On Arnol'd's second nonlinear stability theorem for two-dimensional quasi-geostrophic flow

Arnol'd's second hydrodynamical stability theorem, proven originally for the two-dimensional Euler equations, can establish nonlinear stability of steady flows that are maxima of a suitably chosen energy-Casimir invariant. The usual derivations of this theorem require an assumption of zero disturbance circulation. In the present work an analogue of Arnol'd's second theorem is developed in the more general case of two-dimensional quasi-geostrophic flow, with the important feature that the disturbances are allowed to have non-zero circulation. New nonlinear stability criteria are derived, and explicit bounds are obtained on both the disturbance energy and potential enstrophy which are expressed in terms of the initial disturbance fields. While Arnol'd's stability method relies on the second variation of the energy-Casimir invariant being sign-definite, the new criteria can be applied to cases where the second variation is sign-indefinite because of the disturbance circulations. A version of Andrews' theorem is also established for this problem.

Application of the direct Liapunov method to the problem of symmetric stability in the atmosphere

The problem of symmetric stability is examined within the context of the direct Liapunov method. The sufficient conditions for stability derived by Fjørtoft are shown to imply finite-amplitude, normed stability. This finite-amplitude stability theorem is then used to obtain rigorous upper bounds on the saturation amplitude of disturbances to symmetrically unstable flows.By employing a virial functional, the necessary conditions for instability implied by the stability theorem are shown to be in fact sufficient for instability. The results of Ooyama are improved upon insofar as a tight two-sided (upper and lower) estimate is obtained of the growth rate of (modal or nonmodal) symmetric instabilities.The case of moist adiabatic systems is also considered.

The stability of a two-dimensional vorticity filament under uniform strain

The quantitative effects of uniform strain and background rotation on the stability of a strip of constant vorticity (a simple shear layer) are examined. The thickness of the strip decreases in time under the strain, so it is necessary to formulate the linear stability analysis for a time-dependent basic flow. The results show that even a strain rate γ (scaled with the vorticity of the strip) as small as 0.25 suppresses the conventional Rayleigh shear instability mechanism, in the sense that the r.m.s. wave steepness cannot amplify by more than a certain factor, and must eventually decay. For γ < 0.25 the amplification factor increases as γ decreases; however, it is only 3 when γ e 0.065. Numerical simulations confirm the predictions of linear theory at small steepness and predict a threshold value necessary for the formation of coherent vortices. The results help to explain the impression from numerous simulations of two-dimensional turbulence reported in the literature that filaments of vorticity infrequently roll up into vortices. The stabilization effect may be expected to extend to two- and three-dimensional quasi-geostrophic flows.

Nonlinear stability and the saturation of instabilities to axisymmetric vortices

Nonlinear stability theorems are presented for axisymmetric vortices under the restriction that the disturbance is independent of either the azimuthal or the axial coordinate. These stability theorems are then used, in both cases, to derive rigorous upper bounds on the saturation amplitudes of instabilities. Explicit examples of such bounds are worked out for some canonical profiles. The results establish a minimum order for the dependence of saturation amplitude on supercriticality, and are thereby suggestive as to the nature of the bifurcation at the stability threshold.

An exact local conservation theorem for finite-amplitude disturbances to non-parallel shear flows, with remarks on Hamiltonian structure and on Arnol'd's stability theorems

