Class Numbers, Cyclic Simple Groups and Arithmetic

Here we initiate a program to study relationships between finite groups and arithmetic-geometric invariants in a systematic way. To do this we first introduce a notion of optimal module for a finite group in the setting of holomorphic mock Jacobi forms. Then we classify optimal modules for the cyclic groups of prime order, in the special case of weight two and index one, where class numbers of imaginary quadratic fields play an important role. Finally we exhibit a connection between the classification we establish and the arithmetic geometry of imaginary quadratic twists of modular curves of prime level.Comment: 36 page

Inhibition of Chromium(III) Oxidation through Manganese(IV) Oxide Passivation and Iron(II) Abiotic Reduction

Manganese (Mn) oxides are strong oxidants that are ubiquitous in soils and can oxidize redox-active metals, including chromium (Cr). In soil environments, trivalent chromium (Cr(III)) is a benign, immobile micronutrient, whereas the hexavalent Cr(VI) form is present as a highly mobile, toxic chromate oxyanion. Although many studies have characterized the capacity of Mn(III/IV) oxides to oxidize Cr(III) to toxic Cr(VI), the oxidative capacity of Mn oxides in the presence of potentially passivating soil constituents, specifically reduced soluble iron (Fe(II)aq), remains unresolved. We hypothesized that chemical processes at redox interfaces, such as diffusion-limited environments within soil aggregates, can lead to decreased Cr(VI) production from Mn oxide-driven oxidation due to passivation by Fe(II)aq. A multichamber diffusion-limited reactor was used to simulate transport at soil redox interfaces and investigate the capacity of poorly crystalline and crystalline Mn oxides to oxidize solid Cr(III) minerals to Cr(VI) in the presence of Fe(II)aq. As predicted, Cr(VI) was produced through the Mn oxide-catalyzed oxidation of Cr(III) at a rate controlled by the solubility of Cr(OH)3. However, in the presence of Fe(II)aq, the concentration of aqueous Cr(VI) decreased as a function of the Fe(II)aq concentration, where high concentrations of Fe(II)aq completely inhibited Cr(VI) production, likely through both the passivation of the Mn oxide and the direct reduction of Cr(VI) by Fe(II). At both low (14 μM) and high (100 μM) Fe(II)aq concentrations, the iron oxide minerals hematite (Fe2O3) and goethite (α-FeOOH) were associated with the Mn oxides, which can cause surface passivation, a likely role that decreases Cr(III) oxidation. Additionally, the Cr(III) oxidation rate decreased with increasing crystallinity of the Mn oxides whether or not Fe(II) was present

Nanoscale Fabrication of Microwave Detectors from Commercially-Available CVD-Grown Monolayer Graphene

Using commercially-available monolayer graphene, synthesized by means of chemical vapor deposition, microwave power sensing elements have been nanofabricated and integrated with microwave-grade test structures suitable for on-wafer probing. The graphene, situated on a thermal oxide, was first cleaned of stray contaminants in a forming gas environment briefly held at 250 degrees Celsius using a rapid thermal annealer. Immediately following this step, the graphene was passivated with a protective aluminum oxide layer (approximately S nm in thickness). Micrometer-scale Corbino disc test structures were then fabricated in direct contact with the graphene using a self-aligned process, which relies on the fact that tetramethylammonium hydroxide develops the photoresist while removing the aluminum oxide. Graphene nanoribbons (with widths as small 400 nm) were then fabricated across the Corbino disc gaps using electron-beam writing in conjunction with a negative tone resist. The same developer exposed the majority of the graphene while defining nanometer-scale lines of photoresist stacked upon aluminum oxide. These stacks served as etch-stops while the unprotected graphene was ion-milled in an oxygen plasma. Finally, the photoresist was removed leaving behind passivated graphene nanoribbons. Damage caused by the fabrication was evaluated by comparing the Raman spectra of the grapheme before and after processing

The Saffman-Taylor problem on a sphere

The Saffman-Taylor problem addresses the morphological instability of an interface separating two immiscible, viscous fluids when they move in a narrow gap between two flat parallel plates (Hele-Shaw cell). In this work, we extend the classic Saffman-Taylor situation, by considering the flow between two curved, closely spaced, concentric spheres (spherical Hele-Shaw cell). We derive the mode-coupling differential equation for the interface perturbation amplitudes and study both linear and nonlinear flow regimes. The effect of the spherical cell (positive) spatial curvature on the shape of the interfacial patterns is investigated. We show that stability properties of the fluid-fluid interface are sensitive to the curvature of the surface. In particular, it is found that positive spatial curvature inhibits finger tip-splitting. Hele-Shaw flow on weakly negative, curved surfaces is briefly discussed.Comment: 26 pages, 4 figures, RevTex, accepted for publication in Phys. Rev.

