Wave-activity conservation laws and stability theorems for semi-geostrophic dynamics: part 2. pseudoenergy-based theory

This paper represents the second part of a study of semi-geostrophic (SG) geophysical fluid dynamics. SG dynamics shares certain attractive properties with the better known and more widely used quasi-geostrophic (QG) model, but is also a good prototype for balanced models that are more accurate than QG dynamics. The development of such balanced models is an area of great current interest. The goal of the present work is to extend a central body of QG theory, concerning the evolution of disturbances to prescribed basic states, to SG dynamics. Part 1 was based on the pseudomomentum; Part 2 is based on the pseudoenergy. A pseudoenergy invariant is a conserved quantity, of second order in disturbance amplitude relative to a prescribed steady basic state, which is related to the time symmetry of the system. We derive such an invariant for the semi-geostrophic equations, and use it to obtain: (i) a linear stability theorem analogous to Arnol'd's ‘first theorem’; and (ii) a small-amplitude local conservation law for the invariant, obeying the group-velocity property in the WKB limit. The results are analogous to their quasi-geostrophic forms, and reduce to those forms in the limit of small Rossby number. The results are derived for both the f-plane Boussinesq form of semi-geostrophic dynamics, and its extension to β-plane compressible flow by Magnusdottir & Schubert. Novel features particular to semi-geostrophic dynamics include apparently unnoticed lateral boundary stability criteria. Unlike the boundary stability criteria found in the first part of this study, however, these boundary criteria do not necessarily preclude the construction of provably stable basic states. The interior semi-geostrophic dynamics has an underlying Hamiltonian structure, which guarantees that symmetries in the system correspond naturally to the system's invariants. This is an important motivation for the theoretical approach used in this study. The connection between symmetries and conservation laws is made explicit using Noether's theorem applied to the Eulerian form of the Hamiltonian description of the interior dynamics.

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.

Stability of gradient semigroups under perturbations

In this paper we prove that gradient-like semigroups (in the sense of Carvalho and Langa (2009 J. Diff. Eqns 246 2646-68)) are gradient semigroups (possess a Lyapunov function). This is primarily done to provide conditions under which gradient semigroups, in a general metric space, are stable under perturbation exploiting the known fact (see Carvalho and Langa (2009 J. Diff. Eqns 246 2646-68)) that gradient-like semigroups are stable under perturbation. The results presented here were motivated by the work carried out in Conley (1978 Isolated Invariant Sets and the Morse Index (CBMS Regional Conference Series in Mathematics vol 38) (RI: American Mathematical Society Providence)) for groups in compact metric spaces (see also Rybakowski (1987 The Homotopy Index and Partial Differential Equations (Universitext) (Berlin: Springer)) for the Morse decomposition of an invariant set for a semigroup on a compact metric space).

Fibrinogen stability under surfactant interaction

Differential scanning calorimetry (DSC), circular dichroism (CD), difference spectroscopy (UV-vis), Raman spectroscopy, and small-angle X-ray scattering (SAXS) measurements have been performed in the present work to provide a quantitatively comprehensive physicochemical description of the complexation between bovine fibrinogen and the sodium perfluorooctanoate, sodium octanoate, and sodium dodecanoate in glycine buffer (pH 8.5). It has been found that sodium octanoate and dodecanoate act as fibrinogen destabilizer. Meanwhile, sodium perfluorooctanoate acts as a structure stabilizer at low molar concentration and as a destabilizer at high molar concentration. Fibrinogen`s secondary structure is affected by all three studied surfactants (decrease in alpha-helix and an increase in beta-sheet content) to a different extent. DSC and UV-vis revealed the existence of intermediate states in the thermal unfolding process of fibrinogen. In addition, SAXS data analysis showed that pure fibrinogen adopts a paired-dimer structure in solution. Such a structure is unaltered by sodium octanoate and perfluoroctanoate. However, interaction of sodium dodecanoate with the fibrinogen affects the protein conformation leading to a complex formation. Taken together, all results evidence that both surfactant hydrophobicity and tail length mediate the fibrinogen stability upon interaction. (C) 2011 Elsevier Inc. All rights reserved.

