Knots, Braids and Hedgehogs from the Eikonal Equation

The complex eikonal equation in the three space dimensions is considered. We show that apart from the recently found torus knots this equation can also generate other topological configurations with a non-trivial value of the $\pi_2(S^2)$ index: braided open strings as well as hedgehogs. In particular, cylindric strings i.e. string solutions located on a cylinder with a constant radius are found. Moreover, solutions describing strings lying on an arbitrary surface topologically equivalent to cylinder are presented. We discus them in the context of the eikonal knots. The physical importance of the results originates in the fact that the eikonal knots have been recently used to approximate the Faddeev-Niemi hopfions.Comment: 15 pages, 5 figure

Persistent urinary incontinence and delivery mode history: a six-year longitudinal study.

Objective: To investigate the prevalence of persistent and long term postpartum urinary incontinence and associations with mode of first and subsequent delivery. Setting: Maternity units in Aberdeen (Scotland), Birmingham (England) and Dunedin (New Zealand). Design: Longitudinal study Population: 4214 women who returned postal questionnaires 3 months and 6 years after the index birth. Methods: Symptom data were obtained from both questionnaires and obstetric data from case-notes for the index birth and the second questionnaire for subsequent births. Logistic regression investigated the independent effects of mode of first delivery and delivery mode history. Main outcome measures: Urinary incontinence – persistent (at 3 months and 6 years after index birth) and long-term (at 6 years after index birth). Results: The prevalence of persistent urinary incontinence was 24%. Delivering exclusively by Caesarean section was associated with both less persistent (OR= 0.46, 95% CI 0.32 to 0.68) and long term urinary incontinence (OR=0.50, 95% CI 0.40 to 0.63). Caesarean section birth in addition to vaginal delivery however was not associated with significantly less persistent incontinence (OR 0.93, 95%CI 0.67 to 1.29). There were no significant associations between persistent or long-term urinary incontinence and forceps or vacuum extraction delivery. Other significantly associated factors were increasing number of births and older maternal age. Conclusions: The risk of persistent and long term urinary incontinence is significantly lower following Caesarean section deliveries but not if there is another vaginal birth. Even when delivering exclusively by Caesarean section, the prevalence of persistent symptoms (14%) is still high

Analyses of Special Hazards and Flooding Problems in Tropical Island Environments

Data and results summarized in this paper show that development of urban projects and design of flood control works in tropical island catchments must consider clear water flooding as well as special hazards such as landslides, flow bulking, high sediment concentrations, mud and debris flows and flow avulsions. The needs for and methods to estimate peak flows, event volumes and the potential extent and depths of flooding during severe storm events in urbanizing tropical environments are described

Terrestrial Alteration Mineral Assemblages in the NWA 10416 Olivine Phyric Shergottite

We report on the alteration history of the olivine-phyric, highly depleted (HD) shergottite, Northwest Africa (NWA) 10416, paying particular attention to the origin of the aqueous alteration seen affecting the meteorite’s olivine megacrysts. The rock’s interior displays 1 mm, zoned, altered olivine megacrysts set in a groundmass of clinopyroxene, unzoned olivine, and interstitial plagioclase and maskelynite. Synchrotron micro X-ray diffraction (µ-XRD) and transmission electron microscopy (TEM) show that plagioclase and maskelynite have been partially replaced by kaolinite. The relict olivine megacryst cores display a unique concentric colouration for Martian meteorites, having central amber-coloured zones surrounded by a brown mantle zone, with the rims remaining clear and unaltered. This colouration is a result of fluid alteration and partial replacement, with hydration. TEM analysis revealed the ∼200 nm scale banded and largely amorphous nature of the alteration, but with some (∼ 20%) relict crystalline olivine patches. Although the coloured olivine zones show cation and anion site vacancies compared to stoichiometric olivine, a relict igneous compositional trend is preserved in the megacrysts, from Mg-rich altered cores (Mg# = 76) to unaltered stoichiometric rims (Fo53). Synchrotron Fe-K X-ray absorption near-edge structure (XANES) analysis revealed that the coloured zones of the megacryst have different Fe oxidation values. High ferric contents are present in the brown mantle zones (Fe3+/ΣFe ≤ 0.92) and the amber zones (Fe3+/ΣFe ≤ 0.30), whereas the clear rims are ferrous. This suggests alteration occurred in an oxidising environment and that the sharp contrast in colour of the megacryst (brown to clear) is a record of a relict fluid reaction front. In order to test the terrestrial or extraterrestrial origin of the alteration, olivine material from a shock-melt vein was analysed by TEM. The analysis revealed 0.952 nm curved d-spacing’s from clay alteration undisturbed by any shock effects, strongly suggesting a terrestrial origin. The d-spacing values most likely represent a collapsed saponite or vermiculite, showing that in some places olivine has been replaced by crystalline clay. Oxygen isotope analysis of bulk (Δ17O = 0.309 ± 0.009 (2σ) ‰) and amber-coloured megacryst material (= 0.271 ± 0.002 (2σ) ‰), are also consistent with terrestrial alteration. We propose a model in which, during the meteorite’s time in Northwest Africa, low-temperature, likely acidic, groundwater exploited fractures. The fluid altered the olivine megacrysts in a way that was controlled by the pre-existing, igneous compositional zonation, with Mg-rich olivine being more susceptible to alteration in this fluid environment. The plagioclase and maskelynite were also altered to a high degree. After the alteration event it is likely that NWA 10416 had a significant residence time in Northwest Africa, accounting for terrestrial calcite and the dehydration of some clay phases

