High order fast Laplace solvers for the Dirichlet problem on general regions

Highly accurate finite difference schemes are developed for Laplace's equation with the Dirichlet boundary condition on general bounded regions in R/sup n/. A second order accurate scheme is combined with a deferred correction or Richardson extrapolation method to increase the accuracy. The Dirichlet condition is approximated by a method suggested by Heinz-Otto Kreiss. A convergence proof of his, previously not published, is given which shows that, for the interval size h, one of the methods has an accuracy of at least O(h/sup 5/./sup 5/) in L/sub 2/. The linear systems of algebraic equations are solved by a capacitance matrix method. The results of our numerical experiments show that highly accurate solutions are obtained with only a slight additional use of computer time when compared to the results obtained by second order accurate methods

Numerical solution of the multidimensional Buckley--Leverett equation by a sampling method

A method developed earlier for solving numerically the one-dimensional Buckley--Leverett equation for two phase immiscible flow in a porous medium is extended to the case of non-uniform flow in two space dimensions. The method has the feature of tracking solution discontinuities sharply for purely hyperbolic problems, without requiring devices such as the introduction of artificial dissipation. It is found that the method is computationally efficient for solving a numerical example for the five-spot configuration of water flooding of a petroleum reservoir

The biogeography of the Plastisphere : implications for policy

Author Posting. © Ecological Society of America, 2015. This article is posted here by permission of Ecological Society of America for personal use, not for redistribution. The definitive version was published in Frontiers in Ecology and the Environment 13 (2015): 541–546, doi:10.1890/150017.Microplastics (particles less than 5 mm) numerically dominate marine debris and occur from coastal waters to mid-ocean gyres, where surface circulation concentrates them. Given the prevalence of plastic marine debris (PMD) and the rise in plastic production, the impacts of plastic on marine ecosystems will likely increase. Microscopic life (the “Plastisphere”) thrives on these tiny floating “islands” of debris and can be transported long distances. Using next-generation DNA sequencing, we characterized bacterial communities from water and plastic samples from the North Pacific and North Atlantic subtropical gyres to determine whether the composition of different Plastisphere communities reflects their biogeographic origins. We found that these communities differed between ocean basins – and to a lesser extent between polymer types – and displayed latitudinal gradients in species richness. Our research reveals some of the impacts of microplastics on marine biodiversity, demonstrates that the effects and fate of PMD may vary considerably in different parts of the global ocean, and suggests that PMD mitigation will require regional management efforts.This work was supported by a US National Science Foundation (NSF) collaborative grant to LAA-Z (OCE-1155571), ERZ (OCE-1155379), and TJM (OCE-1155671), and was partially funded by an NSF TUES grant (DUE-1043468) to LAA-Z and ERZ, and by the Richard Saltonstall Charitable Foundation to TJM. GP was funded through the OCE-1155379 grant and assisted with identification of plastic resins via ATR-FTIR

Vertex labeling and routing in expanded Apollonian networks

We present a family of networks, expanded deterministic Apollonian networks, which are a generalization of the Apollonian networks and are simultaneously scale-free, small-world, and highly clustered. We introduce a labeling of their vertices that allows to determine a shortest path routing between any two vertices of the network based only on the labels.Comment: 16 pages, 2 figure

The effect of wind mixing on the vertical distribution of buoyant plastic debris.

[1] Micro-plastic marine debris is widely distributed in vast regions of the subtropical gyres and has emerged as a major open ocean pollutant. The fate and transport of plastic marine debris is governed by poorly understood geophysical processes, such as ocean mixing within the surface boundary layer. Based on profile observations and a one-dimensional column model, we demonstrate that plastic debris is vertically distributed within the upper water column due to wind-driven mixing. These results suggest that total oceanic plastics concentrations are significantly underestimated by traditional surface measurements, requiring a reinterpretation of existing plastic marine debris data sets. A geophysical approach must be taken in order to properly quantify and manage this form of marine pollution. Citation: Kukulka, T.

A deeply branching thermophilic bacterium with an ancient acetyl-CoA pathway dominates a subsurface ecosystem

