Relative Equilibria in the Four-Vortex Problem with Two Pairs of Equal Vorticities

We examine in detail the relative equilibria in the four-vortex problem where two pairs of vortices have equal strength, that is, \Gamma_1 = \Gamma_2 = 1 and \Gamma_3 = \Gamma_4 = m where m is a nonzero real parameter. One main result is that for m > 0, the convex configurations all contain a line of symmetry, forming a rhombus or an isosceles trapezoid. The rhombus solutions exist for all m but the isosceles trapezoid case exists only when m is positive. In fact, there exist asymmetric convex configurations when m < 0. In contrast to the Newtonian four-body problem with two equal pairs of masses, where the symmetry of all convex central configurations is unproven, the equations in the vortex case are easier to handle, allowing for a complete classification of all solutions. Precise counts on the number and type of solutions (equivalence classes) for different values of m, as well as a description of some of the bifurcations that occur, are provided. Our techniques involve a combination of analysis and modern and computational algebraic geometry

Optical properties of MgH2 measured in situ in a novel gas cell for ellipsometry/spectrophotometry

The dielectric properties of alpha-MgH2 are investigated in the photon energy range between 1 and 6.5 eV. For this purpose, a novel sample configuration and experimental setup are developed that allow both optical transmission and ellipsometric measurements of a transparent thin film in equilibrium with hydrogen. We show that alpha-MgH2 is a transparent, colour neutral insulator with a band gap of 5.6 +/- 0.1 eV. It has an intrinsic transparency of about 80% over the whole visible spectrum. The dielectric function found in this work confirms very recent band structure calculations using the GW approximation by Alford and Chou [J.A. Alford and M.Y. Chou (unpublished)]. As Pd is used as a cap layer we report also the optical properties of PdHx thin films.Comment: REVTeX4, 15 pages, 12 figures, 5 table

De novo variants in the RNU4-2 snRNA cause a frequent neurodevelopmental syndrome

Around 60% of individuals with neurodevelopmental disorders (NDD) remain undiagnosed after comprehensive genetic testing, primarily of protein-coding genes1. Large genome-sequenced cohorts are improving our ability to discover new diagnoses in the non-coding genome. Here, we identify the non-coding RNA RNU4-2 as a syndromic NDD gene. RNU4-2 encodes the U4 small nuclear RNA (snRNA), which is a critical component of the U4/U6.U5 tri-snRNP complex of the major spliceosome2. We identify an 18 bp region of RNU4-2 mapping to two structural elements in the U4/U6 snRNA duplex (the T-loop and Stem III) that is severely depleted of variation in the general population, but in which we identify heterozygous variants in 115 individuals with NDD. Most individuals (77.4%) have the same highly recurrent single base insertion (n.64_65insT). In 54 individuals where it could be determined, the de novo variants were all on the maternal allele. We demonstrate that RNU4-2 is highly expressed in the developing human brain, in contrast to RNU4-1 and other U4 homologs. Using RNA-sequencing, we show how 5’ splice site usage is systematically disrupted in individuals with RNU4-2 variants, consistent with the known role of this region during spliceosome activation. Finally, we estimate that variants in this 18 bp region explain 0.4% of individuals with NDD. This work underscores the importance of non-coding genes in rare disorders and will provide a diagnosis to thousands of individuals with NDD worldwide

Experimental observation of a new attenuation mechanism in hcp-metals that may operate in the Earth’s Inner Core

Seismic observations show the Earth's inner core has significant and unexplained variation in seismic attenuation with position, depth and direction. Interpreting these observations is difficult without knowledge of the visco‐ or anelastic dissipation processes active in iron under inner core conditions. Here, a previously unconsidered attenuation mechanism is observed in zinc, a low pressure analog of hcp‐iron, during small strain sinusoidal deformation experiments. The experiments were performed in a deformation‐DIA combined with X‐radiography, at seismic frequencies (∼0.003–0.1 Hz), high pressure and temperatures up to ∼80% of melting temperature. Significant dissipation (0.077 ≤ Q−1(ω) ≤ 0.488) is observed along with frequency dependent softening of zinc's Young's modulus and an extremely small activation energy for creep (⩽7 kJ mol−1). In addition, during sinusoidal deformation the original microstructure is replaced by one with a reduced dislocation density and small, uniform, grain size. This combination of behavior collectively reflects a mode of deformation called “internal stress superplasticity”; this deformation mechanism is unique to anisotropic materials and activated by cyclic loading generating large internal stresses. Here we observe a new form of internal stress superplasticity, which we name as “elastic strain mismatch superplasticity.” In it the large stresses are caused by the compressional anisotropy. If this mechanism is also active in hcp‐iron and the Earth's inner‐core it will be a contributor to inner‐core observed seismic attenuation and constrain the maximum inner‐core grain‐size to ≲10 km

Effect of Investigator Disturbance in Experimental Forensic Entomology: Succession and Community Composition

Carrion insect succession studies have historically used repeated sampling of single or a few carcasses to produce data, either weighing the carcasses, removing a qualitative subsample of the fauna present, or both, on every visit over the course of decomposition and succession. This study, conducted in a set of related experimental hypotheses with two trials in a single season, investigated the effect that repeated sampling has on insect succession, determined by the number of taxa collected on each visit and by community composition. Each trial lasted at least 21 days, with daily visits on the first 14 days. Rat carcasses used in this study were all placed in the field on the same day, but then either sampled qualitatively on every visit (similar to most succession studies) or ignored until a given day of succession, when they were sampled qualitatively (a subsample) and then destructively sampled in their entirety. Carcasses sampled on every visit were in two groups: those from which only a sample of the fauna was taken and those from which a sample of fauna was taken and the carcass was weighed for biomass determination. Of the carcasses visited only once, the number of taxa in subsamples was compared to the actual number of taxa present when the carcass was destructively sampled to determine if the subsamples adequately represented the total carcass fauna. Data from the qualitative subsamples of those carcasses visited only once were also compared to data collected from carcasses that were sampled on every visit to investigate the effect of the repeated sampling. A total of 39 taxa were collected from carcasses during the study and the component taxa are discussed individually in relation to their role in succession. Number of taxa differed on only one visit between the qualitative subsamples and the actual number of taxa present, primarily because the organisms missed by the qualitative sampling were cryptic (hidden deep within body cavities) or rare (only represented by very few specimens). There were no differences discovered between number of taxa in qualitative subsamples from carcasses sampled repeatedly (with or without biomass determinations) and those sampled only a single time. Community composition differed considerably in later stages of decomposition, with disparate communities due primarily to small numbers of rare taxa. These results indicate that the methods used historically for community composition determination in experimental forensic entomology are generally adequate