The twistor spinors of generic 2- and 3-distributions

Generic distributions on 5- and 6-manifolds give rise to conformal structures that were discovered by P. Nurowski resp. R. Bryant. We describe both as Fefferman-type constructions and show that for orientable distributions one obtains conformal spin structures. The resulting conformal spin geometries are then characterized by their conformal holonomy and equivalently by the existence of a twistor spinor which satisfies a genericity condition. Moreover, we show that given such a twistor spinor we can decompose a conformal Killing field of the structure. We obtain explicit formulas relating conformal Killing fields, almost Einstein structures and twistor spinors.Comment: 26 page

Synthesis and characterisation of the hollandite solid solution Ba1.2-xCsxFe2.4-xTi5.6+xO16 for partitioning and conditioning of radiocaesium

The geological disposal of high level radioactive waste requires careful budgeting of the heat load produced by radiogenic decay. Removal of high-heat generating radionuclides, such as 137 Cs, reduces the heat load in the repository allowing the remaining high level waste to be packed closer together therefore reducing demand for repository space and the cost of the disposal of the remaining wastes. Hollandites have been proposed as a possible host matrix for the long-term disposal of Cs separated from HLW raffinate. The incorporation of Cs into the hollandite phase is aided by substitution of cations on the B-site of the hollandite structure, including iron. A range of Cs containing iron hollandites were synthesised via an alkoxide-nitrate route and the structural environment of Fe in the resultant material characterised by Mössbauer and X-ray Absorption Near Edge Spectroscopy. The results of spectroscopic analysis found that Fe was present as octahedrally co-ordinated Fe (III) in all cases and acts as an effective charge compensator over a wide solid solution range

A holonomy characterisation of Fefferman spaces

We prove that Fefferman spaces, associated to non--degenerate CR structures of hypersurface type, are characterised, up to local conformal isometry, by the existence of a parallel orthogonal complex structure on the standard tractor bundle. This condition can be equivalently expressed in terms of conformal holonomy. Extracting from this picture the essential consequences at the level of tensor bundles yields an improved, conformally invariant analogue of Sparling's characterisation of Fefferman spaces.Comment: AMSLaTeX, 15 page

Sliding blocks with random friction and absorbing random walks

With the purpose of explaining recent experimental findings, we study the distribution $A(\lambda)$ of distances $\lambda$ traversed by a block that slides on an inclined plane and stops due to friction. A simple model in which the friction coefficient $\mu$ is a random function of position is considered. The problem of finding $A(\lambda)$ is equivalent to a First-Passage-Time problem for a one-dimensional random walk with nonzero drift, whose exact solution is well-known. From the exact solution of this problem we conclude that: a) for inclination angles $\theta$ less than \theta_c=\tan(\av{\mu}) the average traversed distance \av{\lambda} is finite, and diverges when $\theta \to \theta_c^{-}$ as \av{\lambda} \sim (\theta_c-\theta)^{-1}; b) at the critical angle a power-law distribution of slidings is obtained: $A(\lambda) \sim \lambda^{-3/2}$. Our analytical results are confirmed by numerical simulation, and are in partial agreement with the reported experimental results. We discuss the possible reasons for the remaining discrepancies.Comment: 8 pages, 8 figures, submitted to Phys. Rev.

Smooth metric measure spaces, quasi-Einstein metrics, and tractors

We introduce the tractor formalism from conformal geometry to the study of smooth metric measure spaces. In particular, this gives rise to a correspondence between quasi-Einstein metrics and parallel sections of certain tractor bundles. We use this formulation to give a sharp upper bound on the dimension of the vector space of quasi-Einstein metrics, providing a different perspective on some recent results of He, Petersen and Wylie.Comment: 33 pages; final versio

Lorentz-violating effects on topological defects generated by two real scalar fields

The influence of a Lorentz-violation on soliton solutions generated by a system of two coupled scalar fields is investigated. Lorentz violation is induced by a fixed tensor coefficient that couples the two fields. The Bogomol'nyi method is applied and first-order differential equations are obtained whose solutions minimize energy and are also solutions of the equations of motion. The analysis of the solutions in phase space shows how the stability is modified with the Lorentz violation. It is shown explicitly that the solutions preserve linear stability despite the presence of Lorentz violation. Considering Lorentz violation as a small perturbation, an analytical method is employed to yield analytical solutions.Comment: (9 pages, 11 figures

