An improved result of exponential stability of stochastic semilinear evolution equations

Sufficient conditions for the exponential stability of a class ofnonlinear, non-autonomous stochastic differential equations in infinitedimensions are studied. The analysis consists of introducing a suitableapproximating solution systems and using a limiting argument to pass onstability of strong solutions to mild ones. As a consequence, the classicalcriteriaof stability in A. Ichikawa [8] are improved and extended to cover a class ofnon-autonomous stochastic evolution equations.Two examples are investigated to illustrate our theory.

Ergodicity and stability of generalised Markov branching processes with resurrection

This paper concentrates on investigating ergodicity and stability for generalised Markov branching processes with resurrection. Easy checking criteria including several clear-cut corollaries are established for ordinary and strong ergodicity of such processes. The equilibrium distribution is given in an elegant closed form for the ergodic case. The probabilistic interpretation of the results is clear and thus explained.

Nonlinear MHD stability of aluminium reduction cells

An industrial electrolysis cell used to produce primary aluminium is sensitive to waves at the interface of liquid aluminium and electrolyte. The interface waves are similar to stratified sea layers [1], but the penetrating electric current and the associated magnetic field are intricately involved in the oscillation process, and the observed wave frequencies are shifted from the purely hydrodynamic ones [2]. The interface stability problem is of great practical importance because the electrolytic aluminium production is a major electrical energy consumer, and it is related to environmental pollution rate. The stability analysis was started in [3] and a short summary of the main developments is given in [2]. Important aspects of the multiple mode interaction have been introduced in [4], and a widely used linear friction law first applied in [5]. In [6] a systematic perturbation expansion is developed for the fluid dynamics and electric current problems permitting reduction of the three-dimensional problem to a two dimensional one. The procedure is more generally known as “shallow water approximation” which can be extended for the case of weakly non-linear and dispersive waves. The Boussinesq formulation permits to generalise the problem for non-unidirectionally propagating waves accounting for side walls and for a two fluid layer interface [1]. Attempts to extend the electrolytic cell wave modelling to the weakly nonlinear case have started in [7] where the basic equations are derived, including the nonlinearity and linear dispersion terms. An alternative approach for the nonlinear numerical simulation for an electrolysis cell wave evolution is attempted in [8 and references there], yet, omitting the dispersion terms and without a proper account for the dissipation, the model can predict unstable waves growth only. The present paper contains a generalisation of the previous non linear wave equations [7] by accounting for the turbulent horizontal circulation flows in the two fluid layers. The inclusion of the turbulence model is essential in order to explain the small amplitude self-sustained oscillations of the liquid metal surface observed in real cells, known as “MHD noise”. The fluid dynamic model is coupled to the extended electromagnetic simulation including not only the fluid layers, but the whole bus bar circuit and the ferromagnetic effects [9].

Assessment of the origin and stability of Nifedipine polymorph IV by differential scanning calorimetry (DSC)

Purpose. To examine the thermal transition(s) between different polymorphic forms of Nifedipine and to define experimental conditions that lead to the generation of polymorph IV. Methods. Experiments were performed using a DSC 823e (Mettler Toledo). Nifedipine exists in four polymorphic forms, as well as an amorphous state. Examination of Nifedipine was conducted using the following method(s): cycle 1: 25ºC to 190ºC, 190ºC to 25ºC (formation of amorphous Nifedipine); cycle 2: 25ºC to X (60,70,80...150ºC), X to 25ºC; cycle 3: 25ºC to 190ºC and holding isothermally for 5 min between cycles (heating/cooling rate of 10ºC/min). Results. The amorphous state Nifedipine can sustain heating up to 90ºC without significant changes in its composition. Cycle 2 of amorphous material heated up to 90ºC shows only the glass transition at ~44ºC. In cycle 3 of the same material, a glass transition has been recorded at ~44ºC, followed by two exotherms (~100 and ~115ºC (crystallisation of polymorph III and II, respectively) and an endotherm (169ºC (melting of polymorphs I/II)). Samples that have been heated to temperatures between 100ºC and 120ºC in the second cycle showed a glass transition at ~44ºC and an additional exotherm at ~95ºC (crystallisation of polymorph III) on cooling a exotherm was observed at ~40ºC (crystallisation of polymorph IV). The same material showed no glass transition in cycle 3 but an endotherm at around 62ºC (melting of polymorph IV) an exotherm (~98ºC) and an endotherm (169ºC) melting of polymorph I/II. Heating the sample to a temperatures greater than 130ºC in cycle two results in a glass transition at ~44ºC, and two exotherms at ~102 and 125ºC (crystallisation of polymorphs III and I, respectively). Conclusions. DSC data suggests that polymorph IV can only be produced from amorphous or polymorph III samples. The presence of polymorph I or II drives the conversion of the less stable polymorphic form IV into the most stable form, I. Although form IV of Nifedipine can easily be created, following defined experimental conditions, it may only coexist with amorphous or polymorph III states. When polymorphs I and II are present in the sample polymorph IV cannot be etected.

