Singularities of Algebraic Differential Equations

We combine algebraic and geometric approaches to general systems of algebraic ordinary or partial differential equations to provide a unified framework for the definition and detection of singularities of a given system at a fixed order. Our three main results are firstly a proof that even in the case of partial differential equations regular points are generic. Secondly, we present an algorithm for the effective detection of all singularities at a given order or, more precisely, for the determination of a regularity decomposition. Finally, we give a rigorous definition of a regular differential equation, a notion that is ubiquitous in the geometric theory of differential equations, and show that our algorithm extracts from each prime component a regular differential equation. Our main algorithmic tools are on the one hand the algebraic resp. differential Thomas decomposition and on the other hand the Vessiot theory of differential equations.Comment: 45 pages, 5 figure

On the General Analytical Solution of the Kinematic Cosserat Equations

Based on a Lie symmetry analysis, we construct a closed form solution to the kinematic part of the (partial differential) Cosserat equations describing the mechanical behavior of elastic rods. The solution depends on two arbitrary analytical vector functions and is analytical everywhere except a certain domain of the independent variables in which one of the arbitrary vector functions satisfies a simple explicitly given algebraic relation. As our main theoretical result, in addition to the construction of the solution, we proof its generality. Based on this observation, a hybrid semi-analytical solver for highly viscous two-way coupled fluid-rod problems is developed which allows for the interactive high-fidelity simulations of flagellated microswimmers as a result of a substantial reduction of the numerical stiffness.Comment: 14 pages, 3 figure

Consumption of atmospheric methane by tundra soils

EMISSION of methane from tundra soil contributes about 10% of the global atmospheric methane budget1. Moreover, tundra soils contain 15% of global soil carbon2, so the response of this large carbon reservoir to projected global warming3,4 could be important. Coupled biological models3-6 predict that a warmer climate will increase methane emission through increased rates of methanogenesis. Microbial oxidation of methane is, however, a possible control on emissions that has previously been overlooked. Here we report the results of field and laboratory experiments on methane consumption by tundra soils. For methane concentrations ranging from below to well above ambient, moist soils were found to consume methane rapidly; in non-waterlogged soils, equilibration with atmospheric methane was fast relative to microbial oxidation. We conclude that lowering of the water table in tundra as a result of a warmer, drier climate will decrease methane fluxes and could cause these areas to provide a negative feedback for atmospheric methane. © 1990 Nature Publishing Group

Africa and the global carbon cycle

The African continent has a large and growing role in the global carbon cycle, with potentially important climate change implications. However, the sparse observation network in and around the African continent means that Africa is one of the weakest links in our understanding of the global carbon cycle. Here, we combine data from regional and global inventories as well as forward and inverse model analyses to appraise what is known about Africa's continental-scale carbon dynamics. With low fossil emissions and productivity that largely compensates respiration, land conversion is Africa's primary net carbon release, much of it through burning of forests. Savanna fire emissions, though large, represent a short-term source that is offset by ensuing regrowth. While current data suggest a near zero decadal-scale carbon balance, interannual climate fluctuations (especially drought) induce sizeable variability in net ecosystem productivity and savanna fire emissions such that Africa is a major source of interannual variability in global atmospheric CO(2). Considering the continent's sizeable carbon stocks, their seemingly high vulnerability to anticipated climate and land use change, as well as growing populations and industrialization, Africa's carbon emissions and their interannual variability are likely to undergo substantial increases through the 21st century

From Global to Local and Vice Versa: On the Importance of the 'Globalization' Agenda in Continental Groundwater Research and Policy-Making.

Groundwater is one of the most important environmental resources and its use continuously rises globally for industrial, agricultural, and drinking water supply purposes. Because of its importance, more knowledge about the volume of usable groundwater is necessary to satisfy the global demand. Due to the challenges in quantifying the volume of available global groundwater, studies which aim to assess its magnitude are limited in number. They are further restricted in scope and depth of analysis as, in most cases, they do not explain how the estimates of global groundwater resources have been obtained, what methods have been used to generate the figures and what levels of uncertainty exist. This article reviews the estimates of global groundwater resources. It finds that the level of uncertainty attached to existing numbers often exceeds 100 % and strives to establish the reasons for discrepancy. The outcome of this study outlines the need for a new agenda in water research with a more pronounced focus on groundwater. This new research agenda should aim at enhancing the quality and quantity of data provision on local and regional groundwater stocks and flows. This knowledge enhancement can serve as a basis to improve policy-making on groundwater resources globally. Research-informed policies will facilitate more effective groundwater management practices to ensure a more rapid progress of the global water sector towards the goal of sustainability

A 1-Year Study of Endurance Runners: Training, Laboratory Tests, and Field Tests

Purpose: To compare critical speed (CS) measured from a single-visit field test of the distance–time relationship with the “traditional” treadmill time-to-exhaustion multivisit protocol. Methods: Ten male distance runners completed treadmill and field tests to calculate CS and the maximum distance performed above CS (D′). The field test involved 3 runs on a single visit to an outdoor athletics track over 3600, 2400, and 1200 m. Two field-test protocols were evaluated using either a 30-min recovery or a 60-min recovery between runs. The treadmill test involved runs to exhaustion at 100%, 105%, and 110% of velocity at VO2max, with 24 h recovery between runs. Results: There was no difference in CS measured with the treadmill and 30-min- and 60-minrecovery field tests (P .05). A typical error of the estimate of 0.14 m/s (95% confidence limits 0.09–0.26 m/s) was seen for CS and 88 m (95% confidence limits 60–169 m) for D′. A coefficient of variation of 0.4% (95% confidence limits: 0.3–0.8%) was found for repeat tests of CS and 13% (95% confidence limits 10–27%) for D′. Conclusion: The single-visit method provides a useful alternative for assessing CS in the field

Present state and future perspectives of using pluripotent stem cells in toxicology research

The use of novel drugs and chemicals requires reliable data on their potential toxic effects on humans. Current test systems are mainly based on animals or in vitro–cultured animal-derived cells and do not or not sufficiently mirror the situation in humans. Therefore, in vitro models based on human pluripotent stem cells (hPSCs) have become an attractive alternative. The article summarizes the characteristics of pluripotent stem cells, including embryonic carcinoma and embryonic germ cells, and discusses the potential of pluripotent stem cells for safety pharmacology and toxicology. Special attention is directed to the potential application of embryonic stem cells (ESCs) and induced pluripotent stem cells (iPSCs) for the assessment of developmental toxicology as well as cardio- and hepatotoxicology. With respect to embryotoxicology, recent achievements of the embryonic stem cell test (EST) are described and current limitations as well as prospects of embryotoxicity studies using pluripotent stem cells are discussed. Furthermore, recent efforts to establish hPSC-based cell models for testing cardio- and hepatotoxicity are presented. In this context, methods for differentiation and selection of cardiac and hepatic cells from hPSCs are summarized, requirements and implications with respect to the use of these cells in safety pharmacology and toxicology are presented, and future challenges and perspectives of using hPSCs are discussed