals. One of the first priorities set by ECVAM was the implementation of procedures which would enable it to become well-informed about the state-of-the-art of non-animal test development and validation. and the potential for the possible incorporation of replacement alternative tests into regulatory procedures. It was decided that this would be best achieved by the organisation of ECVAM workshops on specific topics, at which small groups of invited experts would review the current status of various types of in vitro tests and their potential uses, and make recommendations about the best ways forward