Trophodynamics and stability of regional scale ecosystems in the Northeast Atlantic

This study addresses the long-term stability of three trophic groupings in the Northeast Atlantic at regional scales. The most abundant taxa representing phytoplankton, herbivorous copepods, and carnivorous zooplankton were examined from the Continuous Plankton Recorder database. Multivariate control charts using a Bray–Curtis similarity metric were used to assess whether fluctuations within trophic groupings were within or beyond the expected variability. Two evaluation periods were examined: annual changes between 1960 and 1999 (2000–2009 baseline) and recent changes between 2000 and 2009 (1960–1999 baseline). The trends over time in abundance/biomass of trophic levels were region-specific, especially in carnivorous copepods, where abundance did not mirror trends in the overall study area. The stability of phytoplankton was within the expected limits, although not in 2008 and 2009. Higher trophic levels were less stable, perhaps reflecting the added complexity of interactions governing their abundance. In addition, some regions were consistently less stable than others. Correlations in stability between adjacent trophic levels were positive at large marine ecosystem scale but generally non-significant at regional scales. The study suggests that certain regions may be particularly vulnerable to periods of instability in community structure. The benefits of using the control chart method rather than other multivariate measures of plankton dynamics are discussed.

Colloidal stability of nanoparticles derived from simulated cloud-processed mineral dusts

Laboratory simulation of cloud processing of three model dust types with distinct Fe-content (Moroccan dust, Libyan dust and Etna ash) and reference goethite and ferrihydrite were conducted in order to gain a better understanding of natural nanomaterial inputs and their environmental fate and bioavailability. The resulting nanoparticles (NPs) were characterised for Fe dissolution kinetics, aggregation/size distribution, micromorphology and colloidal stability of particle suspensions using a multi-method approach. We demonstrated that the: (i) acid-leachable Fe concentration was highest in volcanic ash (1 m Mg(-1) dust) and was followed by Libyan and Moroccan dust with an order of magnitude lower levels; (ii) acid leached Fe concentration in the<20 nm fraction was similar in samples processed in the dark with those under artificial sunlight, but average hydrodynamic diameter of NPs after cloud-processing (pH~6) was larger in the former; iii) NPs formed at pH~6 were smaller and less poly-disperse than those at low pH, whilst unaltered zeta potentials indicated colloidal instability; iv) relative Fe percentage in the finer particles derived from cloud processing does not reflect Fe content of unprocessed dusts (e.g. volcanic ash>Libyan dust). The common occurrence of Fe-rich "natural nanoparticles" in atmospheric dust derived materials may indicate their more ubiquitous presence in the marine environment than previously thought.

Relationships between biodiversity and the stability of marine ecosystems: comparisons at a European scale using meta-analysis.

