The Cauchy problem for a class of two-dimensional nonlocal nonlinear wave equations governing anti-plane shear motions in elastic materials

This paper is concerned with the analysis of the Cauchy problem of a general class of two-dimensional nonlinear nonlocal wave equations governing anti-plane shear motions in nonlocal elasticity. The nonlocal nature of the problem is reflected by a convolution integral in the space variables. The Fourier transform of the convolution kernel is nonnegative and satisfies a certain growth condition at infinity. For initial data in $L^{2}$ Sobolev spaces, conditions for global existence or finite time blow-up of the solutions of the Cauchy problem are established.Comment: 15 pages. "Section 6 The Anisotropic Case" added and minor changes. Accepted for publication in Nonlinearit

Close Packing of Atoms, Geometric Frustration and the Formation of Heterogeneous States in Crystals

To describe structural peculiarities in inhomogeneous media caused by the tendency to the close packing of atoms a formalism based on the using of the Riemann geometry methods (which were successfully applied lately to the description of structures of quasicrystals and glasses) is developed. Basing on this formalism we find in particular the criterion of stability of precipitates of the Frank-Kasper phases in metallic systems. The nature of the ''rhenium effect'' in W-Re alloys is discussed.Comment: 14 pages, RevTex, 2 PostScript figure

Bumblebees moving up: shifts in elevation ranges in the Pyrenees over 115 years

In a warming climate, species are expected to shift their geographical ranges to higher elevations and latitudes, and if interacting species shift at different rates, networks may be disrupted. To quantify the effects of ongoing climate change, repeating historical biodiversity surveys is necessary. In this study, we compare the distribution of a plant–pollinator community between two surveys 115 years apart (1889 and 2005–06), reporting distribution patterns and changes observed for bumblebee species and bumblebee-visited plants in the Gavarnie-Gèdre commune in the Pyrenees, located in southwest Europe at the French–Spanish border. The region has warmed significantly over this period, alongside shifts in agricultural land use and forest. The composition of the bumblebee community shows relative stability, but we observed clear shifts to higher elevations for bumblebees (averaging 129 m) and plants (229 m) and provide preliminary evidence that some bumblebee species shift with the plants they visit. We also observe that some species have been able to occupy the same climate range in both periods by shifting elevation range. The results suggest the need for long-term monitoring to determine the role and impact of the different drivers of global change, especially in montane habitats where the impacts of climate changes are anticipated to be more extreme

The effect of sampling effort and methodology on range size estimates of poorly-recorded species for IUCN Red List assessments

Geographic range size is the most commonly implemented criterion of species’ extinction risk used in IUCN Red List assessments, especially for poorly-recorded species. IUCN applies two contrasting range size measures to capture different facets of a species’ distribution: Extent of Occurrence (EOO; Criterion B1) is the area bounding all known occurrences and is a proxy for the spatial autocorrelation of risk, while the Area of Occupancy (AOO; Criterion B2) is the area occupied within this boundary and is related to population size at finer grains. Various methods have been proposed to measure both EOO and AOO. We evaluate the impact of applying four methods for each of Criterion B1 and of B2, as well as key parameter choices, on the Red List status of 227 poorly-recorded neotropical pteridophyte species. Between 2 and 100% of species would be considered threatened depending on methodology. The minimum convex polygon method of estimating EOO was relatively robust to sampling effort for all but the least-recorded species. The IUCN-recommended method for estimating AOO of summing occupied 2 × 2 km grid cells was very strongly correlated with the total number of records. It is likely that only a small fraction of species can be adequately assessed using this method, and we recommend caution applying the method to poorly-recorded species in particular, where models predicting occupancy in unsampled areas (e.g. species distribution models) may provide more accurate assessments. It is vital that methodological information is retained with assessments, and comparisons should only be made between assessments utilising equivalent methods

Interpreting 16S metagenomic data without clustering to achieve sub-OTU resolution

The standard approach to analyzing 16S tag sequence data, which relies on clustering reads by sequence similarity into Operational Taxonomic Units (OTUs), underexploits the accuracy of modern sequencing technology. We present a clustering-free approach to multi-sample Illumina datasets that can identify independent bacterial subpopulations regardless of the similarity of their 16S tag sequences. Using published data from a longitudinal time-series study of human tongue microbiota, we are able to resolve within standard 97% similarity OTUs up to 20 distinct subpopulations, all ecologically distinct but with 16S tags differing by as little as 1 nucleotide (99.2% similarity). A comparative analysis of oral communities of two cohabiting individuals reveals that most such subpopulations are shared between the two communities at 100% sequence identity, and that dynamical similarity between subpopulations in one host is strongly predictive of dynamical similarity between the same subpopulations in the other host. Our method can also be applied to samples collected in cross-sectional studies and can be used with the 454 sequencing platform. We discuss how the sub-OTU resolution of our approach can provide new insight into factors shaping community assembly.Comment: Updated to match the published version. 12 pages, 5 figures + supplement. Significantly revised for clarity, references added, results not change

