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.

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

Thermal and pressure stability of myrosinase enzymes from black mustard (Brassica nigra L. W.D.J Koch. var. nigra), brown mustard (Brassica juncea L. Czern. var. juncea) and yellow mustard (Sinapsis alba L. Subsp Maire) seeds

This study investigates the effects of temperature and pressure on inactivation of myrosinase extracted from black, brown and yellow mustard seeds. Brown mustard had higher myrosinase activity (2.75 un/mL) than black (1.50 un/mL) and yellow mustard (0.63 un/mL). The extent of enzyme inactivation increased with pressure (600-800 MPa) and temperature (30-70 °C) for all the mustard seeds. However, at combinations of lower pressures (200-400 MPa) and high temperatures (60-80 °C), there was less inactivation. For example, application of 300 MPa and 70 °C for 10 minutes retained 20%, 80% and 65% activity in yellow, black and brown mustard, respectively, whereas the corresponding activity retentions when applying only heat (70 °C, 10min) were 0%, 59% and 35%. Thus, application of moderate pressures (200-400 MPa) can potentially be used to retain myrosinase activity needed for subsequent glucosinolate hydrolysis.

Peptide based hydrogels for cancer drug release: modulation of stiffness, drug release and proteolytic stability of hydrogels by incorporating D-amino acid residue(s)

Synthetic tripeptide based noncytotoxic hydrogelators have been discovered for releasing an anticancer drug at physiological pH and temparature. Interestingly, gel stiffness, drug release capacity and proteolytic stability of these hydrogels have been successfully modulated by incorporating D-amino acid residues, indicating their potential use for drug delivery in the future.

Temperature and moist-stability effects on midlatitude orographic precipitation

Idealized, convection-resolving simulations of moist orographic flows are conducted to investigate the influence of temperature and moist stability on the drying ratio (DR), defined as the fraction of the impinging water mass removed as orographic precipitation. In flow past a long ridge, where most of the air rises over the barrier rather than detouring around it, DR decreases as the surface temperature (Ts) increases, even as the orographic cap cloud becomes statically unstable at higher Ts and develops embedded convection. This behaviour is explained by a few physical principles: (1) the Clausius–Clapeyron equation dictates that the normalized condensation rate decreases as the flow gets warmer, (2) the replacement of ice-phase precipitation growth with warm-rain processes decreases the efficiency by which condensate is converted to precipitation, thereby lowering precipitation efficiency, and (3) embedded convection acts more to vertically redistribute moisture than to enhance precipitation. Over an isolated mountain, the effects of (1) and (2) are counteracted by moisture deflection around the barrier, which is stronger in the colder, more stable flows.

Effects of different calcium salts on properties of milk related to heat stability

Insoluble calcium salts were added to milk to increase total calcium by 30 mM, without changing properties influencing heat stability, such as pH and ionic calcium. There were no major signs of instability associated with coagulation, sediment formation or fouling when subjected to ultra high temperature (UHT) and in-container sterilisation. The buffering capacity was also unaltered. On the other hand, addition of soluble calcium salts reduced pH, increased ionic calcium and caused coagulation to occur. Calcium chloride showed the largest destabilising effect, followed by calcium lactate and calcium gluconate. Milk became unstable to UHT processing at lower calcium additions compared to in-container sterilisation.

Interference competition and high temperature reduce the ‘virulence’ of fig wasps and contribute to stability of a fig-wasp mutualism

Fig trees are pollinated by fig wasps, which also oviposit in female flowers. The wasp larvae gall and eat developing seeds. Although fig trees benefit from allowing wasps to oviposit, because the wasp offspring disperse pollen, figs must prevent wasps from ovipositing in all flowers, or seed production would cease, and the mutualism would go extinct. In Ficus racemosa, we find that syconia (‘figs’) that have few foundresses (ovipositing wasps) are underexploited in the summer (few seeds, few galls, many empty ovules) and are overexploited in the winter (few seeds, many galls, few empty ovules). Conversely, syconia with many foundresses produce intermediate numbers of galls and seeds, regardless of season. We use experiments to explain these patterns, and thus, to explain how this mutualism is maintained. In the hot summer, wasps suffer short lifespans and therefore fail to oviposit in many flowers. In contrast, cooler temperatures in the winter permit longer wasp lifespans, which in turn allows most flowers to be exploited by the wasps. However, even in winter, only in syconia that happen to have few foundresses are most flowers turned into galls. In syconia with higher numbers of foundresses, interference competition reduces foundress lifespans, which reduces the proportion of flowers that are galled. We further show that syconia encourage the entry of multiple foundresses by delaying ostiole closure. Taken together, these factors allow fig trees to reduce galling in the wasp-benign winter and boost galling (and pollination) in the wasp-stressing summer. Interference competition has been shown to reduce virulence in pathogenic bacteria. Our results show that interference also maintains cooperation in a classic, cooperative symbiosis, thus linking theories of virulence and mutualism. More generally, our results reveal how frequency-dependent population regulation can occur in the fig-wasp mutualism, and how a host species can ‘set the rules of the game’ to ensure mutualistic behavior in its symbionts.