Stability and related properties of vacua and ground states

We consider the formal non-relativistic limit (nrl) of the : phi(4):(s+1) relativistic quantum field theory (rqft), where s is the space dimension. Following the work of R. Jackiw [R. Jackiw, in: A. Ali, P. Hood-bhoy (Eds.), Beg Memorial Volume, World Scientific, Singapore, 1991], we show that, for s = 2 and a given value of the ultraviolet cutoff K, there are two ways to perform the nrl: (i) fixing the renormalized mass m(2) equal to the bare mass m(0)(2); (ii) keeping the renormalized mass fixed and different from the bare mass mo. In the (infinite-volume) two-particle sector the scattering amplitude tends to zero as K -> infinity in case (i) and, in case (ii), there is a bound state, indicating that the interaction potential is attractive. As a consequence, stability of matter fails for our boson system. We discuss why both alternatives do not reproduce the low-energy behaviour of the full rqft. The singular nature of the nrl is also nicely illustrated for s = 1 by a rigorous stability/instability result of a different nature. (C) 2007 Elsevier Inc. All rights reserved.

Energetics and stability of vacancies in carbon nanotubes

In this work we present ab initio calculations of the formation energies and stability of different types of multi-vacancies in carbon nanotubes. We demonstrate that, as in the case of graphene, the reconstruction of the defects has drastic effects on the energetics of the tubes. In particular, the formation of pentagons eliminates the dangling bonds thus lowering the formation energy. This competition leads to vacancies having an even number of carbon atoms removed to be more stable. Finally the appearance of magic numbers indicating more stable defects can be represented by a model for the formation energies that is based on the number of dangling bonds of the unreconstructed system, the pentagons and the relaxation of the final form of the defect formed after the relaxation. (C) 2011 Elsevier Ltd. All rights reserved.

STABILITY ANALYSIS WITH APPLICATIONS OF A TWO-DIMENSIONAL DYNAMICAL SYSTEM ARISING FROM A STOCHASTIC MODEL FOR AN ASSET MARKET

We analyze the stability properties of equilibrium solutions and periodicity of orbits in a two-dimensional dynamical system whose orbits mimic the evolution of the price of an asset and the excess demand for that asset. The construction of the system is grounded upon a heterogeneous interacting agent model for a single risky asset market. An advantage of this construction procedure is that the resulting dynamical system becomes a macroscopic market model which mirrors the market quantities and qualities that would typically be taken into account solely at the microscopic level of modeling. The system`s parameters correspond to: (a) the proportion of speculators in a market; (b) the traders` speculative trend; (c) the degree of heterogeneity of idiosyncratic evaluations of the market agents with respect to the asset`s fundamental value; and (d) the strength of the feedback of the population excess demand on the asset price update increment. This correspondence allows us to employ our results in order to infer plausible causes for the emergence of price and demand fluctuations in a real asset market. The employment of dynamical systems for studying evolution of stochastic models of socio-economic phenomena is quite usual in the area of heterogeneous interacting agent models. However, in the vast majority of the cases present in the literature, these dynamical systems are one-dimensional. Our work is among the few in the area that construct and study analytically a two-dimensional dynamical system and apply it for explanation of socio-economic phenomena.

Thermal behavior and stability of biodegradable spray-dried microparticles containing triamcinolone