The relationship between biodiversity and stability of marine benthic assemblages was investigated using existing data sets (n = 28) covering various spatial (m-km) and temporal (1973-2006) scales in different benthic habitats (emergent rock, rock pools and sedimentary habitats) through meta-analyses. Assemblage stability was estimated by measuring temporal variances of species richness, total abundance (density or % cover) and community species composition and abundance structure (using multivariate analyses). Positive relationships between temporal variability in species number and richness were generally observed at both quadrat (<1 m2) and site (100 m2) scales, while no relationships were observed by multivariate analyses. Positive relationships were also observed at the scale of site between temporal variability in species number and variability in community structure with evenness estimates. This implies that the relationship between species richness or evenness and species richness variability is slightly positive and depends on the scale of observation, suggesting that biodiversity per se is important for the stability of ecosystems. Changes within community assemblages in terms of structure are, however, generally independent of biodiversity, suggesting no effect of diversity, but the potential impact of individual species, and/or environmental factors. Except for sedimentary and rock pool habitats, no relationship was observed between temporal variation of the aggregated variable of total abundances and diversity at either scale. Overall our results emphasise that relationships depend on scale of measurements, type of habitats and the marine systems (North Atlantic and Mediterranean) considered.

The Influence of Copper Binding on the Stability of the SCO Protein from Bacillus subtilis

Every aerobic organism expresses cytochrome c oxidase to catalyze reduction of molecular oxygen to water, and takes advantage of this energy releasing reaction to produce an electrochemical gradient used in cellular energy production. The protein SCO (Synthesis of cytochrome c oxidase) is a required assembly factor for the oxidase, conserved across many species. SCO is implicated in the assembly of one of two copper centres (ie., CuA) of cytochrome oxidase. The exact mechanism of SCO’s participation in CuA assembly is not known. SCO has been proposed to bind and deliver copper, or alternatively to act in reductive preparation of the CuA site within the oxidase. In this body of work, the strength and stability of Cu(II) binding to Bacillus subtilis SCO is explored via electronic absorption and fluorescence spectroscopies and by calorimetric methods. An equilibrium dissociation constant (Kd) of 3.5x10-12 M was determined as an upper limit for the BsSCO-Cu(II) interaction, via differential scanning calorimetry. In the first reported case for a SCO homolog, dissociation kinetics of Cu(II) from BsSCO were characterized, and found to be dependent on both ionic strength and the presence of free Cu(II) in solution. Further differential scanning calorimetry experiments performed at high ionic strength support a two-step model of BsSCO and Cu(II) binding. The implications of this model for the BsSCO-Cu(II) interaction are presented in relation to the mechanism of interaction between SCO and the CuA site of cytochrome c oxidase.

Stability of 5-aminolevulinic acid in novel non-aqueous gel and patch-type systems intended for topical application.

Aminolevulinic acid (ALA) stability within topical formulations intended for photodynamic therapy (PDT) is poor due to dimerisation to pyrazine-2,5-dipropionic acid (PY). Most strategies to improve stability use low pH vehicles, which can cause cutaneous irritancy. To overcome this problem, a novel approach is investigated that uses a non-aqueous vehicle to retard proton-induced charge separation across the 4-carbonyl group on ALA and lessen nucleophilic attack that leads to condensation dimerisation. Bioadhesive anhydrous vehicles based on methylvinylether-maleic anhydride copolymer patches and poly(ethyleneglycol) or glycerol thickened poly(acrylic acid) gels were formulated. ALA stability fell below pharmaceutically acceptable levels after 6 months, with bioadhesive patches stored at 5°C demonstrating the best stability by maintaining 86.2% of their original loading. Glycerol-based gels maintained 40.2% in similar conditions. However, ALA loss did not correspond to expected increases in PY, indicating the presence of another degradative process that prevented dimerisation. Nuclear magnetic resonance (NMR) analysis was inconclusive in respect of the mechanism observed in the patch system, but showed clearly that an esterification reaction involving ALA and both glycerol and poly(ethyleneglycol) was occurring. This was especially marked in the glycerol gels, where only 2.21% of the total expected PY was detected after 204 days at 5°C. Non-specific esterase hydrolysis demonstrated that ALA was recoverable from the gel systems, further supporting esterified binding within the gel matrices. It is conceivable that skin esterases could duplicate this finding upon topical application of the gel and convert these derivatives back to ALA in situ, provided skin penetration is not affected adversely.