Blow-up behavior of collocation solutions to Hammerstein-type volterra integral equations

We analyze the blow-up behavior of one-parameter collocation solutions for Hammerstein-type Volterra integral equations (VIEs) whose solutions may blow up in finite time. To approximate such solutions (and the corresponding blow-up time), we will introduce an adaptive stepsize strategy that guarantees the existence of collocation solutions whose blow-up behavior is the same as the one for the exact solution. Based on the local convergence of the collocation methods for VIEs, we present the convergence analysis for the numerical blow-up time. Numerical experiments illustrate the analysis

Adjustable mount for electro-optic transducers in an evacuated cryogenic system

The invention is an adjustable mount for positioning an electro-optic transducer in an evacuated cryogenic environment. Electro-optic transducers are used in this manner as high sensitivity detectors of gas emission lines of spectroscopic analysis. The mount is made up of an adjusting mechanism and a transducer mount. The adjusting mechanism provided five degrees of freedom, linear adjustments and angular adjustments. The mount allows the use of an internal lens to focus energy on the transducer element thereby improving the efficiency of the detection device. Further, the transducer mount, although attached to the adjusting mechanism, is isolated thermally such that a cryogenic environment can be maintained at the transducer while the adjusting mechanism remains at room temperature. Radiation shields also are incorporated to further reduce heat flow to the transducer location

EarthN: A new Earth System Nitrogen Model

The amount of nitrogen in the atmosphere, oceans, crust, and mantle have important ramifications for Earth's biologic and geologic history. Despite this importance, the history and cycling of nitrogen in the Earth system is poorly constrained over time. For example, various models and proxies contrastingly support atmospheric mass stasis, net outgassing, or net ingassing over time. In addition, the amount available to and processing of nitrogen by organisms is intricately linked with and provides feedbacks on oxygen and nutrient cycles. To investigate the Earth system nitrogen cycle over geologic history, we have constructed a new nitrogen cycle model: EarthN. This model is driven by mantle cooling, links biologic nitrogen cycling to phosphate and oxygen, and incorporates geologic and biologic fluxes. Model output is consistent with large (2-4x) changes in atmospheric mass over time, typically indicating atmospheric drawdown and nitrogen sequestration into the mantle and continental crust. Critical controls on nitrogen distribution include mantle cooling history, weathering, and the total Bulk Silicate Earth+atmosphere nitrogen budget. Linking the nitrogen cycle to phosphorous and oxygen levels, instead of carbon as has been previously done, provides new and more dynamic insight into the history of nitrogen on the planet.Comment: 36 pages, 12 figure

New synchronization method for <i>Plasmodium falciparum</i>

&lt;b&gt;Background&lt;/b&gt;: Plasmodium falciparum is usually asynchronous during in vitro culture. Although various synchronization methods are available, they are not able to narrow the range of ages of parasites. A newly developed method is described that allows synchronization of parasites to produce cultures with an age range as low as 30 minutes. &lt;b&gt;Methods&lt;/b&gt;: Trophozoites and schizonts are enriched using Plasmion. The enriched late stage parasites are immobilized as a monolayer onto plastic Petri dishes using concanavalin A. Uninfected erythrocytes are placed onto the monolayer for a limited time period, during which time schizonts on the monolayer rupture and the released merozoites invade the fresh erythrocytes. The overlay is then taken off into a culture flask, resulting in a highly synchronized population of parasites. &lt;b&gt;Results&lt;/b&gt;: Plasmion treatment results in a 10- to 13-fold enrichment of late stage parasites. The monolayer method results in highly synchronized cultures of parasites where invasion has occurred within a very limited time window, which can be as low as 30 minutes. The method is simple, requiring no specialized equipment and relatively cheap reagents. &lt;b&gt;Conclusions&lt;/b&gt;: The new method for parasite synchronization results in highly synchronized populations of parasites, which will be useful for studies of the parasite asexual cell cycle

Selective incorporation of proteinaceous over nonproteinaceous cationic amino acids in model prebiotic oligomerization reactions.

