The Einstein-Vlasov sytem/Kinetic theory

The main purpose of this article is to guide the reader to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades where the main focus has been on nonrelativistic- and special relativistic physics, e.g. to model the dynamics of neutral gases, plasmas and Newtonian self-gravitating systems. In 1990 Rendall and Rein initiated a mathematical study of the Einstein-Vlasov system. Since then many theorems on global properties of solutions to this system have been established. The Vlasov equation describes matter phenomenologically and it should be stressed that most of the theorems presented in this article are not presently known for other such matter models (e.g. fluid models). The first part of this paper gives an introduction to kinetic theory in non-curved spacetimes and then the Einstein-Vlasov system is introduced. We believe that a good understanding of kinetic theory in non-curved spacetimes is fundamental in order to get a good comprehension of kinetic theory in general relativity.Comment: 31 pages. This article has been submitted to Living Rev. Relativity (http://www.livingreviews.org

The Einstein-Vlasov System/Kinetic Theory

The main purpose of this article is to provide a guide to theorems on global properties of solutions to the Einstein--Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades in which the main focus has been on non-relativistic and special relativistic physics, i.e., to model the dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In 1990, Rendall and Rein initiated a mathematical study of the Einstein--Vlasov system. Since then many theorems on global properties of solutions to this system have been established.Comment: Published version http://www.livingreviews.org/lrr-2011-

Food for pollinators: quantifying the nectar and pollen resources of urban flower meadows

Planted meadows are increasingly used to improve the biodiversity and aesthetic amenity value of urban areas. Although many ‘pollinator-friendly’ seed mixes are available, the floral resources these provide to flower-visiting insects, and how these change through time, are largely unknown. Such data are necessary to compare the resources provided by alternative meadow seed mixes to each other and to other flowering habitats. We used quantitative surveys of over 2 million flowers to estimate the nectar and pollen resources offered by two exemplar commercial seed mixes (one annual, one perennial) and associated weeds grown as 300m2 meadows across four UK cities, sampled at six time points between May and September 2013. Nectar sugar and pollen rewards per flower varied widely across 65 species surveyed, with native British weed species (including dandelion, Taraxacum agg.) contributing the top five nectar producers and two of the top ten pollen producers. Seed mix species yielding the highest rewards per flower included Leontodon hispidus, Centaurea cyanus and C. nigra for nectar, and Papaver rhoeas, Eschscholzia californica and Malva moschata for pollen. Perennial meadows produced up to 20x more nectar and up to 6x more pollen than annual meadows, which in turn produced far more than amenity grassland controls. Perennial meadows produced resources earlier in the year than annual meadows, but both seed mixes delivered very low resource levels early in the year and these were provided almost entirely by native weeds. Pollen volume per flower is well predicted statistically by floral morphology, and nectar sugar mass and pollen volume per unit area are correlated with flower counts, raising the possibility that resource levels can be estimated for species or habitats where they cannot be measured directly. Our approach does not incorporate resource quality information (for example, pollen protein or essential amino acid content), but can easily do so when suitable data exist. Our approach should inform the design of new seed mixes to ensure continuity in floral resource availability throughout the year, and to identify suitable species to fill resource gaps in established mixes

An evaluation of the Land and Environment Planning Toolkit for advancing soil and nutrient management on sheep and beef farms

Publishe

Using DNA metabarcoding to investigate honey bee foraging reveals limited flower use despite high floral availability

Understanding which flowers honey bees (Apis mellifera) use for forage can help us to provide suitable plants for healthy honey bee colonies. Accordingly, honey DNA metabarcoding provides a valuable tool for investigating pollen and nectar collection. We investigated early season (April and May) floral choice by honey bees provided with a very high diversity of flowering plants within the National Botanic Garden of Wales. There was a close correspondence between the phenology of flowering and the detection of plants within the honey. Within the study area there were 437 genera of plants in flower during April and May, but only 11% of these were used. Thirty-nine plant taxa were recorded from three hives but only ten at greater than 1%. All three colonies used the same core set of native or near-native plants, typically found in hedgerows and woodlands. The major plants were supplemented with a range of horticultural species, with more variation in plant choice between the honey bee colonies. We conclude that during the spring, honey bees need access to native hedgerows and woodlands to provide major plants for foraging. Gardens provide supplementary flowers that may increase the nutritional diversity of the honey bee diet