Pathway Analysis Integrating Genome-Wide and Functional Data Identifies PLCG2 as a Candidate Gene for Age-Related Macular Degeneration

PURPOSE. Age-related macular degeneration (AMD) is the worldwide leading cause of blindness among the elderly. Although genome-wide association studies (GWAS) have identified AMD risk variants, their roles in disease etiology are not well-characterized, and they only explain a portion of AMD heritability. METHODS. We performed pathway analyses using summary statistics from the International AMD Genomics Consortium’s 2016 GWAS and multiple pathway databases to identify biological pathways wherein genetic association signals for AMD may be aggregating. We determined which genes contributed most to significant pathway signals across the databases. We characterized these genes by constructing protein-protein interaction networks and performing motif analysis. RESULTS. We determined that eight genes (C2, C3, LIPC, MICA, NOTCH4, PLCG2, PPARA, and RAD51B) ‘‘drive’’ the statistical signals observed across pathways curated in the Kyoto Encyclopedia of Genes and Genomes (KEGG), Reactome, and Gene Ontology (GO) databases. We further refined our definition of statistical driver gene to identify PLCG2 as a candidate gene for AMD due to its significant gene-level signals (P < 0.0001) across KEGG, Reactome, GO, and NetPath pathways. CONCLUSIONS. We performed pathway analyses on the largest available collection of advanced AMD cases and controls in the world. Eight genes strongly contributed to significant pathways from the three larger databases, and one gene (PLCG2) was central to significant pathways from all four databases. This is, to our knowledge, the first study to identify PLCG2 as a candidate gene for AMD based solely on genetic burden. Our findings reinforce the utility of integrating in silico genetic and biological pathway data to investigate the genetic architecture of AMD

Synthesis and characterisation of HIP Ca0.80Ce0.20ZrTi1.60Cr0.40O7 zirconolite and observations of the ceramic–canister interface

A sample of zirconolite with nominal composition Ca0.80Ce0.20ZrTi1.60Cr0.40O7 was processed via Hot Isostatic Pressing (HIP), with a dwell temperature and pressure of 1320 °C/100 MPa maintained for 4 h. The produced wasteform was characterised by powder XRD, SEM–EDS, Ce L3 and Cr K-edge XANES. A significant portion of the Ce inventory did not fully partition within the zirconolite phase, instead remaining as CeO2 within the microstructure. Inspection of the stainless steel–ceramic interface detailed the presence of an interaction region dominated by a Cr-rich oxide layer. No significant Cr or Fe migration was observed, although a greater concentration of perovskite was observed at the periphery, relative to the bulk ceramic matrix. The X-ray absorption features of Cr remained analogous with Cr3+ accommodation within TiO6 octahedra in the zirconolite matrix. The absorption edge of Ce was comprised of contributions from zirconolite-2M and unincorporated CeO2, with an average oxidation state of Ce3.9+. As zirconolite-2M accounted for > 92 wt% of the overall phase assemblage, it is clear that the dominant oxidation state of Ce in this phase was Ce4+

Horizontal Branch Stars: The Interplay between Observations and Theory, and Insights into the Formation of the Galaxy

We review HB stars in a broad astrophysical context, including both variable and non-variable stars. A reassessment of the Oosterhoff dichotomy is presented, which provides unprecedented detail regarding its origin and systematics. We show that the Oosterhoff dichotomy and the distribution of globular clusters (GCs) in the HB morphology-metallicity plane both exclude, with high statistical significance, the possibility that the Galactic halo may have formed from the accretion of dwarf galaxies resembling present-day Milky Way satellites such as Fornax, Sagittarius, and the LMC. A rediscussion of the second-parameter problem is presented. A technique is proposed to estimate the HB types of extragalactic GCs on the basis of integrated far-UV photometry. The relationship between the absolute V magnitude of the HB at the RR Lyrae level and metallicity, as obtained on the basis of trigonometric parallax measurements for the star RR Lyrae, is also revisited, giving a distance modulus to the LMC of (m-M)_0 = 18.44+/-0.11. RR Lyrae period change rates are studied. Finally, the conductive opacities used in evolutionary calculations of low-mass stars are investigated. [ABRIDGED]Comment: 56 pages, 22 figures. Invited review, to appear in Astrophysics and Space Scienc