The relative importance of local and regional processes to metapopulation dynamics

Metapopulation dynamics - patch occupancy, colonization and extinction - are the result of complex processes at both local (e.g. environmental conditions) and regional (e.g. spatial arrangement of habitat patches) scales. A large body of work has focused on habitat patch area and connectivity (area-isolation paradigm). However, these approaches often do not incorporate local environmental conditions or fully address how the spatial arrangement of habitat patches (and resulting connectivity) can influence metapopulation dynamics. Here, we utilize long-term data on a classic metapopulation system - the Glanville fritillary butterfly occupying a set of dry meadows and pastures in the angstrom land islands - to investigate the relative roles of local environmental conditions, geographic space and connectivity in capturing patch occupancy, colonization and extinction. We defined connectivity using traditional measures as well as graph-theoretic measures of centrality. Using boosted regression tree models, we find roughly comparable model performance among models trained on environmental conditions, geographic space or patch centrality. In models containing all of the covariates, we find strong and consistent evidence for the roles of resource abundance, longitude and centrality (i.e. connectivity) in predicting habitat patch occupancy and colonization, while patch centrality (connectivity) was relatively unimportant for predicting extinction. Relative variable importance did not change when geographic coordinates were not considered and models underwent spatially stratified cross-validation. Together, this suggests that the combination of regional-scale connectivity measures and local-scale environmental conditions is important for predicting metapopulation dynamics and that a stronger integration of ideas from network theory may provide insight into metapopulation processes.Peer reviewe

U.S. Citizens Working in International Organizations in Vienna, Austria

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Mapping between dissipative and Hamiltonian systems

Theoretical studies of nonequilibrium systems are complicated by the lack of a general framework. In this work we first show that a transformation introduced by Ao recently (J. Phys. A {\bf 37}, L25 (2004)) is related to previous works of Graham (Z. Physik B {\bf 26}, 397 (1977)) and Eyink {\it et al.} (J. Stat. Phys. {\bf 83}, 385 (1996)), which can also be viewed as the generalized application of the Helmholtz theorem in vector calculus. We then show that systems described by ordinary stochastic differential equations with white noise can be mapped to thermostated Hamiltonian systems. A steady-state of a dissipative system corresponds to the equilibrium state of the corresponding Hamiltonian system. These results provides a solid theoretical ground for corresponding studies on nonequilibrium dynamics, especially on nonequilibrium steady state. The mapping permits the application of established techniques and results for Hamiltonian systems to dissipative non-Hamiltonian systems, those for thermodynamic equilibrium states to nonequilibrium steady states. We discuss several implications of the present work.Comment: 18 pages, no figure. final version for publication on J. Phys. A: Math & Theo

Structure of Disk Dominated Galaxies I. Bulge/Disk Parameters, Simulations, and Secular Evolution