Disturbances of arbitrary amplitude are superposed on a basic flow which is assumed to be steady and either (a) two-dimensional, homogeneous, and incompressible (rotating or non-rotating) or (b) stably stratified and quasi-geostrophic. Flow over shallow topography is allowed in either case. The basic flow, as well as the disturbance, is assumed to be subject neither to external forcing nor to dissipative processes like viscosity. An exact, local ‘wave-activity conservation theorem’ is derived in which the density A and flux F are second-order ‘wave properties’ or ‘disturbance properties’, meaning that they are O(a2) in magnitude as disturbance amplitude a [rightward arrow] 0, and that they are evaluable correct to O(a2) from linear theory, to O(a3) from second-order theory, and so on to higher orders in a. For a disturbance in the form of a single, slowly varying, non-stationary Rossby wavetrain, $\overline{F}/\overline{A}$ reduces approximately to the Rossby-wave group velocity, where (${}^{-}$) is an appropriate averaging operator. F and A have the formal appearance of Eulerian quantities, but generally involve a multivalued function the correct branch of which requires a certain amount of Lagrangian information for its determination. It is shown that, in a certain sense, the construction of conservable, quasi-Eulerian wave properties like A is unique and that the multivaluedness is inescapable in general. The connection with the concepts of pseudoenergy (quasi-energy), pseudomomentum (quasi-momentum), and ‘Eliassen-Palm wave activity’ is noted. The relationship of this and similar conservation theorems to dynamical fundamentals and to Arnol'd's nonlinear stability theorems is discussed in the light of recent advances in Hamiltonian dynamics. These show where such conservation theorems come from and how to construct them in other cases. An elementary proof of the Hamiltonian structure of two-dimensional Eulerian vortex dynamics is put on record, with explicit attention to the boundary conditions. The connection between Arnol'd's second stability theorem and the suppression of shear and self-tuning resonant instabilities by boundary constraints is discussed, and a finite-amplitude counterpart to Rayleigh's inflection-point theorem noted

The kinetics of αIIbβ3 activation determines the size and stability of thrombi in mice: implications for antiplatelet therapy.

Two major pathways contribute to Ras-proximate-1-mediated integrin activation in stimulated platelets. Calcium and diacyglycerol-regulated guanine nucleotide exchange factor I (CalDAG-GEFI, RasGRP2) mediates the rapid but reversible activation of integrin αIIbβ3, while the adenosine diphosphate receptor P2Y12, the target for antiplatelet drugs like clopidogrel, facilitates delayed but sustained integrin activation. To establish CalDAG-GEFI as a target for antiplatelet therapy, we compared how each pathway contributes to thrombosis and hemostasis in mice. Ex vivo, thrombus formation at arterial or venous shear rates was markedly reduced in CalDAG-GEFI(-/-) blood, even in the presence of exogenous adenosine diphosphate and thromboxane A(2). In vivo, thrombosis was virtually abolished in arterioles and arteries of CalDAG-GEFI(-/-) mice, while small, hemostatically active thrombi formed in venules. Specific deletion of the C1-like domain of CalDAG-GEFI in circulating platelets also led to protection from thrombus formation at arterial flow conditions, while it only marginally increased blood loss in mice. In comparison, thrombi in the micro- and macrovasculature of clopidogrel-treated wild-type mice grew rapidly and frequently embolized but were hemostatically inactive. Together, these data suggest that inhibition of the catalytic or the C1 regulatory domain in CalDAG-GEFI will provide strong protection from athero-thrombotic complications while maintaining a better safety profile than P2Y12 inhibitors like clopidogrel.

Pulsating equilibria: stability through migration

This paper is to present a model of spatial equilibrium using a nonlinear generalization of Markov-chain type model, and to show the dynamic stability of a unique equilibrium. Even at an equilibrium, people continue to migrate among regions as well as among agent-types, and yet their overall distribution remain unchanged. The model is also adapted to suggest a theory of traffic distribution in a city.

High Resolution Melt (HRM) analysis is an efficient tool to genotype EMS mutants in complex crop genomes

Background: Targeted Induced Loci Lesions IN Genomes (TILLING) is increasingly being used to generate and identify mutations in target genes of crop genomes. TILLING populations of several thousand lines have been generated in a number of crop species including Brassica rapa. Genetic analysis of mutants identified by TILLING requires an efficient, high-throughput and cost effective genotyping method to track the mutations through numerous generations. High resolution melt (HRM) analysis has been used in a number of systems to identify single nucleotide polymorphisms (SNPs) and insertion/deletions (IN/DELs) enabling the genotyping of different types of samples. HRM is ideally suited to high-throughput genotyping of multiple TILLING mutants in complex crop genomes. To date it has been used to identify mutants and genotype single mutations. The aim of this study was to determine if HRM can facilitate downstream analysis of multiple mutant lines identified by TILLING in order to characterise allelic series of EMS induced mutations in target genes across a number of generations in complex crop genomes. Results: We demonstrate that HRM can be used to genotype allelic series of mutations in two genes, BraA.CAX1a and BraA.MET1.a in Brassica rapa. We analysed 12 mutations in BraA.CAX1.a and five in BraA.MET1.a over two generations including a back-cross to the wild-type. Using a commercially available HRM kit and the Lightscanner™ system we were able to detect mutations in heterozygous and homozygous states for both genes. Conclusions: Using HRM genotyping on TILLING derived mutants, it is possible to generate an allelic series of mutations within multiple target genes rapidly. Lines suitable for phenotypic analysis can be isolated approximately 8-9 months (3 generations) from receiving M3 seed of Brassica rapa from the RevGenUK TILLING service.

