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.

Optimising the analysis of transcript data using high density oligonucleotide arrays and genomic DNA-based probe selection

Background: Affymetrix GeneChip arrays are widely used for transcriptomic studies in a diverse range of species. Each gene is represented on a GeneChip array by a probe- set, consisting of up to 16 probe-pairs. Signal intensities across probe- pairs within a probe-set vary in part due to different physical hybridisation characteristics of individual probes with their target labelled transcripts. We have previously developed a technique to study the transcriptomes of heterologous species based on hybridising genomic DNA (gDNA) to a GeneChip array designed for a different species, and subsequently using only those probes with good homology. Results: Here we have investigated the effects of hybridising homologous species gDNA to study the transcriptomes of species for which the arrays have been designed. Genomic DNA from Arabidopsis thaliana and rice (Oryza sativa) were hybridised to the Affymetrix Arabidopsis ATH1 and Rice Genome GeneChip arrays respectively. Probe selection based on gDNA hybridisation intensity increased the number of genes identified as significantly differentially expressed in two published studies of Arabidopsis development, and optimised the analysis of technical replicates obtained from pooled samples of RNA from rice. Conclusion: This mixed physical and bioinformatics approach can be used to optimise estimates of gene expression when using GeneChip arrays.

A Brassica exon array for whole-transcript gene expression profiling

Affymetrix GeneChip (R) arrays are used widely to study transcriptional changes in response to developmental and environmental stimuli. GeneChip (R) arrays comprise multiple 25-mer oligonucleotide probes per gene and retain certain advantages over direct sequencing. For plants, there are several public GeneChip (R) arrays whose probes are localised primarily in 39 exons. Plant whole-transcript (WT) GeneChip (R) arrays are not yet publicly available, although WT resolution is needed to study complex crop genomes such as Brassica, which are typified by segmental duplications containing paralogous genes and/or allopolyploidy. Available sequence data were sampled from the Brassica A and C genomes, and 142,997 gene models identified. The assembled gene models were then used to establish a comprehensive public WT exon array for transcriptomics studies. The Affymetrix GeneChip (R) Brassica Exon 1.0 ST Array is a 5 mu M feature size array, containing 2.4 million 25-base oligonucleotide probes representing 135,201 gene models, with 15 probes per gene distributed among exons. Discrimination of the gene models was based on an E-value cut-off of 1E(-5), with <= 98 sequence identity. The 135 k Brassica Exon Array was validated by quantifying transcriptome differences between leaf and root tissue from a reference Brassica rapa line (R-o-18), and categorisation by Gene Ontologies (GO) based on gene orthology with Arabidopsis thaliana. Technical validation involved comparison of the exon array with a 60-mer array platform using the same starting RNA samples. The 135 k Brassica Exon Array is a robust platform. All data relating to the array design and probe identities are available in the public domain and are curated within the BrassEnsembl genome viewer at http://www.brassica.info/BrassEnsembl/index.html.

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.

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.

Enrichment and stability: a phenomenological coupling of energy value and carrying capacity

Simple predator–prey models with a prey-dependent functional response predict that enrichment (increased carrying capacity) destabilizes community dynamics: this is the ‘paradox of enrichment’. However, the energy value of prey is very important in this context. The intraspecific chemical composition of prey species determines its energy value as a food for the potential predator. Theoretical and experimental studies establish that variable chemical composition of prey affects the predator–prey dynamics. Recently, experimental and theoretical approaches have been made to incorporate explicitly the stoichiometric heterogeneity of simple predator–prey systems. Following the results of the previous experimental and theoretical advances, in this article we propose a simple phenomenological formulation of the variation of energy value at increased level of carrying capacity. Results of our study demonstrate that coupling the parameters representing the phenomenological energy value and carrying capacity in a realistic way, may avoid destabilization of community dynamics following enrichment. Additionally, under such coupling the producer–grazer system persists for only an intermediate zone of production—a result consistent with recent studies. We suggest that, while addressing the issue of enrichment in a general predator–prey model, the phenomenological relationship that we propose here might be applicable to avoid Rosenzweig’s paradox.

