Linear and nonlinear decay of cat's eyes in two-dimensional vortices, and the link to Landau poles

Copyright © 2007 Cambridge University Press. Published version reproduced with the permission of the publisher.This paper considers the evolution of smooth, two-dimensional vortices subject to a rotating external strain field, which generates regions of recirculating, cat's eye stream line topology within a vortex. When the external strain field is smoothly switched off, the cat's eyes may persist, or they may disappear as the vortex relaxes back to axisymmetry. A numerical study obtains criteria for the persistence of cat's eyes as a function of the strength and time scale of the imposed strain field, for a Gaussian vortex profile. In the limit of a weak external strain field and high Reynolds number, the disturbance decays exponentially, with a rate that is linked to a Landau pole of the linear inviscid problem. For stronger strain fields, but not strong enough to give persistent cat's eyes, the exponential decay of the disturbance varies: as time increases the decay slows down, because of the nonlinear feedback on the mean profile of the vortex. This is confirmed by determining the decay rate given by the Landau pole for these modified profiles. For strain fields strong enough to generate persistent cat's eyes, their location and rotation rate are determined for a range of angular velocities of the external strain field, and are again linked to Landau poles of the mean profiles, modified through nonlinear effects

Developmental evolution of flowering plant pollen tube cell walls: callose synthase (CalS) gene expression patterns

<p>Abstract</p> <p>Background</p> <p>A number of innovations underlie the origin of rapid reproductive cycles in angiosperms. A critical early step involved the modification of an ancestrally short and slow-growing pollen tube for faster and longer distance transport of sperm to egg. Associated with this shift are the predominantly callose (1,3-β-glucan) walls and septae (callose plugs) of angiosperm pollen tubes. Callose synthesis is mediated by callose synthase (CalS). Of 12 <it>CalS </it>gene family members in <it>Arabidopsis</it>, only one (<it>CalS5</it>) has been directly linked to pollen tube callose. <it>CalS5 </it>orthologues are present in several monocot and eudicot genomes, but little is known about the evolutionary origin of <it>CalS5 </it>or what its ancestral function may have been.</p> <p>Results</p> <p>We investigated expression of <it>CalS </it>in pollen and pollen tubes of selected non-flowering seed plants (gymnosperms) and angiosperms within lineages that diverged below the monocot/eudicot node. First, we determined the nearly full length coding sequence of a <it>CalS5 </it>orthologue from <it>Cabomba caroliniana </it>(<it>CcCalS5</it>) (Nymphaeales). Semi-quantitative RT-PCR demonstrated low <it>CcCalS5 </it>expression within several vegetative tissues, but strong expression in mature pollen. <it>CalS </it>transcripts were detected in pollen tubes of several species within Nymphaeales and Austrobaileyales, and comparative analyses with a phylogenetically diverse group of sequenced genomes indicated homology to <it>CalS5</it>. We also report <it>in silico </it>evidence of a putative <it>CalS5 </it>orthologue from <it>Amborella</it>. Among gymnosperms, <it>CalS5 </it>transcripts were recovered from germinating pollen of <it>Gnetum </it>and <it>Ginkgo</it>, but a novel <it>CalS </it>paralog was instead amplified from germinating pollen of <it>Pinus taeda</it>.</p> <p>Conclusion</p> <p>The finding that CalS5 is the predominant callose synthase in pollen tubes of both early-diverging and model system angiosperms is an indicator of the homology of their novel callosic pollen tube walls and callose plugs. The data suggest that <it>CalS5 </it>had transient expression and pollen-specific functions in early seed plants and was then recruited to novel expression patterns and functions within pollen tube walls in an ancestor of extant angiosperms.</p

Developmental evolution of flowering plant pollen tube cell walls: callose synthase (\u3cem\u3eCalS\u3c/em\u3e) gene expression patterns