On the role of the ocean in projected atmospheric stability changes in the Atlantic polar low region

The occurrence of destructive mesoscale ‘polar low’ cyclones in the subpolar North Atlantic is projected to decline under anthropogenic change, due to an increase in atmospheric static stability. This letter reports on the role of changes in ocean circulation in shaping the atmospheric stability. In particular, the Atlantic Meridional Overturning Circulation (AMOC) is projected to weaken in response to anthropogenic forcing, leading to a local minimum in warming in this region. The reduced warming is restricted to the lower troposphere, hence contributing to the increase in static stability. Linear correlation analysis of the CMIP3 climate model ensemble suggests that around half of the model uncertainty in the projected stability response arises from the varied response of the AMOC between models.

The Mid-Brunhes Event and West Antarctic ice sheet stability

The complex cyclical nature of Pleistocene climate, driven by the evolving orbital configuration of the Earth, is well known but not well understood. A major climatic transition took place at the Mid-Brunhes Event (MBE), ca. 430 ka ago after which the amplitude of the ca.100 ka climate oscillations increased, with substantially warmer interglacials, including periods warmer than present. Recent modelling has indicated that while the timing of these warmer-than-present transient (WPT) events is consistent with southern warming due to a deglaciation-forced slowdown of the Atlantic Meridional Overturning Circulation, the magnitude of warming requires a local amplification, for which a candidate is the feedback of significant West Antarctic Ice Sheet (WAIS) retreat. We here extend this argument, based on the absence of WPTs in the early ice core record (450–800 ka ago), to hypothesize that the MBE could be a manifestation of decreased WAIS stability, triggered by ongoing subglacial erosion.

APOA5 genotype influences the association between 25-hydroxyvitamin D and high density lipoprotein cholesterol

OBJECTIVE: Circulating levels of 25-hydroxyvitamin D (25OHD) are positively associated with high density lipoprotein (HDL) cholesterol. We sought to replicate a previously reported interaction between APOA5 genotype and vitamin D, and to examine whether HDL-associated genetic loci modify the association between serum 25OHD and HDL cholesterol. METHODS: We examined whether 42 single nucleotide polymorphisms (SNPs) modify the association between serum 25OHD and HDL cholesterol in the 1958 British Birth cohort (aged 45 years, n = 4978). RESULTS: We identified a borderline interaction between the SNP rs12272004 (near the APOA5) and serum 25OHD on HDL cholesterol (P(interaction) = 0.05). The interaction was particularly prominent among the samples collected during winter (P(interaction) = 0.001). None of the other loci showed an interaction with serum 25OHD concentrations on HDL cholesterol. CONCLUSIONS: Our study in 4978 British Whites provides further support that APOA5 genotype modifies the association between vitamin D metabolites and HDL cholesterol.

The Gly482Ser genotype at the PPARGC1A gene and elevated blood pressure: a meta-analysis involving 13,949 individuals.