2-{[2,8-Bis(trifluoro­meth­yl)quinolin-4-yl](hy­droxy)meth­yl}piperidin-1-ium 3-amino-5-nitro­benzoate sesquihydrate

The asymmetric unit of the title salt solvate, C17H17F6N2O+·C7H5N2O4 −·1.5H2O, comprises a piperidin-1-ium cation, a 3-amino-5-nitro­benzoate anion, and three fractionally occupied [i.e. 0.414 (3), 0.627 (6) and 0.459 (5)] disordered water mol­ecules of solvation. The cation has an L shape with a C—C—C—C torsion angle of −102.9 (3)° for the atoms linking the quinolinyl group to the rest of the cation. In the anion, the carboxyl­ate and nitro groups are essentially coplanar with the benzene ring [O—C—C—C torsion angle = 179.7 (2)° and O—N—C—C torsion angle = −3.9 (3)°]. In the crystal, extensive O—H⋯O, O—H⋯F and N—H⋯·O hydrogen bonding leads to the formation of a layer in the ab plane

(R*,S*)-(±)-1-(2-{[2,8-Bis(trifluoromethyl)quinolin-4-yl](hydroxy)methyl}piperidin-1-yl)ethanone methanol monosolvate

The title mefloquine derivative has been crystallized as its 1:1 methanol solvate, C19H18F6N2O2·CH3OH. Each of the meth­ine­hydroxyl residue [the C—C—C—O torsion angle is −16.35 (17) °] and the piperidinyl group [distorted chair conformation] lies to one side of the quinolinyl ring system. The hydroxyl and carbonyl groups lie to either side of the mol­ecule, enabling their participation in inter­molecular inter­actions. Thus, the hydroxyl and carbonyl groups of two centrosymmetrically related mol­ecules are bridged by two methanol mol­ecules via O—H⋯O hydrogen bonds, leading to a four-mol­ecule aggregate. These are linked into a supra­molecular chain along the a axis via C—H⋯O inter­actions involving the hydroxyl-O atom. The chains assemble into layers that inter­digitate along the c axis being connected by C—H⋯F inter­actions

Where is the UK's pollinator biodiversity? The importance of urban areas for flower-visiting insects

Insect pollinators provide a crucial ecosystem service, but are under threat. Urban areas could be important for pollinators, though their value relative to other habitats is poorly known. We compared pollinator communities using quantified flower-visitation networks in 36 sites (each 1 km2) in three landscapes: urban, farmland and nature reserves. Overall, flower-visitor abundance and species richness did not differ significantly between the three landscape types. Bee abundance did not differ between landscapes, but bee species richness was higher in urban areas than farmland. Hoverfly abundance was higher in farmland and nature reserves than urban sites, but species richness did not differ significantly. While urban pollinator assemblages were more homogeneous across space than those in farmland or nature reserves, there was no significant difference in the numbers of rarer species between the three landscapes. Network-level specialization was higher in farmland than urban sites. Relative to other habitats, urban visitors foraged from a greater number of plant species (higher generality) but also visited a lower proportion of available plant species (higher specialization), both possibly driven by higher urban plant richness. Urban areas are growing, and improving their value for pollinators should be part of any national strategy to conserve and restore pollinators

The closest elastic tensor of arbitrary symmetry to an elasticity tensor of lower symmetry

The closest tensors of higher symmetry classes are derived in explicit form for a given elasticity tensor of arbitrary symmetry. The mathematical problem is to minimize the elastic length or distance between the given tensor and the closest elasticity tensor of the specified symmetry. Solutions are presented for three distance functions, with particular attention to the Riemannian and log-Euclidean distances. These yield solutions that are invariant under inversion, i.e., the same whether elastic stiffness or compliance are considered. The Frobenius distance function, which corresponds to common notions of Euclidean length, is not invariant although it is simple to apply using projection operators. A complete description of the Euclidean projection method is presented. The three metrics are considered at a level of detail far greater than heretofore, as we develop the general framework to best fit a given set of moduli onto higher elastic symmetries. The procedures for finding the closest elasticity tensor are illustrated by application to a set of 21 moduli with no underlying symmetry.Comment: 48 pages, 1 figur