Background A number of innovations underlie the origin of rapid reproductive cycles in angiosperms. A critical early step involved the modification of an ancestrally short and slow-growing pollen tube for faster and longer distance transport of sperm to egg. Associated with this shift are the predominantly callose (1,3-β-glucan) walls and septae (callose plugs) of angiosperm pollen tubes. Callose synthesis is mediated by callose synthase (CalS). Of 12 CalS gene family members in Arabidopsis, only one (CalS5) has been directly linked to pollen tube callose. CalS5 orthologues are present in several monocot and eudicot genomes, but little is known about the evolutionary origin of CalS5 or what its ancestral function may have been. Results We investigated expression of CalS in pollen and pollen tubes of selected non-flowering seed plants (gymnosperms) and angiosperms within lineages that diverged below the monocot/eudicot node. First, we determined the nearly full length coding sequence of a CalS5 orthologue from Cabomba caroliniana (CcCalS5) (Nymphaeales). Semi-quantitative RT-PCR demonstrated low CcCalS5 expression within several vegetative tissues, but strong expression in mature pollen. CalS transcripts were detected in pollen tubes of several species within Nymphaeales and Austrobaileyales, and comparative analyses with a phylogenetically diverse group of sequenced genomes indicated homology to CalS5. We also report in silico evidence of a putative CalS5 orthologue from Amborella. Among gymnosperms, CalS5 transcripts were recovered from germinating pollen of Gnetum and Ginkgo, but a novel CalS paralog was instead amplified from germinating pollen of Pinus taeda. Conclusion The finding that CalS5 is the predominant callose synthase in pollen tubes of both early-diverging and model system angiosperms is an indicator of the homology of their novel callosic pollen tube walls and callose plugs. The data suggest that CalS5 had transient expression and pollen-specific functions in early seed plants and was then recruited to novel expression patterns and functions within pollen tube walls in an ancestor of extant angiosperms

Kinematic dynamo in spherical Couette flow

We investigate numerically kinematic dynamos driven by flow of electrically conducting fluid in the shell between two concentric differentially rotating spheres, a configuration normally referred to as spherical Couette flow. We compare between axisymmetric (2D) and fully three dimensional flows, between low and high global rotation rates, between prograde and retrograde differential rotations, between weak and strong nonlinear inertial forces, between insulating and conducting boundaries, and between two aspect ratios. The main results are as follows. Azimuthally drifting Rossby waves arising from the destabilisation of the Stewartson shear layer are crucial to dynamo action. Differential rotation and helical Rossby waves combine to contribute to the spherical Couette dynamo. At a slow global rotation rate, the direction of differential rotation plays an important role in the dynamo because of different patterns of Rossby waves in prograde and retrograde flows. At a rapid global rotation rate, stronger flow supercriticality (namely the difference between the differential rotation rate of the flow and its critical value for the onset of nonaxisymmetric instability) facilitates the onset of dynamo action. A conducting magnetic boundary condition and a larger aspect ratio both favour dynamo action

Variational data assimilation for the initial-value dynamo problem

The secular variation of the geomagnetic field as observed at the Earth's surface results from the complex magnetohydrodynamics taking place in the fluid core of the Earth. One way to analyze this system is to use the data in concert with an underlying dynamical model of the system through the technique of variational data assimilation, in much the same way as is employed in meteorology and oceanography. The aim is to discover an optimal initial condition that leads to a trajectory of the system in agreement with observations. Taking the Earth's core to be an electrically conducting fluid sphere in which convection takes place, we develop the continuous adjoint forms of the magnetohydrodynamic equations that govern the dynamical system together with the corresponding numerical algorithms appropriate for a fully spectral method. These adjoint equations enable a computationally fast iterative improvement of the initial condition that determines the system evolution. The initial condition depends on the three dimensional form of quantities such as the magnetic field in the entire sphere. For the magnetic field, conservation of the divergence-free condition for the adjoint magnetic field requires the introduction of an adjoint pressure term satisfying a zero boundary condition. We thus find that solving the forward and adjoint dynamo system requires different numerical algorithms. In this paper, an efficient algorithm for numerically solving this problem is developed and tested for two illustrative problems in a whole sphere: one is a kinematic problem with prescribed velocity field, and the second is associated with the Hall-effect dynamo, exhibiting considerable nonlinearity. The algorithm exhibits reliable numerical accuracy and stability. Using both the analytical and the numerical techniques of this paper, the adjoint dynamo system can be solved directly with the same order of computational complexity as that required to solve the forward problem. These numerical techniques form a foundation for ultimate application to observations of the geomagnetic field over the time scale of centuries

The ITGAV rs3738919 variant and susceptibility to rheumatoid arthritis in four Caucasian sample sets