The protein encoded by the PPARGC1A gene is expressed at high levels in metabolically active tissues and is involved in the control of oxidative stress via reactive oxygen species detoxification. Several recent reports suggest that the PPARGC1A Gly482Ser (rs8192678) missense polymorphism may relate inversely with blood pressure. We used conventional meta-analysis methods to assess the association between Gly482Ser and systolic (SBP) or diastolic blood pressures (DBP) or hypertension in 13,949 individuals from 17 studies, of which 6,042 were previously unpublished observations. The studies comprised cohorts of white European, Asian, and American Indian adults, and adolescents from South America. Stratified analyses were conducted to control for population stratification. Pooled genotype frequencies were 0.47 (Gly482Gly), 0.42 (Gly482Ser), and 0.11 (Ser482Ser). We found no evidence of association between Gly482Ser and SBP [Gly482Gly: mean = 131.0 mmHg, 95% confidence interval (CI) = 130.5-131.5 mmHg; Gly482Ser mean = 133.1 mmHg, 95% CI = 132.6-133.6 mmHg; Ser482Ser: mean = 133.5 mmHg, 95% CI = 132.5-134.5 mmHg; P = 0.409] or DBP (Gly482Gly: mean = 80.3 mmHg, 95% CI = 80.0-80.6 mmHg; Gly482Ser mean = 81.5 mmHg, 95% CI = 81.2-81.8 mmHg; Ser482Ser: mean = 82.1 mmHg, 95% CI = 81.5-82.7 mmHg; P = 0.651). Contrary to previous reports, we did not observe significant effect modification by sex (SBP, P = 0.966; DBP, P = 0.715). We were also unable to confirm the previously reported association between the Ser482 allele and hypertension [odds ratio: 0.97, 95% CI = 0.87-1.08, P = 0.585]. These results were materially unchanged when analyses were focused on whites only. However, statistical evidence of gene-age interaction was apparent for DBP [Gly482Gly: 73.5 (72.8, 74.2), Gly482Ser: 77.0 (76.2, 77.8), Ser482Ser: 79.1 (77.4, 80.9), P = 4.20 x 10(-12)] and SBP [Gly482Gly: 121.4 (120.4, 122.5), Gly482Ser: 125.9 (124.6, 127.1), Ser482Ser: 129.2 (126.5, 131.9), P = 7.20 x 10(-12)] in individuals <50 yr (n = 2,511); these genetic effects were absent in those older than 50 yr (n = 5,088) (SBP, P = 0.41; DBP, P = 0.51). Our findings suggest that the PPARGC1A Ser482 allele may be associated with higher blood pressure, but this is only apparent in younger adults.

Stability of an ice sheet on an elastic bed

The stability of stationary flow of a two-dimensional ice sheet is studied when the ice obeys a power flow law (Glen's flow law). The mass accumulation rate at the top is assumed to depend on elevation and span and the bed supporting the ice sheet consists of an elastic layer lying on a rigid surface. The normal perturbation of the free surface of the ice sheet is a singular eigenvalue problem. The singularity of the perturbation at the front of the ice sheet is considered using matched asymptotic expansions, and the eigenvalue problem is seen to reduce to that with fixed ice front. Numerical solution of the perturbation eigenvalue problem shows that the dependence of accumulation rate on elevation permits the existence of unstable solutions when the equilibrium line is higher than the bed at the ice divide. Alternatively, when the equilibrium line is lower than the bed, there are only stable solutions. Softening of the bed, expressed through a decrease of its elastic modulus, has a stabilising effect on the ice sheet.

Greater impact of dietary fat manipulation than apolipoprotein E genotype on ex-vivo cytokine production – insights from the SATgenε study

Apolipoprotein E (APOE) genotype is believed to play an important role in cardiovascular risk. APOE4 carriers have been associated with higher blood lipid levels and a more pro-inflammatory state compared with APOE3/E3 individuals. Although dietary fat composition has been considered to modulate the inflammatory state in humans, very little is known about how APOE genotype can impact on this response. In a follow-up to the main SATgene study, we aimed to explore the effects of APOE genotype, as well as, dietary fat manipulation on ex vivo cytokine production. Blood samples were collected from a subset of SATgene participants (n = 52/88), prospectively recruited according to APOE genotype (n = 26 E3/E3 and n = 26 E3/E4) after low-fat (LF), high saturated fat (HSF) and HSF with 3.45 g docosahexaenoic acid (DHA) dietary periods (each diet eight weeks in duration assigned in the same order) for the measurement of ex vivo cytokine production using whole blood culture (WBC). Concentrations of IL-1beta, IL-6, IL-8, IL-10 and TNF-alpha were measured in WBC supernatant samples after stimulation for 24 h with either 0.05 or 1 lg/ml of bacterial lipopolysaccharide (LPS). Cytokine levels were not influenced by genotype, whereas, dietary fat manipulation had a significant impact on TNF-a and IL-10 production; TNF-a concentration was higher after consumption of the HSF diet compared with baseline and the LF diet (P < 0.05), whereas, IL-10 concentration was higher after the LF diet compared with baseline (P < 0.05). In conclusion, our study has revealed the amount and type of dietary fat can significantly modulate the production of TNF-a and IL-10 by ex vivo LPS-stimulated WBC samples obtained from normolipidaemic subjects.