<div><p>A nearly complete genome sequence of <em>Candidatus</em> ‘Acetothermum autotrophicum’, a presently uncultivated bacterium in candidate division OP1, was revealed by metagenomic analysis of a subsurface thermophilic microbial mat community. Phylogenetic analysis based on the concatenated sequences of proteins common among 367 prokaryotes suggests that <em>Ca.</em> ‘A. autotrophicum’ is one of the earliest diverging bacterial lineages. It possesses a folate-dependent Wood-Ljungdahl (acetyl-CoA) pathway of CO₂ fixation, is predicted to have an acetogenic lifestyle, and possesses the newly discovered archaeal-autotrophic type of bifunctional fructose 1,6-bisphosphate aldolase/phosphatase. A phylogenetic analysis of the core gene cluster of the acethyl-CoA pathway, shared by acetogens, methanogens, some sulfur- and iron-reducers and dechlorinators, supports the hypothesis that the core gene cluster of <em>Ca.</em> ‘A. autotrophicum’ is a particularly ancient bacterial pathway. The habitat, physiology and phylogenetic position of <em>Ca.</em> ‘A. autotrophicum’ support the view that the first bacterial and archaeal lineages were H₂-dependent acetogens and methanogenes living in hydrothermal environments.</p> </div

Bio-inspired CO₂ conversion by iron sulfide catalysts under sustainable conditions

The mineral greigite presents similar surface structures to the active sites found in many modern-day enzymes. We show that particles of greigite can reduce CO2 under ambient conditions into chemicals such as methanol, formic, acetic and pyruvic acid. Our results also lend support to the Origin of Life theory on alkaline hydrothermal vents

Metagenomic Comparison of Two Thiomicrospira Lineages Inhabiting Contrasting Deep-Sea Hydrothermal Environments

Background: The most widespread bacteria in oxic zones of carbonate chimneys at the serpentinite-hosted Lost City hydrothermal field, Mid-Atlantic Ridge, belong to the Thiomicrospira group of sulfur-oxidizing chemolithoautotrophs. It is unclear why Thiomicrospira-like organisms thrive in these chimneys considering that Lost City hydrothermal fluids are notably lacking in hydrogen sulfide and carbon dioxide. Methodology/Principal Findings: Here we describe metagenomic sequences obtained from a Lost City carbonate chimney that are highly similar to the genome of Thiomicrospira crunogena XCL-2, an isolate from a basalt-hosted hydrothermal vent in the Pacific Ocean. Even though T. crunogena and Lost City Thiomicrospira inhabit different types of hydrothermal systems in different oceans, their genomic contents are highly similar. For example, sequences encoding the sulfur oxidation and carbon fixation pathways (including a carbon concentration mechanism) of T. crunogena are also present in the Lost City metagenome. Comparative genomic analyses also revealed substantial genomic changes that must have occurred since the divergence of the two lineages, including large genomic rearrangements, gene fusion events, a prophage insertion, and transposase activity. Conclusions/Significance: Our results show significant genomic similarity between Thiomicrospira organisms inhabiting different kinds of hydrothermal systems in different oceans, suggesting that these organisms are widespread and highl

Sulfide geochronology along the Endeavour Segment of the Juan de Fuca Ridge

Forty-nine hydrothermal sulfide-sulfate rock samples from the Endeavour Segment of the Juan de Fuca Ridge, northeastern Pacific Ocean, were dated by measuring the decay of 226Ra (half-life of 1600 years) in hydrothermal barite to provide a history of hydrothermal venting at the site over the past 6000 years. This dating method is effective for samples ranging in age from ∼200 to 20,000 years old and effectively bridges an age gap between shorter- and longer-lived U-series dating techniques for hydrothermal deposits. Results show that hydrothermal venting at the active High Rise, Sasquatch, and Main Endeavour fields began at least 850, 1450, and 2300 years ago, respectively. Barite ages of other inactive deposits on the axial valley floor are between ∼1200 and ∼2200 years old, indicating past widespread hydrothermal venting outside of the currently active vent fields. Samples from the half-graben on the eastern slope of the axial valley range in age from ∼1700 to ∼2925 years, and a single sample from outside the axial valley, near the westernmost valley fault scarp is ∼5850 ± 205 years old. The spatial relationship between hydrothermal venting and normal faulting suggests a temporal relationship, with progressive younging of sulfide deposits from the edges of the axial valley toward the center of the rift. These relationships are consistent with the inward migration of normal faulting toward the center of the valley over time and a minimum age of onset of hydrothermal activity in this region of 5850 years

Single-crossover recombination and ancestral recombination trees

We consider the Wright-Fisher model for a population of $N$ individuals, each identified with a sequence of a finite number of sites, and single-crossover recombination between them. We trace back the ancestry of single individuals from the present population. In the $N \to \infty$ limit without rescaling of parameters or time, this ancestral process is described by a random tree, whose branching events correspond to the splitting of the sequence due to recombination. With the help of a decomposition of the trees into subtrees, we calculate the probabilities of the topologies of the ancestral trees. At the same time, these probabilities lead to a semi-explicit solution of the deterministic single-crossover equation. The latter is a discrete-time dynamical system that emerges from the Wright-Fisher model via a law of large numbers and has been waiting for a solution for many decades.Comment: J. Math. Biol., in press. 26 pages, 8 figure