INTRODUCTION: Angiogenesis is an important process in the development of destructive synovial pannus in rheumatoid arthritis (RA). The ITGAV +gene encodes a cell cycle-associated antigen, integrin alphanubeta 3, which plays a role in RA angiogenesis. Previously, two independent studies identified an association between the major allele of the ITGAV single-nucleotide polymorphism (SNP) rs3738919 and RA. We therefore tested this association in an independent study using New Zealand (NZ) and Oxford (UK) RA case control samples. METHODS: We compared genotype frequencies in 740 NZ Caucasian RA patients and 553 controls genotyped for rs3738919, using a polymerase chain reaction-restriction fragment length polymorphism assay. A TaqMan genotyping SNP assay was used to type 713 Caucasian RA patients and 515 control samples from Oxford for the rs3738919 variant. Association of rs3738919 with RA was tested in these two sample sets using the chi-square goodness-of-fit test. The Mantel-Haenszel test was used to perform a meta-analysis, combining the genetic results from four independent Caucasian case control cohorts, consisting of 3,527 cases and 4,126 controls. Haplotype analysis was also performed using SNPs rs3911238, rs10174098 and rs3738919 in the Wellcome Trust Case Control Consortium, NZ and Oxford case control samples. RESULTS: We found no evidence for association between ITGAV and RA in either the NZ or Oxford sample set (odds ratio [OR] = 0.88, P(allelic) = 0.11 and OR = 1.18, P(allelic) = 0.07, respectively). Inclusion of these data in a meta-analysis (random effects) of four independent cohorts (3,527 cases and 4,126 controls) weakens support for the hypothesis that rs3738919 plays a role in the development of RA (OR(combined) = 0.92, 95% confidence interval 0.80 to 1.07; P = 0.29). No consistent haplotype associations were evident. CONCLUSIONS: Association of ITGAV SNP rs7378919 with RA was not replicated in NZ or Oxford case control sample sets. Meta-analysis of these and previously published data lends limited support for a role for the ITGAV in RA in Caucasians of European ancestry

Only one independent genetic association with rheumatoid arthritis within the KIAA1109-TENR-IL2-IL21 locus in Caucasian sample sets: confirmation of association of rs6822844 with rheumatoid arthritis at a genome-wide level of significance

INTRODUCTION: The single nucleotide polymorphism (SNP) rs6822844 within the KIAA1109-TENR-IL2-IL21 gene cluster has been associated with rheumatoid arthritis (RA). Other variants within this cluster, including rs17388568 that is not in linkage disequilibrium (LD) with rs6822844, and rs907715 that is in moderate LD with rs6822844 and rs17388568, have been associated with a number of autoimmune phenotypes, including type 1 diabetes (T1D). Here we aimed to: one, confirm at a genome-wide level of significance association of rs6822844 with RA and, two, evaluate whether or not there were effects independent of rs6822844 on RA at the KIAA1109-TENR-IL2-IL21 locus. METHODS: A total of 842 Australasian RA patients and 1,115 controls of European Caucasian ancestry were genotyped for rs6822844, rs17388568 and rs907715. Meta-analysis of these data with published and publicly-available data was conducted using STATA. RESULTS: No statistically significant evidence for association was observed in the Australasian sample set for rs6822844 (odds ratio (OR)=0.95 (0.80 to 1.12), P=0.54), or rs17388568 (OR=1.03 (0.90 to 1.19), P=0.65) or rs907715 (OR=0.98 (0.86 to 1.12), P=0.69). When combined in a meta-analysis using data from a total of 9,772 cases and 10,909 controls there was a genome-wide level of significance supporting association of rs6822844 with RA (OR=0.86 (0.82 to 0.91), P=8.8x10(-8), P=2.1x10(-8) including North American Rheumatoid Arthritis Consortium data). Meta-analysis of rs17388568, using a total of 6,585 cases and 7,528 controls, revealed no significant association with RA (OR=1.03, (0.98 to 1.09); P=0.22) and meta-analysis of rs907715 using a total of 2,689 cases and 4,045 controls revealed a trend towards association (OR=0.93 (0.87 to 1.00), P=0.07). However, this trend was not independent of the association at rs6822844. CONCLUSIONS: The KIAA1109-TENR-IL2-IL21 gene cluster, that encodes an interleukin (IL-21) that plays an important role in Th17 cell biology, is the 20th locus for which there is a genome-wide (P ≤ 5x10(-8)) level of support for association with RA. As for most other autoimmune diseases, with the notable exception of T1D, rs6822844 is the dominant association in the locus. The KIAA1109-TENR-IL2-IL21 locus also confers susceptibility to other autoimmune phenotypes with a heterogeneous pattern of association

