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

Three-year tracking of fatty acid composition of plasma phospholipids in healthy children

Objectives: The fatty acid composition of plasma phospholipids reflects the dietary fatty acid intake as well as endogenous turnover. We aimed at investigating the potential tracking of plasma phospholipid fatty acid composition in children that participated in a prospective cohort study. Methods: 26 healthy children participated in a longitudinal study on health risks and had been enrolled after birth. All children were born at term with birth weights appropriate for gestational age. Follow-up took place at ages 24, 36 and 60 months. At each time point a 24-hour dietary recall was obtained, anthropometric parameters were measured and a blood sample for phospholipid fatty acid analysis was taken. Results: Dietary intake of saturated (SFA), monounsaturated (MUFA) and polyunsaturated (PUFA) fatty acids at the three time points were not correlated. We found lower values for plasma MUFA and the MUFA/SFA ratio at 60 months compared to 24 months. In contrast, total PUFA, total n-6 and n-6 long-chain polyunsaturated fatty acids (LC-PUFA) were higher at 60 months. Significant averaged correlation coefficients (average of Pearson's R for 24 versus 36 months and 36 versus 60 months) were found for n-6 LC-PUFA (r = 0.67), n-6/n-3 LC-PUFA ratio (r = 0.59) and arachidonic acid/linoleic acid ratio (r = 0.64). Partial tracking was found for the docosahexaenoic acid/alpha-linolenic acid ratio (r = 0.33). Body mass index and sum of skinfolds Z-scores were similar in the three evaluations. Conclusions: A significant tracking of n-6 LC-PUFA, n-6 LC-PUFA/n-3 LC-PUFA ratio, arachidonic acid/ linoleic acid ratio and docosahexaenoic acid/alpha-linolenic acid ratio may reflect an influence of individual endogenous fatty acid metabolism on plasma concentrations of some, but not all, fatty acids. Copyright (c) 2007 S. Karger AG, Basel

Wall Crossing, Quivers and Crystals

We study the spectrum of BPS D-branes on a Calabi-Yau manifold using the 0+1 dimensional quiver gauge theory that describes the dynamics of the branes at low energies. The results of Kontsevich and Soibelman predict how the degeneracies change. We argue that Seiberg dualities of the quiver gauge theories, which change the basis of BPS states, correspond to crossing the "walls of the second kind." There is a large class of examples, including local del Pezzo surfaces, where the BPS degeneracies of quivers corresponding to one D6 brane bound to arbitrary numbers of D4, D2 and D0 branes are counted by melting crystal configurations. We show that the melting crystals that arise are a discretization of the Calabi-Yau geometry. The shape of the crystal is determined by the Calabi-Yau geometry and the background B-field, and its microscopic structure by the quiver Q. We prove that the BPS degeneracies computed from Q and Q' are related by the Kontsevich Soibelman formula, using a geometric realization of the Seiberg duality in the crystal. We also show that, in the limit of infinite B-field, the combinatorics of crystals arising from the quivers becomes that of the topological vertex. We thus re-derive the Gromov-Witten/Donaldson-Thomas correspondence

Reaction rates and transport in neutron stars

Understanding signals from neutron stars requires knowledge about the transport inside the star. We review the transport properties and the underlying reaction rates of dense hadronic and quark matter in the crust and the core of neutron stars and point out open problems and future directions.Comment: 74 pages; commissioned for the book "Physics and Astrophysics of Neutron Stars", NewCompStar COST Action MP1304; version 3: minor changes, references updated, overview graphic added in the introduction, improvements in Sec IV.A.

Performance benchmarks for a next generation numerical dynamo model

Numerical simulations of the geodynamo have successfully represented many observable characteristics of the geomagnetic field, yielding insight into the fundamental processes that generate magnetic fields in the Earth's core. Because of limited spatial resolution, however, the diffusivities in numerical dynamo models are much larger than those in the Earth's core, and consequently, questions remain about how realistic these models are. The typical strategy used to address this issue has been to continue to increase the resolution of these quasi-laminar models with increasing computational resources, thus pushing them toward more realistic parameter regimes. We assess which methods are most promising for the next generation of supercomputers, which will offer access to O(106) processor cores for large problems. Here we report performance and accuracy benchmarks from 15 dynamo codes that employ a range of numerical and parallelization methods. Computational performance is assessed on the basis of weak and strong scaling behavior up to 16,384 processor cores. Extrapolations of our weak-scaling results indicate that dynamo codes that employ two-dimensional or three-dimensional domain decompositions can perform efficiently on up to ∼106 processor cores, paving the way for more realistic simulations in the next model generation