The complement of protein kinases of the microsporidium Encephalitozoon cuniculi in relation to those of Saccharomyces cerevisiae and Schizosaccharomyces pombe.

RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are.BACKGROUND: Microsporidia, parasitic fungi-related eukaryotes infecting many cell types in a wide range of animals (including humans), represent a serious health threat in immunocompromised patients. The 2.9 Mb genome of the microsporidium Encephalitozoon cuniculi is the smallest known of any eukaryote. Eukaryotic protein kinases are a large superfamily of enzymes with crucial roles in most cellular processes, and therefore represent potential drug targets. We report here an exhaustive analysis of the E. cuniculi genomic database aimed at identifying and classifying all protein kinases of this organism with reference to the kinomes of two highly-divergent yeast species, Saccharomyces cerevisiae and Schizosaccharomyces pombe. RESULTS: A database search with a multi-level protein kinase family hidden Markov model library led to the identification of 29 conventional protein kinase sequences in the E. cuniculi genome, as well as 3 genes encoding atypical protein kinases. The microsporidian kinome presents striking differences from those of other eukaryotes, and this minimal kinome underscores the importance of conserved protein kinases involved in essential cellular processes. Approximately 30% of its kinases are predicted to regulate cell cycle progression while another approximately 28% have no identifiable homologues in model eukaryotes and are likely to reflect parasitic adaptations. E. cuniculi lacks MAP kinase cascades and almost all protein kinases that are involved in stress responses, ion homeostasis and nutrient signalling in the model fungi S. cerevisiae and S. pombe, including AMPactivated protein kinase (Snf1), previously thought to be ubiquitous in eukaryotes. A detailed database search and phylogenetic analysis of the kinomes of the two model fungi showed that the degree of homology between their kinomes of approximately 85% is much higher than that previously reported. CONCLUSION: The E. cuniculi kinome is by far the smallest eukaryotic kinome characterised to date. The difficulty in assigning clear homology relationships for nine out of the twentynine microsporidian conventional protein kinases despite its compact genome reflects the phylogenetic distance between microsporidia and other eukaryotes. Indeed, the E. cuniculi genome presents a high proportion of genes in which evolution has been accelerated by up to four-fold. There are no orthologues of the protein kinases that constitute MAP kinase pathways and many other protein kinases with roles in nutrient signalling are absent from the E. cuniculi kinome. However, orthologous kinases can nonetheless be identified that correspond to members of the yeast kinomes with roles in some of the most fundamental cellular processes. For example, E. cuniculi has clear orthologues of virtually all the major conserved protein kinases that regulate the core cell cycle machinery (Aurora, Polo, DDK, CDK and Chk1). A comprehensive comparison of the homology relationships between the budding and fission yeast kinomes indicates that, despite an estimated 800 million years of independent evolution, the two model fungi share approximately 85% of their protein kinases. This will facilitate the annotation of many of the as yet uncharacterised fission yeast kinases, and also those of novel fungal genomes.Published versio

Parallel flow in Hele-Shaw cells with ferrofluids

Parallel flow in a Hele-Shaw cell occurs when two immiscible liquids flow with relative velocity parallel to the interface between them. The interface is unstable due to a Kelvin-Helmholtz type of instability in which fluid flow couples with inertial effects to cause an initial small perturbation to grow. Large amplitude disturbances form stable solitons. We consider the effects of applied magnetic fields when one of the two fluids is a ferrofluid. The dispersion relation governing mode growth is modified so that the magnetic field can destabilize the interface even in the absence of inertial effects. However, the magnetic field does not affect the speed of wave propagation for a given wavenumber. We note that the magnetic field creates an effective interaction between the solitons.Comment: 12 pages, Revtex, 2 figures, revised version (minor changes