Order-of-magnitude speedup for steady states and traveling waves via Stokes preconditioning in Channelflow and Openpipeflow

Steady states and traveling waves play a fundamental role in understanding hydrodynamic problems. Even when unstable, these states provide the bifurcation-theoretic explanation for the origin of the observed states. In turbulent wall-bounded shear flows, these states have been hypothesized to be saddle points organizing the trajectories within a chaotic attractor. These states must be computed with Newton's method or one of its generalizations, since time-integration cannot converge to unstable equilibria. The bottleneck is the solution of linear systems involving the Jacobian of the Navier-Stokes or Boussinesq equations. Originally such computations were carried out by constructing and directly inverting the Jacobian, but this is unfeasible for the matrices arising from three-dimensional hydrodynamic configurations in large domains. A popular method is to seek states that are invariant under numerical time integration. Surprisingly, equilibria may also be found by seeking flows that are invariant under a single very large Backwards-Euler Forwards-Euler timestep. We show that this method, called Stokes preconditioning, is 10 to 50 times faster at computing steady states in plane Couette flow and traveling waves in pipe flow. Moreover, it can be carried out using Channelflow (by Gibson) and Openpipeflow (by Willis) without any changes to these popular spectral codes. We explain the convergence rate as a function of the integration period and Reynolds number by computing the full spectra of the operators corresponding to the Jacobians of both methods.Comment: in Computational Modelling of Bifurcations and Instabilities in Fluid Dynamics, ed. Alexander Gelfgat (Springer, 2018

A global transition to ferruginous conditions in the early Neoproterozoic oceans

Eukaryotic life expanded during the Proterozoic eon1, 2.5 to 0.542 billion years ago, against a background of fluctuating ocean chemistry2, 3, 4. After about 1.8 billion years ago, the global ocean is thought to have been characterized by oxygenated surface waters, with anoxic and sulphidic waters in middle depths along productive continental margins and anoxic and iron-containing (ferruginous) deeper waters5, 6, 7. The spatial extent of sulphidic waters probably varied through time5, 6, but this surface-to-deep redox structure is suggested to have persisted until the first Neoproterozoic glaciation about 717 million years ago8, 9, 10, 11. Here we report an analysis of ocean redox conditions throughout the Proterozoic using new and existing iron speciation and sulphur isotope data from multiple cores and outcrops. We find a global transition from sulphidic to ferruginous mid-depth waters in the earliest Neoproterozoic, coincident with the amalgamation of the supercontinent Rodinia at low latitudes. We suggest that ferruginous conditions were initiated by an increase in the oceanic influx of highly reactive iron relative to sulphate, driven by a change in weathering regime and the uptake of sulphate by extensive continental evaporites on Rodinia. We propose that this transition essentially detoxified ocean margin settings, allowing for expanded opportunities for eukaryote diversification following a prolonged evolutionary stasis before one billion years ago

Unique Neoproterozoic carbon isotope excursions sustained by coupled evaporite dissolution and pyrite burial

The Neoproterozoic era witnessed a succession of biological innovations that culminated in diverse animal body plans and behaviours during the Ediacaran–Cambrian radiations. Intriguingly, this interval is also marked by perturbations to the global carbon cycle, as evidenced by extreme fluctuations in climate and carbon isotopes. The Neoproterozoic isotope record has defied parsimonious explanation because sustained 12C-enrichment (low δ13C) in seawater seems to imply that substantially more oxygen was consumed by organic carbon oxidation than could possibly have been available. We propose a solution to this problem, in which carbon and oxygen cycles can maintain dynamic equilibrium during negative δ13C excursions when surplus oxidant is generated through bacterial reduction of sulfate that originates from evaporite weathering. Coupling of evaporite dissolution with pyrite burial drives a positive feedback loop whereby net oxidation of marine organic carbon can sustain greenhouse forcing of chemical weathering, nutrient input and ocean margin euxinia. Our proposed framework is particularly applicable to the late Ediacaran ‘Shuram’ isotope excursion that directly preceded the emergence of energetic metazoan metabolisms during the Ediacaran–Cambrian transition. Here we show that non-steady-state sulfate dynamics contributed to climate change, episodic ocean oxygenation and opportunistic radiations of aerobic life during the Neoproterozoic era

Rise to modern levels of ocean oxygenation coincided with the Cambrian radiation of animals.

The early diversification of animals (∼630 Ma), and their development into both motile and macroscopic forms (∼575-565 Ma), has been linked to stepwise increases in the oxygenation of Earth's surface environment. However, establishing such a linkage between oxygen and evolution for the later Cambrian 'explosion' (540-520 Ma) of new, energy-sapping body plans and behaviours has proved more elusive. Here we present new molybdenum isotope data, which demonstrate that the areal extent of oxygenated bottom waters increased in step with the early Cambrian bioradiation of animals and eukaryotic phytoplankton. Modern-like oxygen levels characterized the ocean at ∼521 Ma for the first time in Earth history. This marks the first establishment of a key environmental factor in modern-like ecosystems, where animals benefit from, and also contribute to, the 'homeostasis' of marine redox conditions

Should the Arteriovenous Fistula Be Created before Starting Dialysis?: A Decision Analytic Approach