Enrichment and ecosystem stability: effect of toxic food

Enrichment in resource availability theoretically destabilizes predator–prey dynamics (the paradox of enrichment). However, a minor change in the resource stoichiometry may make a prey toxic for the predator, and the presence of toxic prey affects the dynamics significantly. Here, theoretically we explore how, at increased carrying capacity, a toxic prey affects the oscillation or destabilization of predator–prey dynamics, and how its presence influences the growth of the predator as well as that of a palatable prey. Mathematical analysis determines the bounds on the food toxicity that allow the coexistence of a predator along with a palatable and a toxic prey. The overall results demonstrate that toxic food counteracts oscillation (destabilization) arising from enrichment of resource availability. Moreover, our results show that, at increased resource availability, toxic food that acts as a source of extra mortality may increase the abundance of the predator as well as that of the palatable prey.

The stability of ecosystems: a brief overview of the paradox of enrichment

In theory, enrichment of resource in a predator-prey model leads to destabilization of the system, thereby collapsing the trophic interaction, a phenomenon referred to as "the paradox of enrichment". After it was first proposed by Rosenzweig (1971), a number of subsequent studies were carried out on this dilemma over many decades. In this article, we review these theoretical and experimental works and give a brief overview of the proposed solutions to the paradox. The mechanisms that have been discussed are modifications of simple predator-prey models in the presence of prey that is inedible, invulnerable, unpalatable and toxic. Another class of mechanisms includes an incorporation of a ratio-dependent functional form, inducible defence of prey and density-dependent mortality of the predator. Moreover, we find a third set of explanations based on complex population dynamics including chaos in space and time. We conclude that, although any one of the various mechanisms proposed so far might potentially prevent destabilization of the predator-prey dynamics following enrichment, in nature different mechanisms may combine to cause stability, even when a system is enriched. The exact mechanisms, which may differ among systems, need to be disentangled through extensive field studies and laboratory experiments coupled with realistic theoretical models.

Long-term cultivation-independent microbial diversity analysis demonstrates that bacterial communities infecting the adult cystic fibrosis lung show stability and resilience.

Whilst not true in all cases, the microbial communities that chronically infect the airways of patients with CF can vary little over a year despite antibiotic perturbation. The species present tended to vary more between than within subjects, suggesting that each CF airway infection is unique, with relatively stable and resilient bacterial communities. The inverse relationship between community richness and disease severity is similar to findings reported in other mucosal infections.

Stability of dobutamine 500 mg in 50 ml syringes prepared using a Central Intravenous Additive Service

Objectives A pharmacy Central Intravenous Additives Service (CIVAS) provides ready to use injectable medicines. However, manipulation of a licensed injectable medicine may significantly alter the stability of drug(s) in the final product. The aim of this study was to develop a stability indicating assay for CIVAS produced dobutamine 500 mg in 50 ml dextrose 1% (w/v) prefilled syringes, and to allocate a suitable shelf life. Methods A stability indicating high performance liquid chromatography (HPLC) assay was established for dobutamine. The stability of dobutamine prefilled syringes was evaluated under storage conditions of 4°C (protected from light), room temperature (protected from light), room temperature (exposed to light) and 40°C (protected from light) at various time points (up to 42 days). Results An HPLC method employing a Hypersil column, mobile phase (pH=4.0) consisting of 82:12:6 (v/v/v) 0.05 M KH2PO4:acetonitrile:methanol plus 0.3% (v/v) triethylamine with UV detection at λ=280 nm was specific for dobutamine. Under different storage conditions only samples stored at 40°C showed greater than 5% degradation (5.08%) at 42 days and had the shortest T95% based on this criterion (44.6 days compared with 111.4 days for 4°C). Exposure to light also reduced dobutamine stability. Discolouration on storage was the limiting factor in shelf life allocation, even when dobutamine remained within 5% of the initial concentration. Conclusions A stability indicating HPLC assay for dobutamine was developed. The shelf life recommended for the CIVAS product was 42 days at 4°C and 35 days at room temperature when protected from light.

The importance of loop length on the stability of i-motif structures

Using UV and srCD spectroscopy it is found that loop length within the i-motif structure is important for both thermal and pH stability, but in contrast to previous statements, it is the shorter loops that exhibit the highest stability.