Thermal analysis has been widely used for obtaining information about drug-polymer interactions and for pre-formulation studies of pharmaceutical dosage forms. In this work, biodegradable microparticles Of Poly (D,L-lactide-co-glycolide) (PLGA) containing triamcinolone (TR) in various drug:polymer ratios were produced by spray drying. The main purpose of this study was to study the effect of the spray-drying process not only on the drug-polymer interactions but also on the stability of microparticles using differential scanning calorimetry (DSC), thermogravimetry (TG) and derivative thermogravimetry (DTG), X-ray analysis (XRD), and infrared spectroscopy (IR). The evaluation of drug-polymer interactions and the pre-formulation studies were assessed using the DSC, TG and DTG, and IR. The quantitative analysis of drugs entrapped in PLGA microparticles was performed by the HPLC method. The results showed high levels of drug-loading efficiency for all used drug: polymer ratio, and the polymorph used for preparing the microparticles was the form B. The DSC and TG/DTG profiles for drug-loaded microparticles were very similar to those for the physical mixtures of the components. Therefore, a correlation between drug content and the structural and thermal properties of drug-loaded PLGA microparticles was established. These data indicate that the spray-drying technique does not affect the physico-chemical stability of the microparticle components. These results are in agreement with the IR analysis demonstrating that no significant chemical interaction occurs between TR and PLGA in both physical mixtures and microparticles. The results of the X-ray analysis are in agreement with the thermal analysis data showing that the amorphous form of TR prevails over a small fraction of crystalline phase of the drug also present in the TR-loaded microparticles. From the pre-formulation studies, we have found that the spray-drying methodology is an efficient process for obtaining TR-loaded PLGA microparticles. (C) 2008 Elsevier B.V. All rights reserved.

Isoelectric Point Determination for Glossoscolex paulistus Extracellular Hemoglobin: Oligomeric Stability in Acidic pH and Relevance to Protein-Surfactant Interactions

The extracellular hemoglobin from Glossoscolex paulistus (HbGp) has a molecular mass of 3.6 M Da, It has a high oligomeric stability at pH 7.0 and low autoxidation rates, as compared to vertebrate hemoglobins. In this work, fluorescence and light scattering experiments were performed with the three oxidation forms of HbGp exposed to acidic pH. Our focus is on the HbGp stability at acidic pH and also on the determination of the isoelectric point (pI) of the protein. Our results show that the protein in the cyanomet form is more stable than in the other two forms, in the whole range. Our zeta-potential data are consistent with light scattering results. Average values apt obtained by different techniques were 5.6 +/- 0.5, 5.4 +/- 0.2 and 5.2 +/- 0.5 for the oxy, met, and cyanomet forms. Dynamic light scattering (DLS) experiments have shown that, at pH 6.0, the aggregation (oligomeric) state of oxy-, met- and cyanomet-HbGp remains the same as that at 7.0. The interaction between the oxy-HbGp and ionic surfactants at pH 5.0 and 6.0 was also monitored in the present study. At pH 5,0, below the protein pI, the effects of sodium dodecyl sulfate (SDS) and cetyltrimethylammonium chloride (CTAC) are inverted when compared to pH 7.0. For CTAC, in acid pH 5.0, no precipitation is observed, while for SDS an intense light scattering appears due to a precipitation process. HbGp interacts strongly with the cationic surfactant at pH 7.0 and with the anionic one at pH 5.0. This effect is due to the predominance, in the protein surface, of residues presenting opposite charges to the surfactant headgroups. This information can be relevant for the development of extracellular hemoglobin-based artificial blood substitutes.

Stability and Local Toxicity Evaluation of a Liposomal Prilocaine Formulation

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Study of liposomes stability containing soy phosphatidyleholine and hydrogenated soy phosphatydylcholine adding or not cholesterol by turbidity method

Study of Liposomes Stability Containing Soy Phosphatidyleholine and Hydrogenated Soy Phosphatydylcholine Adding or Not Cholesterol by Turbidity Method. Liposomes are structures composed by phospholipids as soy phosphatidylcholine (PC) and hydrogenated soy phosphatydylcholine (PCH). Among the methods used to prove liposomes stability, turbidity method is widely used. The objective of this work was to study the liposomes stability containing PC or PCH with and without cholesterol (CHOL) by turbidity method. Liposomes were stored a 30 degrees C during 90 days and periodically absorbance readings at 410 nm were made to verify possible turbidity alterations. Increases in the turbidity with time occurred for PC liposomes. In the presence of CHOL higher turbidity was obtained probably reflecting the increase in the size of liposomes. For PCH liposomes the presence of CHOL did not affect the turbidity suggesting higher physical stability of the structures.

Thermal behavior and stability of biodegradable spray-dried microparticles containing triamcinolone

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Attitude stability of artificial satellites subject to gravity gradient torque

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On the stability of the satellites of asteroid 87 Sylvia

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Study of Stability of Rotational Motion of Spacecraft with Canonical Variables

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)