(Abridged) A robust analysis of galaxy structural parameters, based on the modeling of bulge and disk brightnesses in the BVRH bandpasses, is presented for 121 face-on and moderately inclined late-type spirals. Each surface brightness (SB) profile is decomposed into a sum of a generalized Sersic bulge and an exponential disk. The reliability and limitations of our bulge-to-disk (B/D) decompositions are tested with extensive simulations of galaxy brightness profiles (1D) and images (2D). Galaxy types are divided into 3 classes according to their SB profile shapes; Freeman Type-I and Type-II, and a third ``Transition'' class for galaxies whose profiles change from Type-II in the optical to Type-I in the infrared. We discuss possible interpretations of Freeman Type-II profiles. The Sersic bulge shape parameter for nearby Type-I late-type spirals shows a range between n=0.1-2 but, on average, the underlying surface density profile for the bulge and disk of these galaxies is adequately described by a double-exponential distribution. We confirm a coupling between the bulge and disk with a scale length ratio r_e/h=0.22+/-0.09, or h_bulge/h_disk=0.13+/-0.06 for late-type spirals, in agreement with recent N-body simulations of disk formation and models of secular evolution. This ratio increases from ~0.20 for late-type spirals to ~0.24 for earlier types. The similar scaling relations for early and late-type spirals suggest comparable formation and/or evolution scenarios for disk galaxies of all Hubble types.Comment: 78 pages with 23 embedded color figures + tables of galaxy structural parameters. Accepted for publication in the Astrophysical Journal. The interested reader is strongly encouraged to ignore some of the low res figures within; instead, download the high resolution version from http://www.astro.ubc.ca/people/courteau/public/macarthur02_disks.ps.g

The diverse nature of island isolation and its effect on land bridge insular faunas

Aim: Isolation is a key factor in island biology. It is usually defined as the distance to the geographically nearest mainland, but many other definitions exist. We explored how testing different isolation indices affects the inference of impacts of isolation on faunal characteristics. We focused on land bridge islands and compared the relationships of many spatial and temporal (i.e., through time) isolation indices with community‐, population‐ and individual‐level characteristics (species richness, population density and body size, respectively). Location: Aegean Sea islands, Greece. Time period: Current. Taxon: Many animal taxa. Methods: We estimated 21 isolation indices for 205 islands and recorded species richness data for 15 taxa (invertebrates and vertebrates). We obtained body size data for seven lizard species and population density data for three. We explored how well indices predict each characteristic, in each taxon, by conducting a series of ordinary least squares regressions (controlling for island area when needed) and a meta‐analysis. Results: Isolation was significantly (and negatively) associated with species richness in 10 of 15 taxa. It was significantly (and positively) associated with body size in only one of seven species and was not associated with population density. The effect of isolation on species richness was much weaker than that of island area, regardless of the index tested. Spatial indices generally out‐performed temporal indices, and indices directly related to the mainland out‐performed those related mainly to neighbouring islands. No index was universally superior to others, including the distance to the geographically nearest mainland. Main conclusions: The choice of index can alter our perception of the impacts of isolation on biological patterns. The nearly automatic, ubiquitous use of distance to the geographically nearest mainland misrepresents the complexity of the effects of isolation. We recommend the simultaneous testing of several indices that represent different aspects of isolation, in order to produce more constructive and thorough investigations and avoid imprecise inference

Quantifying resistance and resilience to local extinction for conservation prioritization

This is the final version. Available on open access from Ecological Society of America via the DOI in this recordSpecies-focused conservation planning is often based on reducing local extinction risk at key sites. However, with increasing levels of habitat fragmentation and pressures from climate change and overexploitation, surrounding landscapes also influence the persistence of species populations, and their effects are increasingly incorporated in conservation planning and management for both species and communities. Here, we present a framework based on metapopulation dynamics in fragmented landscapes, for quantifying the survival (resistance) and reestablishment of species populations following localized extinction events (resilience). We explore the application of this framework to guide the conservation of a group of threatened bird species endemic to papyrus (Cyperus papyrus) swamps in East and Central Africa. Using occupancy data for five species collected over two years from a network of wetlands in Uganda, we determine the local and landscape factors that influence local extinction and colonization, and map expected rates of population turnover across the network to draw inferences about the locations which contribute most to regional resistance and resilience for all species combined. Slight variation in the factors driving extinction and colonization between individual papyrus birds led to species-specific differences in the spatial patterns of site-level resistance and resilience. However, despite this, locations with the highest resistance and/or resilience overlapped for most species and reveal where resources could be invested for multi-species persistence. This novel simplified framework can aid decision making associated with conservation planning and prioritization for multiple species residing in overlapping, fragmented habitats; helping to identify key sites that warrant urgent conservation protection, with consideration of the need to adapt and respond to future change. This article is protected by copyright. All rights reserved.Natural Environment Research Council (NERC)The Explorers ClubBritish Ornithologists’ UnionRoyal Geographic SocietyJohn Muir TrustGilchrist Educational Trus