Landscape-Level Wolf Space Use is Correlated With Prey Abundance, Ease of Mobility and the Distribution of Prey Habitat

Predator space use influences ecosystem dynamics, and a fundamental goal assumed for a foraging predator is to maximize encounter rate with prey. This can be achieved by disproportionately utilizing areas of high prey density or, where prey are mobile and therefore spatially unpredictable, utilizing patches of their prey\u27s preferred resources. A third, potentially complementary strategy is to increase mobility by using linear features like roads and/or frozen waterways. Here, we used novel population-level predator utilization distributions (termed localized density distributions ) in a single-predator (Wolf), two-prey (moose and caribou) system to evaluate these space-use hypotheses. The study was conducted in contrasting sections of a large boreal forest area in northern Ontario, Canada, with a spatial gradient of human disturbances and predator and prey densities. Our results indicated that wolves consistently used forest stands preferred by moose, their main prey species in this part of Ontario. Direct use of prey-rich areas was also significant but restricted to where there was a high local density of moose, whereas use of linear features was pronounced where local moose density was lower. These behaviors suggest that Wolf foraging decisions, while consistently influenced by spatially anchored patches of prey forage resources, were also determined by local ecological conditions, specifically prey density. Wolves appeared to utilize prey-rich areas when regional preferred prey density exceeded a threshold that made this profitable, whereas they disproportionately used linear features that promoted mobility when low prey density made directly tracking prey distribution unprofitable

Non-local effects in the mean-field disc dynamo. II. Numerical and asymptotic solutions

The thin-disc global asymptotics are discussed for axisymmetric mean-field dynamos with vacuum boundary conditions allowing for non-local terms arising from a finite radial component of the mean magnetic field at the disc surface. This leads to an integro-differential operator in the equation for the radial distribution of the mean magnetic field strength, $Q(r)$ in the disc plane at a distance $r$ from its centre; an asymptotic form of its solution at large distances from the dynamo active region is obtained. Numerical solutions of the integro-differential equation confirm that the non-local effects act similarly to an enhanced magnetic diffusion. This leads to a wider radial distribution of the eigensolution and faster propagation of magnetic fronts, compared to solutions with the radial surface field neglected. Another result of non-local effects is a slowly decaying algebraic tail of the eigenfunctions outside the dynamo active region, $Q(r)\sim r^{-4}$, which is shown to persist in nonlinear solutions where $\alpha$-quenching is included. The non-local nature of the solutions can affect the radial profile of the regular magnetic field in spiral galaxies and accretion discs at large distances from the centre.Comment: Revised version, as accepted; Geophys. Astrophys. Fluid Dyna

LIMPRINT: the UK experience - subjective control of swelling in patients attending specialist lymphedema services

Background and study design: This study was undertaken as part of the UK LIMPRINT international study to determine the number of people with chronic oedema and its impact on health services. Overall 7436 with chronic oedema (CO) were recruited in the main UK study from a range of health settings. Methods and results: Subjective control of arm and leg chronic oedema (CO) was defined for patients attending three Lymphoedema services in the UK. Of the total available in the UK dataset 5165 (69.4%)/ 7436(100%) of participants were included. Reasons for exclusions included the following: lack of information (1669), having both arm and leg swelling (272), lack of description of control (5) and professional inability to decide whether CO was controlled (325). Arm swelling occurred in 953 (18.5%), with leg CO in 4212 (81.5%). Poor control was found in 1430 (27.7%) and good control in 3735 (72.3%). Control of arm swelling was worse in men and control increased overall in those aged over 45 years. In contrast control of CO worsened in those with leg CO with increasing age and multiple co-morbidities. Obesity and cellulitis, particularly an episode in the last year were associated with poor control. Independent risk factors for arm CO were obesity, neurological disease and cellulitis in the last year and for leg CO: obesity, poor mobility, heart disease, presence of a wound, cellulitis in the last year and duration of swelling. Conclusion: Control of CO within specialised centres is complex due to sociodemographic and clinical comorbidities