Background: An arteriovenous fistula (AVF) is considered the vascular access of choice, but uncertainty exists about the\ud optimal time for its creation in pre-dialysis patients. The aim of this study was to determine the optimal vascular access\ud referral strategy for stage 4 (glomerular filtration rate ,30 ml/min/1.73 m2) chronic kidney disease patients using a decision\ud analytic framework.\ud Methods: A Markov model was created to compare two strategies: refer all stage 4 chronic kidney disease patients for an\ud AVF versus wait until the patient starts dialysis. Data from published observational studies were used to estimate the\ud probabilities used in the model. A Markov cohort analysis was used to determine the optimal strategy with life expectancy\ud and quality adjusted life expectancy as the outcomes. Sensitivity analyses, including a probabilistic sensitivity analysis, were\ud performed using Monte Carlo simulation.\ud Results: The wait strategy results in a higher life expectancy (66.6 versus 65.9 months) and quality adjusted life expectancy\ud (38.9 versus 38.5 quality adjusted life months) than immediate AVF creation. It was robust across all the parameters except\ud at higher rates of progression and lower rates of ischemic steal syndrome.\ud Conclusions: Early creation of an AVF, as recommended by most guidelines, may not be the preferred strategy in all predialysis\ud patients. Further research on cost implications and patient preferences for treatment options needs to be done\ud before recommending early AVF creation

Genetic Association Study Identifies HSPB7 as a Risk Gene for Idiopathic Dilated Cardiomyopathy

Dilated cardiomyopathy (DCM) is a structural heart disease with strong genetic background. Monogenic forms of DCM are observed in families with mutations located mostly in genes encoding structural and sarcomeric proteins. However, strong evidence suggests that genetic factors also affect the susceptibility to idiopathic DCM. To identify risk alleles for non-familial forms of DCM, we carried out a case-control association study, genotyping 664 DCM cases and 1,874 population-based healthy controls from Germany using a 50K human cardiovascular disease bead chip covering more than 2,000 genes pre-selected for cardiovascular relevance. After quality control, 30,920 single nucleotide polymorphisms (SNP) were tested for association with the disease by logistic regression adjusted for gender, and results were genomic-control corrected. The analysis revealed a significant association between a SNP in HSPB7 gene (rs1739843, minor allele frequency 39%) and idiopathic DCM (p = 1.06×10−6, OR = 0.67 [95% CI 0.57–0.79] for the minor allele T). Three more SNPs showed p < 2.21×10−5. De novo genotyping of these four SNPs was done in three independent case-control studies of idiopathic DCM. Association between SNP rs1739843 and DCM was significant in all replication samples: Germany (n = 564, n = 981 controls, p = 2.07×10−3, OR = 0.79 [95% CI 0.67–0.92]), France 1 (n = 433 cases, n = 395 controls, p = 3.73×10−3, OR = 0.74 [95% CI 0.60–0.91]), and France 2 (n = 249 cases, n = 380 controls, p = 2.26×10−4, OR = 0.63 [95% CI 0.50–0.81]). The combined analysis of all four studies including a total of n = 1,910 cases and n = 3,630 controls showed highly significant evidence for association between rs1739843 and idiopathic DCM (p = 5.28×10−13, OR = 0.72 [95% CI 0.65–0.78]). None of the other three SNPs showed significant results in the replication stage

Low-oxygen waters limited habitable space for early animals

The oceans at the start of the Neoproterozoic Era (1,000–541 million years ago, Ma) were dominantly anoxic, but may have become progressively oxygenated, coincident with the rise of animal life. However, the control that oxygen exerted on the development of early animal ecosystems remains unclear, as previous research has focussed on the identification of fully anoxic or oxic conditions, rather than intermediate redox levels. Here we report anomalous cerium enrichments preserved in carbonate rocks across bathymetric basin transects from nine localities of the Nama Group, Namibia (~550–541 Ma). In combination with Fe-based redox proxies, these data suggest that low-oxygen conditions occurred in a narrow zone between well-oxygenated surface waters and fully anoxic deep waters. Although abundant in well-oxygenated environments, early skeletal animals did not occupy oxygen impoverished regions of the shelf, demonstrating that oxygen availability (probably >10 μM) was a key requirement for the development of early animal-based ecosystems

Earth: Atmospheric Evolution of a Habitable Planet

Our present-day atmosphere is often used as an analog for potentially habitable exoplanets, but Earth's atmosphere has changed dramatically throughout its 4.5 billion year history. For example, molecular oxygen is abundant in the atmosphere today but was absent on the early Earth. Meanwhile, the physical and chemical evolution of Earth's atmosphere has also resulted in major swings in surface temperature, at times resulting in extreme glaciation or warm greenhouse climates. Despite this dynamic and occasionally dramatic history, the Earth has been persistently habitable--and, in fact, inhabited--for roughly 4 billion years. Understanding Earth's momentous changes and its enduring habitability is essential as a guide to the diversity of habitable planetary environments that may exist beyond our solar system and for ultimately recognizing spectroscopic fingerprints of life elsewhere in the Universe. Here, we review long-term trends in the composition of Earth's atmosphere as it relates to both planetary habitability and inhabitation. We focus on gases that may serve as habitability markers (CO2, N2) or biosignatures (CH4, O2), especially as related to the redox evolution of the atmosphere and the coupled evolution of Earth's climate system. We emphasize that in the search for Earth-like planets we must be mindful that the example provided by the modern atmosphere merely represents a single snapshot of Earth's long-term evolution. In exploring the many former states of our own planet, we emphasize Earth's atmospheric evolution during the Archean, Proterozoic, and Phanerozoic eons, but we conclude with a brief discussion of potential atmospheric trajectories into the distant future, many millions to billions of years from now. All of these 'Alternative Earth' scenarios provide insight to the potential diversity of Earth-like, habitable, and inhabited worlds.Comment: 34 pages, 4 figures, 4 tables. Review chapter to appear in Handbook of Exoplanet