Numerous long-standing questions in origins-of-life research center on the history of biopolymers. For example, how and why did nature select the polypeptide backbone and proteinaceous side chains? Depsipeptides, containing both ester and amide linkages, have been proposed as ancestors of polypeptides. In this paper, we investigate cationic depsipeptides that form under mild dry-down reactions. We compare the oligomerization of various cationic amino acids, including the cationic proteinaceous amino acids (lysine, Lys; arginine, Arg; and histidine, His), along with nonproteinaceous analogs of Lys harboring fewer methylene groups in their side chains. These analogs, which have been discussed as potential prebiotic alternatives to Lys, are ornithine, 2,4-diaminobutyric acid, and 2,3-diaminopropionic acid (Orn, Dab, and Dpr). We observe that the proteinaceous amino acids condense more extensively than these nonproteinaceous amino acids. Orn and Dab readily cyclize into lactams, while Dab and Dpr condense less efficiently. Furthermore, the proteinaceous amino acids exhibit more selective oligomerization through their α-amines relative to their side-chain groups. This selectivity results in predominantly linear depsipeptides in which the amino acids are α-amine-linked, analogous to today's proteins. These results suggest a chemical basis for the selection of Lys, Arg, and His over other cationic amino acids for incorporation into proto-proteins on the early Earth. Given that electrostatics are key elements of protein-RNA and protein-DNA interactions in extant life, we hypothesize that cationic side chains incorporated into proto-peptides, as reported in this study, served in a variety of functions with ancestral nucleic acid polymers in the early stages of life

Powerful alliances in graphs

AbstractFor a graph G=(V,E), a non-empty set S⊆V is a defensive alliance if for every vertex v in S, v has at most one more neighbor in V−S than it has in S, and S is an offensive alliance if for every v∈V−S that has a neighbor in S, v has more neighbors in S than in V−S. A powerful alliance is both defensive and offensive. We initiate the study of powerful alliances in graphs

Transition from localized surface plasmon resonance to extended surface plasmon-polariton as metallic nanoparticles merge to form a periodic hole array

W. Andrew Murray, Simion Astilean, and William L. Barnes, Physical Review B, Vol. 69, article 165407 (2004). "Copyright © 2004 by the American Physical Society."We present results of experiments to determine the dispersion of the plasmon modes associated with periodic silver nanoparticle and nanohole arrays fabricated using an extension of the nanosphere lithography technique. Ordered monolayers of polystyrene nanospheres were used as a deposition mask through which silver was deposited by thermal evaporation, subsequent removal of the nanospheres thus leaving an array of metallic nanoparticles. By reactive-ion etching of the nanospheres in an oxygen plasma prior to silver deposition, arrays consisting of particles of increasing size were fabricated. The extremities of the particles eventually merge to create a continuous metallic network perforated by subwavelength holes, thus allowing a study of the particle-hole transition. Combining optical measurements of transmittance and reflectance with information gained using scanning electron microscopy, three separate regimes were observed. For low etch times the samples comprise mainly individual nanoparticles and the optical response is dominated by localized surface plasmon resonances that show no dispersion. As the etch time is increased almost all of the nanoparticles merge with adjacent particles, although many defects are present—notably where some particles fail to merge, a small gap being left between them. The presence of these defects prevents an abrupt structural transition from metallic nanoparticles to a continuous metallic film perforated by an array of nanoholes. The presence of such gaps also results in dispersion data that lack clearly defined features. A further increase in etch time leads to samples with no gaps: instead, a continuous metal film perforated by a nanohole array is produced. The optical response of these structures is dominated by extended surface plasmon-polariton modes

Discovery of Extreme Examples of Superclustering in Aquarius

We report the discovery of two highly extended filaments and one extremely high density knot within the region of Aquarius. The supercluster candidates were chosen via percolation analysis of the Abell and ACO catalogs and include only the richest clusters (R >= 1). The region examined is a 10x45 degree strip and is now 87% complete in cluster redshift measurements to mag_10 = 18.3. In all, we report 737 galaxy redshifts in 46 cluster fields. One of the superclusters, dubbed Aquarius, is comprised of 14 Abell/ACO clusters and extends 110h^-1Mpc in length only 7 degrees off the line-of-sight. On the near-end of the Aquarius filament, another supercluster, dubbed Aquarius-Cetus, extends for 75h^-1Mpc perpendicular to the line-of-sight. After fitting ellipsoids to both Aquarius and Aquarius-Cetus, we find axis ratios (long-to- midlength axis) of 4.3 for Aquarius and 3.0 for Aquarius-Cetus. We fit ellipsoids to all N>=5 clumps of clusters in the Abell/ACO measured-z cluster sample. The frequency of filaments with axis ratios >=3.0 (~20%) is nearly identical with that found among `superclusters' in Monte Carlo simulations of random and random- clumped clusters, however, so the rich Abell/ACO clusters have no particular tendency toward filamentation. The Aquarius filament also contains a `knot' of 6 clusters at Z ~0.11, with five of the clusters near enough togeteher to represent an apparent overdensity of 150. There are three other R >= 1 cluster density enhancements similar to this knot at lower redshifts: Corona Borealis, the Shapely Concentration, and another grouping of seven clusters in Microscopium. All four of these dense superclusters appear near the point of breaking away from the Hubble Flow, and some may now be in collapse, but there is little evidence of any being virialized.Comment: 45 pages (+ e-tables), 7 figures, AASTeX Accepted for Publication in Ap