Longevity, early emergence and body size in a pollinating fig wasp - implications for stability in a fig-pollinator mutualism

1. Fig trees (Ficus) are pollinated only by agaonid wasps, whose larvae also gall fig ovules. Each ovule develops into either a seed (when pollinated) or a wasp (when an egg is also laid inside) but not both. 2. Ovipositing wasps (foundresses) favour ovules near the centre of the enclosed inflorescence (syconium or 'fig'), leaving ovules near the outer wall to develop into seeds. This spatial stratification of wasps and seeds ensures reproduction in both partners, and thereby enables mutualism persistence. However, the mechanism(s) responsible remain(s) unknown. 3. Theory shows that foundresses will search for increasingly rare inner ovules and ignore outer ovules, as long as ovipositing in outer ovules is sufficiently slow and/or if inner ovules confer greater fitness to wasps. The fig-pollinator mutualism can therefore be stabilized by strong time constraints on foundresses and by offspring fitness gradients over variation in ovule position. 4. Female fig wasps cannot leave their galls without male assistance. We found that females in outer ovules were unlikely to be released. Inner ovules thus have added value to foundresses, because their female offspring are more likely to mate and disperse. 5. For those offspring that did emerge, gall position (inner/outer) and body size did not influence the order in which female pollinators exited syconia, nor did early emerging wasps enjoy increased life spans. 6. We also found that the life spans of female wasps nearly doubled when given access to moisture. We suggest that conflict resolution in the fig-pollinator mutualism may thus be influenced by tropical seasonality, because wasps may be less able to over-exploit ovules in dry periods due to time constraints.

On the stability of populations of mammals, birds, fish and insects

A key concern for conservation biologists is whether populations of plants and animals are likely to fluctuate widely in number or remain relatively stable around some steady-state value. In our study of 634 populations of mammals, birds, fish and insects, we find that most can be expected to remain stable despite year to year fluctuations caused by environmental factors. Mean return rates were generally around one but were higher in insects (1.09 +/- 0.02 SE) and declined with body size in mammals. In general, this is good news for conservation, as stable populations are less likely to go extinct. However, the lower return rates of the large mammals may make them more vulnerable to extinction. Our estimates of return rates were generally well below the threshold for chaos, which makes it unlikely that chaotic dynamics occur in natural populations - one of ecology's key unanswered questions.

Metal complexes of cyclen and cyclam derivatives useful for medical applications: a discussion based on thermodynamic stability constants and structural data

A series of the most common chelators used in magnetic resonance imaging ( MRI) and in radiopharmaceuticals for medical diagnosis and tumour therapy, H(4)dota, H(4)teta, H(8)dotp and H(8)tetp, is examined from a chemical point of view. Differences between 12- and 14-membered tetraazamacrocyclic derivatives with methylcarboxylate and methylphosphonate pendant arms and their chelates with divalent first-series transition metal and trivalent lanthanide ions are discussed on the basis of their thermodynamic stability constants, X- ray structures and theoretical studies.

Reactions of artemisinin and arteether with acid: Implications for stability and mode of antimalarial action

The currently accepted mechanism of trioxane antimalarial action involves generation of free radicals within or near susceptible sites probably arising from the production of distonic radical anions. An alternative mechanistic proposal involving the ionic scission of the peroxide group and consequent generation of a carbocation at C-4 has been suggested to account for antimalarial activity. We have investigated this latter mechanism using DFT (B3LYP/6-31+G* level) and established the preferred Lewis acid protonation sites (artemisinin O5a >> O4a approximate to O3a > O2a > O1a; arteether O4a >= O3a > O5b >> O2a > O1a; Figure 3) and the consequent decomposition pathways and hydrolysis sites. In neither molecule is protonation likely to occur on the peroxide bond O1-O2 and therefore lead to scission. Therefore, the alternative radical pathway remains the likeliest explanation for antimalarial action.

The adsorption and stability of sulfur containing amino acids on Cu{531}

The adsorption of L-CySteine and L-methionine amino acids on a chiral Cu{5 3 1} surface was investigated with high resolution X-ray photoelectron spectroscopy (XPS) and carbon K-edge near edge X-ray absorption fine structure (NEXAFS) Spectroscopy using synchrotron radiation. XPS shows that at 300 K L-cysteine adsorbs through two oxygen, a nitrogen and a sulfur atom, in a four point 'quadrangular footprint', whereas L-methionine adsorbs through only two oxygen and a nitrogen atom in a 'triangular footprint'. NEWS was used to clarify the adsorption geometry of both molecules, which suggests a binding orientation to the top layer and second layer atoms in two different orientations associated with adsorption sites on {1 1 0} and {3 1 1} microfacets; of the Cu{5 3 1} surface. (C) 2009 Elsevier B.V. All rights reserved.