Search for new phenomena in final states with an energetic jet and large missing transverse momentum in pp collisions at √ s = 8 TeV with the ATLAS detector

Results of a search for new phenomena in final states with an energetic jet and large missing transverse momentum are reported. The search uses 20.3 fb−1 of √ s = 8 TeV data collected in 2012 with the ATLAS detector at the LHC. Events are required to have at least one jet with pT > 120 GeV and no leptons. Nine signal regions are considered with increasing missing transverse momentum requirements between Emiss T > 150 GeV and Emiss T > 700 GeV. Good agreement is observed between the number of events in data and Standard Model expectations. The results are translated into exclusion limits on models with either large extra spatial dimensions, pair production of weakly interacting dark matter candidates, or production of very light gravitinos in a gauge-mediated supersymmetric model. In addition, limits on the production of an invisibly decaying Higgs-like boson leading to similar topologies in the final state are presente

Dynamic sea level changes following changes in the thermohaline circulation

Using the coupled climate model CLIMBER-3a, we investigate changes in sea surface elevation due to a weakening of the thermohaline circulation (THC). In addition to a global sea level rise due to a warming of the deep sea, this leads to a regional dynamic sea level change which follows quasi-instantaneously any change in the ocean circulation. We show that the magnitude of this dynamic effect can locally reach up to ~1m, depending on the initial THC strength. In some regions the rate of change can be up to 20-25 mm/yr. The emerging patterns are discussed with respect to the oceanic circulation changes. Most prominent is a south-north gradient reflecting the changes in geostrophic surface currents. Our results suggest that an analysis of observed sea level change patterns could be useful for monitoring the THC strength.Comment: Climate Dynamics (2004), submitted. See also http://www.pik-potsdam.de/~ander

Theorems on existence and global dynamics for the Einstein equations

This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is surveyed. Global results for solutions with various types of symmetry are discussed. A selection of results from Newtonian theory and special relativity that offer useful comparisons is presented. Treatments of global results in the case of small data and results on constructing spacetimes with prescribed singularity structure or late-time asymptotics are given. A conjectural picture of the asymptotic behaviour of general cosmological solutions of the Einstein equations is built up. Some miscellaneous topics connected with the main theme are collected in a separate section.Comment: Submitted to Living Reviews in Relativity, major update of Living Rev. Rel. 5 (2002)

FADS2 Genetic Variance in Combination with Fatty Acid Intake Might Alter Composition of the Fatty Acids in Brain

Multiple lines of evidence suggest that fatty acids (FA) play an important role in cognitive function. However, little is known about the functional genetic pathways involved in cognition. The main goals of this study were to replicate previously reported interaction effects between breast feeding (BF) and FA desaturase (FADS) genetic variation on IQ and to investigate the possible mechanisms by which these variants might moderate BF effect, focusing on brain expression. Using a sample of 534 twins, we observed a trend in the moderation of BF effects on IQ by FADS2 variation. In addition, we made use of publicly available gene expression databases from both humans (193) and mice (93) and showed that FADS2 variants also correlate with FADS1 brain expression (P-value<1.1E-03). Our results provide novel clues for the understanding of the genetic mechanisms regulating FA brain expression and improve the current knowledge of the FADS moderation effect on cognition

Nothing Lasts Forever: Environmental Discourses on the Collapse of Past Societies

The study of the collapse of past societies raises many questions for the theory and practice of archaeology. Interest in collapse extends as well into the natural sciences and environmental and sustainability policy. Despite a range of approaches to collapse, the predominant paradigm is environmental collapse, which I argue obscures recognition of the dynamic role of social processes that lie at the heart of human communities. These environmental discourses, together with confusion over terminology and the concepts of collapse, have created widespread aporia about collapse and resulted in the creation of mixed messages about complex historical and social processes